Factors influencing sediment re-
suspension and cross-shore suspended
sediment flux in the frequency domain
Samantha Rangajeewa Kularatne
B. Sc. (Engineering), M. Eng.
This thesis is submitted in fulfillment of the requirements for the degree of
Doctor of Philosophy of the University of Western Australia
School of Environmental Systems Engineering
Faculty of Engineering, Computing and Mathematics – July 2006 –
Dedicated with love and gratitude to my parents
Abstract
With rapidly increasing population densities along coastlines and rising global sea levels,
coastal protection has become a major concern for coastal communities. Predicting
sediment transport in nearshore regions, however, is one of the most challenging tasks
faced by coastal researchers in designing coastal structures or beach nourishment schemes.
Although nearshore sediment transport mainly occurs in the longshore direction, cross-
shore sediment transport is crucial in determining the shoreline evolution and beach
morphology. Moreover, a range of mean (undertow) and oscillatory (wind waves, swell,
wave groups, infragravity waves) flow components drive the cross-shore sediment
transport; it has been observed that the direction and the magnitude of cross-shore
suspended sediment flux varied markedly at these different frequency components under
different conditions. This inconsistency in cross-shore suspended sediment flux was
attributed to many different factors such as bed ripples, cross-shore location with respect to
the breaker line, velocity skewness, and grain size. However, the relative significance of
these factors has not been explored. This study investigated the factors influencing
sediment re-suspension and cross-shore suspended sediment flux in the frequency domain
through a series of field measurements conducted at several different locations and a
numerical model. Only oscillatory flow components were examined and the mean flow
components were not considered. Although many different factors such as cross-shore
location with respect to breaker line, significant wave height to water depth ratio (Hs/h),
normalised horizontal velocity skewness (‹u3›⁄‹u2›3⁄2), median grain size (d50), breaker type,
and wave groupiness appeared to influence the magnitude of cross-shore suspended
sediment flux, bed ripples was identified as the major contributing factor in changing the
direction of suspended sediment flux due to incident swell waves. Moreover, the direction
changed significantly with ripple type. High frequency measurements, obtained to examine
the influence of turbulent kinetic energy (TKE) on higher sediment suspension events
observed under wave groups indicated that higher TKE was generated at the seabed by
approaching wave groups, which in turn resulted in higher suspension events.
Contents Preface
Acknowledgements
1. Introduction…..…………………………………………………………….....…… 1
Outline of the thesis………………………………………………………... …. 3
2. Literature review…….…………………………………………………………….. 5
2.1 Wave components……………………………………………………………… 5
2.1.1 Wave groups…………………………………………………………... 6
2.1.2 Group bound long wave………………………………………………. 6
2.2 Sediment re-suspension due to wave groups………………………………….. 7
2.3 Cross-shore suspended sediment flux in the frequency domain………….….. 10
Wave height to water depth ratio (H/h)…………..……..…………………… 13
Normalised velocity skewness (‹u3›⁄‹u2›3⁄2)………………………………... 13
Tidal cycle………………………………..……………………………..……. 13
Inside the surf zone…………………….……..……………………………... 14
2.4 Suspended sediment flux over rippled beds……………….………………… 15
2.4.1 Ripple classification………………………………………………… 17
Ripple classification (used in this study)…………………………………… 18
2.5 Turbulence close to seabed under wave groups…………………….………. 20
2.5.1 Turbulent bursts…………………………………………………….. 21
2.6 Concluding remarks………………………………………………………… 23
3. Factors influencing cross-shore suspended sediment flux in the frequency
domain……………………………………………………………………………… 25
3.1 Introduction…………………………………………………………………. 25
3.2 Methodology………………………………………………………………… 29
3.2.1 Field sites…………………………………………………….……... 29
3.2.2 Field data collection………………………………….……………... 31
3.2.3 Data analysis techniques…………………….……………………… 32
3.2.4 Ripple classification…………………………………….………….. 32
3.3 Results……………………………………………………………...……….. 33
3.3.1 Sediment re-suspension………………………………..……………. 33
3.3.2 Cross-shore sediment flux…………………….……………………. 35
Shoaling, non-breaking waves over a flat bed……………………….……… 35
Temporal variability: tidal cycle…………………………….……….……… 40
Spatial variability: inside and outside the surf zone…………….….……….. 45
Variation with the Dean number (Dean, 1973)………………….….……….. 47
3.4 Discussion…………………………………………………………………… 48
3.4.1 Cross-shore location…………………………………..…………….. 49
3.4.2 Bed ripples…………………………………………..………………. 50
3.4.3 Velocity skewness (‹u3›⁄‹u2›3⁄2)…………………………….…........ 51
3.4.4 Dean number (D)………………………………………….………… 52
3.5 Concluding remarks…………………………………………………………. 52
4. A numerical study of cross-shore suspended sediment flux in the frequency
domain……………………………………………………………….………….….. 55
4.1 Introduction……………………………………………………….…………. 55
4.2 Numerical model…………………………………………………………….. 57
4.2.1 Wave model…………………………………………………..……… 57
4.2.2 Wave Boundary Layer model……………….………………………. 58
4.2.3 Sediment suspension model……………..…………….…………….. 59
4.3 Field measurements………………………………………….……..………... 60
4.4 Model tests…………………………………………………….…….………. 61
4.4.1 Model domain…………………………………………….…………. 61
Co-spectral analysis………………………………………………..………… 62
4.4.2 Shoaling waves over a flat bed………………………..……………... 62
4.4.3 Inside the surf zone……………………………………..…………… 65
4.5 Results and discussion……………………………………………..………… 67
4.5.1 Mean grain size (d50)………………………………………………… 68
4.5.2 Cross-shore location (Hs/h)…………………………………………... 70
4.5.3 Bed roughness (Kn)…………………………………………………... 73
4.5.4 Over equivalent ripples……………………………………………….. 75
4.6 Implications…………………………………………………………………... 76
4.7 Concluding remarks……………………………………………………….…. 77
5. The role of ripple types on cross-shore suspended
sediment flux…………………………………………………..…………………….. 79
5.1 Introduction……………………………………………………….………….. 79
5.2 Methodology…………………………………………...………….…. 82
5.2.1 Field sites……………………………………………….………….… 82
5.2.2 Data collection……………………………………………..………… 83
5.2.3 Data analysis……………………………………..………………….. 84
Spectral analysis…………………………………………………..…………. 84
Net suspended sediment flux…………………………………….…….…….. 84
5.2.4 Ripple classification…………………………………..……………… 85
5.3 Results and discussion…………………………………………….….………. 86
5.3.1 Ripple geometry……………………………………..………….……. 86
5.3.2 Ripple patterns………………………………………..……………… 87
5.3.3 Suspended sediment concentration……………………………..……. 89
5.3.4 Sediment suspension and wave groups…………………………..….. 90
5.3.5 Cross-shore suspended sediment flux…………………………..…… 92
Flat bed………………………………………………………………..……… 93
Post-vortex ripples…………………………………………………..……….. 97
2D ripples……………………………………………………………..……… 101
2D/3D ripples…………………………………………………………..…….. 105
3D ripples……………………………………………………..……………… 107
Cross ripples……………………………………………………..…………… 111
5.4 Implications……………………………………………………………..……. 113
5.5 Concluding remarks…………………………………………………………... 115
6. Turbulent kinetic energy and sediment re-suspension
Due to wave groups………………………..……………………….…………….….. 117
6.1 Introduction…………………………………………………………………… 117
6.1.1 Turbulent bursts……………………………………….……………… 118
6.2 Methodology…………………………………………………………..……… 120
6.2.1 Field site and conditions…………………………….………………… 120
6.2.2 Instrumentation………………………………………….……………. 122
6.2.3 Data analysis techniques……………………………………………… 123
Inertial subrange of turbulence……………………………………………….. 123
6.3 Results and discussion………………………………………………..……… 126
6.3.1 Sediment suspension under wave groups……………………………. 126
6.3.2 Spectral analysis between u and c……………………………………. 126
6.3.3 Turbulent Kinetic Energy (TKE)…………………………………….. 129
6.3.4 Bursting phenomenon………………………………………………… 134
6.4 Concluding remarks…………………………………………...……………… 135
7. Discussion and conclusions……………………………………..……………..… 137
Cross-shore sediment flux in the frequency domain…………………………. 137
Sediment re-suspension under wave groups…………………………………. 138
7.1 Future work…………………………………………………….……………. 139
References………………………………………………………………………….... 141
Preface
I hereby declare that all material presented in this thesis is original except where due
acknowledgment is given, and has not been accepted for the award of any other degree or
diploma. The main body of this thesis is comprised of four chapters (3 to 6), each of
which is a paper written for journal publication:
Paper 1 (Chapter 3):
“Factors influencing cross-shore suspended sediment flux in the frequency domain”.
Continental Shelf Research (in review).
Paper 2 (Chapter 4):
“A numerical study of cross-shore suspended sediment flux in the frequency domain”. To
be submitted to Journal of Coastal Research.
Paper 3 (Chapter 5):
“The role of ripple types on cross-shore suspended sediment flux”. Submitted to Marine
Geology.
Paper 4 (Chapter 6):
“Turbulent kinetic energy and sediment re-suspension under wave groups”. To be
submitted to Marine Geology.
All the work presented in this thesis was carried out by the author under the supervision
of Prof. Charitha Pattiaratchi unless otherwise stated. For the jointly written paper,
Chapter 5, Dr Jeff Doucette provided the data set. As the author of all material within
this thesis, I am completely responsible for all data analyses, figures and written text
contained herein.
Acknowledgements
First, I would like to thank my supervisor, Prof. Charitha Pattiaratchi. for all the help,
encouragement and advice during the last four years. He supported me with his time, effort
and encouragement throughout this work, ensuring it was an enjoyable and rewarding
experience. A big thank you to Dr Jeff Doucette for sharing some of his valuable data and
for all the fruitful discussions. Thanks also to Ben and Joanna for the help in field
measurements, David and Andres for the help in numerical modelling work and Ruth for
proof reading most of my papers.
I would like to thank Dr Gerd Masselink for leading the field campaign in Broome. The
data in Chilaw were collected in conjunction with the Lanka Hydraulic Institute and funded
by the Ministry of Fisheries and Aquatic Resources (Sri Lanka).
FUNWAVE 1D, from the Center for Applied Coastal Research, University of Delaware,
was used in numerical modelling work. The high quality source code and documentation
that is freely available to the scientific community is gratefully acknowledged.
Throughout this work, I was supported financially by an International Postgraduate
Research Scholarship, a University Postgraduate Award, and an ad-Hoc SESE scholarship,
for which I am grateful.
Thanks to all my friends; Alexis, Alessio, Alicia, Andres, Arthur, Brendon, Daniel, David,
Dell, Ed, Geoff, Giulia, Jona, Kelsey, Laura, Leon, Paul, Peter, Ryan, Seba, Sheree, Ursala,
and Vadim for making my stay in Australia such a wonderful time.
At last but by no means least, I would like to thank my parents and family for their constant
encouragement and love, even though thousands of kilometers separate us.
Chapter 1: Introduction 1
Chapter 1 Introduction
With rising global sea levels and rapidly increasing population densities along coastal
stretches, coastal stability has become a major issue for coastal communities and managers.
Accurate prediction of sediment transport in nearshore environments, however, is one of
the most complex challenges encountered by coastal researchers in designing coastal
structures or beach nourishment schemes. Although nearshore sediment transport mainly
occurs in the alongshore direction, the cross-shore transport can play a dominant role in
determining seasonal shoreline evolution and beach morphology (Masselink and
Pattiaratchi, 1998). Further, it has been noted that longshore transport is predominantly due
to steady motions (Sternberg et al., 1989), whereas a range of mean and oscillatory
components (wind waves, swell, wave groups, infra-gravity oscillations, and tides) drives
cross-shore transport.
Observations made under different conditions and at various locations worldwide have
revealed that the direction and magnitude of cross-shore suspended sediment flux under
different frequency components is variable. Huntley and Hanes (1987) originally found
that, for shoaling waves outside the breaker zone, the cross-shore suspended sediment flux
was directed onshore at the incident wave frequencies (e.g. wind waves, swell) and offshore
at lower frequencies (e.g. wave groups, group bound long wave). However, other
investigators have documented cases where offshore fluxes of sediment at incident swell
frequencies and vice-versa (Osborne and Greenwood, 1992a, b; Brander and Greenwood,
1993; Davidson et al., 1993; Aagaard and Greenwood, 1995). This inconsistency was
attributed to various factors such as bed ripples, cross-shore location with respect to the
breaker line, velocity skewness, and grain size. In addition, sediment re-suspension and
cross-shore sediment flux over different ripple types can also be highly variable (Nielsen,
1981; Brander and Greenwood, 1993; Osborne and Vincent, 1993, 1996).
Chapter 1: Introduction 2
Even though, there have been several studies related to sediment re-suspension and cross-
shore suspended sediment flux in nearshore regions, there is still much to be resolved.
Especially, in terms of the inconsistency in direction and magnitude of cross-shore
suspended sediment flux observed under different conditions at various locations and the
dominant influencing factors such as such as bed ripples, cross-shore location with respect
to the breaker line, velocity skewness, and grain size. The relative importance of these
factors has not been investigated previously even though it is of great interest as these
factors may operate simultaneously. In addition, extended investigations on these factors
would help obtaining a better understanding of the processes. This could be undertaken
using field measurements collected from different sites where the local hydrodynamics and
sediment grain size vary and through the use of a simple numerical model the contribution
of each of these factors to the cross-shore sediment transport may be defined.
There is only a been limited number of field investigations undertaken exploring sediment
re-suspension and flux over different ripple types and further they have not covered the
range of ripple types present in nearshore environments. This emphasises the importance
of investigating sediment resuspension and flux over different ripple types.
Sediment suspension events caused by wave groups were observed to be more pronounced
than the suspension events occurred at the incident frequency band (Hanes and Huntley,
1986; Huntley and Hanes, 1987; Hanes, 1991; Vincent et al., 1991; Osborne and
Greenwood, 1993; Williams et al., 2002). Persistent turbulence resulting from larger waves
of the wave groups has been attributed as a major cause for these higher suspension events
(Hanes and Huntley, 1986; Osborne and Greenwood, 1993). However, field measurements
of flow generated turbulence close to the seabed and their relation to sediment suspension
events caused by wave groups do not appear in the literature.
The primary objective of this study is to investigate the factors influencing sediment re-
suspension and cross-shore suspended sediment flux in the frequency domain. This was
mainly accomplished through a series of field measurements conducted at several locations
in Western Australia and in Sri Lanka (Fig. 1.1), covering variety conditions (differing bed
Chapter 1: Introduction 3
topography, cross-shore location, tide level, wave/velocity skewness, wave groupiness,
grain size). Measurements included time series records of water surface elevation, cross-
shore current velocity and suspended sediment concentration obtained both inside and
outside the surf zone. These data were analysed to investigate the potential factors
influencing the direction and magnitude of cross-shore suspended sediment flux and to
evaluate the relative importance of those factors.
The ripple geometry was recorded at some places and was used to explore the variability in
suspended sediment flux over different ripple types. Moreover, the turbulent velocity
records close to the seabed were measured at one location and were used to study the effect
of flow generated turbulent kinetic energy on higher sediment suspension events observed
under wave groups.
Field studies are extremely useful in understanding factors governing sediment re-
suspension and flux in nearshore regions. However, estimating the influence of governing
parameters separately may remain difficult in the field due to the complex nature of
processes occurring in this highly dynamic region. A simple numerical model was
developed to study the influence of potential governing factors over a flat bed. The
numerical model used in this study included three major components: (a) a Boussinesq
model to simulate wave shoaling; (b) a simple wave boundary layer model to predict the
instantaneous bed shear stress; and (c) a finite difference scheme solving turbulent diffusion
equation to predict the suspended sediment concentration; the numerical model was
validated with field observations.
Outline of the thesis
Following this introduction, Chapter 2 presents a literature review which provides an
overview of present state of knowledge on sediment re-suspension and cross-shore
suspended sediment flux in nearshore regions. The main thrust of the original work
includes Chapters 3 – 6 and is presented as a compilation of four journal papers submitted /
to be submitted to international journals. Chapter 3 presents results of field measurements
Chapter 1: Introduction 4
conducted at several locations (Mullaloo Beach, Perth, Western Australia; Cable Beach,
Broome, north-western Australia; and Chilaw, Sri Lanka) examining factors influencing the
cross-shore suspended sediment flux in the frequency domain. Numerical modelling results
exploring some of the factors influencing cross-shore suspended sediment flux in the
−3000 −2750 −2500 −2250 −2000−400
−200
00
200
SRI LANKA
AUSTRALIA
Broome
Perth
Chilaw
south−westernAustralia
Indian Ocean
Figure 1.1. Map showing locations of field measurements (Chilaw, Broome, Perth and
several locations in south-western Australia).
frequency domain due to shoaling waves over a flat bed are presented in Chapter 4. Results
of field measurements, conducted at 15 micro-tidal, sandy beaches in south-western
Australia, of cross-shore suspended sediment flux over different ripples types is presented
in Chapter 5. Chapter 6 discusses the influence of turbulent kinetic energy on higher
sediment suspension events observed under wave groups using a set of high frequency
velocity records obtained close to the seabed. Finally, Chapter 7 is an overall discussion of
the work, including general conclusions and suggestions for future research. Note that, as
Chapters 3, 4, 5 and 6 are self-contained papers, there is some repetition of introductory
material and to a lesser extent discussion.
Chapter 2: Literature review 5
Chapter 2 Literature review
An overview of the current knowledge on sediment re-suspension and cross-shore
suspended sediment flux under different frequency components in nearshore regions is
presented in this chapter.
2.1 Wave components
Sediment re-suspension and cross-shore transport in nearshore regions are driven by a
range of mean (undertow, longshore currents) and oscillatory (wind waves, swell, wave
groups, infragravity waves, tides) flow components. Period of swell or wind waves is of
the order of seconds, that of wave groups or infragravity waves (e.g. group bound long
wave, edge waves) is of the order of minutes, and the period of tides are of the order of
days.
Field measurements presented in this study were obtained from sites in Western Australia
and Sri Lanka. At all these locations, under the wave dominated nearshore conditions,
three distinct regimes of local wave climate can be identified in general: (a) periods of
storm activity associated with passage of frontal systems during winter; (b) periods of
locally generated waves due to sea breeze systems; and, (c) swell wave activity during
‘calm’ periods (Pattiaratchi et al., 1997; Masselink and Pattiaratchi, 2001). Storm or sea
breeze systems occur over a short duration and swell waves dominate the nearshore wave
climate for longer periods. Further, a nearshore wave climate dominated by swell, which is
the focus of this study, provides ideal conditions for formation of pronounced wave groups
(Masselink and Pattiaratchi, 2000).
Chapter 2: Literature review 6
2.1.1 Wave groups
With any combination of waves a point will occur where all frequencies cancel and the
resulting wave has minimal amplitude. The set of waves between two of these points is
called a wave group (Fig. 2.1).
short waves (form wave group)
mean water level bound long wave envelope function
Figure 2.1. Wave groups and group bound long wave
2.1.2 Group bound long wave
When there is an incoming swell, Munk (1949) and Tucker (1950) first noticed the
existence of longer waves, of 2-3 min period, similar to the envelope of the visual swell,
and suggested that the long waves may be caused by an excess of mass transported forward
by groups of high swell. Longuet-Higgins and Stewart (1962; 1964) explained the
formation of these long waves as a wave group, containing larger than average waves,
would depress the mean water surface and thereby forces a long wave which was defined as
group bound long wave. Longuet-Higgins and Stewart (1964) theoretically demonstrated
the formation of group bound long wave using the gradient in radiation stress as a wave
group passes. Therefore, wave groups are always associated with a group bound long wave
(Fig. 2.1).
Chapter 2: Literature review 7
2.2 Sediment re-suspension due to wave groups
The suspension of sediment due to shoaling waves in nearshore regions has been observed
to occur in an event-like manner corresponding to a range of time scales ranging from
seconds (e.g. swell, wind waves) to minutes (e.g. wave groups, infragravity waves)
(Brenninkmeyer, 1976; Sternberg et al., 1984; Hanes and Huntley, 1986; Osborne and
Greenwood, 1993). Further, sediment suspension events corresponding to wave groups
caused higher suspension events than at the incident wave frequency band (Fig. 2.2) (Hanes
and Huntley, 1986; Huntley and Hanes, 1987; Hanes, 1991; Vincent et al., 1991; Osborne
and Greenwood, 1993; Hay and Bowen, 1994a, b; Williams et al., 2002). Williams et al.
(2002) observed that average suspended sediment concentration caused by a wave group
was approximately three times larger than values measured under a single wave of
comparable height.
Figure 2.2. Time series records of: a) the instantaneous cross-shore velocity (U); b) the
maximum cross-shore velocity for each wave cycle (Um); and the wave averaged suspended
sediment concentration (Cwave). Note: the solid line = 4 cm elevation, the dot-dashed line =
10 cm elevation (from Osborne and Greenwood, 1993)
Chapter 2: Literature review 8
There are few explanations for the higher suspension events observed under wave groups.
Vincent et al. (1991) attributed this phenomenon to change in bedform geometry
responding to the variability in the wave conditions: Here, steeper ripples would be present
on the sea bed when the smaller waves of the wave group pass and these ripples would
become less steep when the larger waves of the group pass (assuming the break-off point
had been exceeded). Considering the time lag in changing ripple geometry to the wave
forcing, larger waves of the wave groups would encounter steeper than expected ripples and
hence cause higher suspension events enhanced by sand-laden vortices formed in the
leeside of the ripples (Vincent et al., 1991).
Villard et al. (2000), Villard and Osborne (2002) studied the influence of wave groups on
suspended sediment concentration over vortex ripples with the help of large scale
laboratory experiments (Fig. 2.3). Villard and Osborne (2002) suggested the effect of
antecedent larger waves could lead to coupling between antecedent and developing vortices
above a rippled bed and hence cause higher suspension events. Villard and Osborne (2002)
further observed that these suspension events were more persistent when smaller waves
followed larger waves.
Figure 2.3. a) Group ensemble-averaged horizontal velocity; b) group ensemble-averaged
logarithmic SSC profiles; and c) associated coefficient of variation profiles, CV =
J(SSC)/<SSC> (from Villard et al., 2000)
Chapter 2: Literature review 9
Higher suspension events coincided with the passing of wave groups, however, these events
were observed both in the presence (Vincent et al., 1991; Osborne and Greenwood, 1993)
and absence of ripples (Davidson et al., 1993; Hay and Bowen, 1994a).
Hanes and Huntley (1986) suggested that some form of nonlinear ‘pumping’ of sediment
up into the water column during the passing of wave groups may be responsible for higher
suspension events. Hanes and Huntley (1986) and Osborne and Greenwood (1993) related
these events to the persistence of turbulence generated by a sequence of large waves in a
wave group. They suggested that turbulence generated at the seabed by the larger waves of
wave groups persisted longer and caused higher suspension events (Hanes and Huntley,
1986; Osborne and Greenwood, 1993). Hanes and Huntley (1986) observed that turbulence
persisted and propagated upward into the water column during the passage of wave groups.
Hanes and Huntley (1986) and Osborne and Greenwood (1993), however, did not measure
the turbulence close to seabed.
With multi-frequency acoustic backscatter measurements, Hay and Bowen (1994a)
suggested that the coherent suspension clouds observed at wave group time scales could
have more than one origin. Vortex shedding from megaripples, an enhanced interaction
between largest waves of the wave groups and the seabed, perhaps via the bound long
wave, and coherent structures in combined flow were thought as possible mechanisms (Hay
and Bowen, 1994a).
Hay and Bowen (1994b) pointed at: the bedforms, surface-injected vortices, and the sensor
support structure as possible influences on pumping up of sediments observed at wave
group frequency. Hay and Bowen (1994a), however, suggested that keeping the sensors 5-
10 diameters from the nearest support would minimise the risk of supporting structure’s
influence.
Chapter 2: Literature review 10
2.3 Cross-shore suspended sediment flux in the frequency domain
Huntley and Hanes (1987) originally found that for shoaling waves outside the breaker
zone, the cross-shore sediment flux was directed onshore at the incident wave frequencies
(wind waves, swell) and offshore at lower frequencies (wave groups, infragravity waves)
(Fig. 2.4). The shoreward sediment flux under incident waves as the waves shoaled was
attributed to the increasing velocity skewness in the propagation direction (Doering and
Bowen, 1988; Osborne and Greenwood, 1992a). The sediment suspended at wave group
(low) frequencies coupled with the offshore phase of the group bound long wave (Longuet-
Higgins and Stewart, 1964) (Fig. 2.1), resulting in a net offshore sediment transport at those
frequencies (Larsen, 1982; Shi and Larsen, 1984). Huntley and Hanes (1987) did not
measure the seabed topography, but calculations showed that ripples of ripple height 3 to 5
cm and ripple length 0.3 m may have been present.
Figure 2.4. Cospectrum of cross-shore velocity and suspended sediment concentration at
MOB1 (from Huntley and Hanes, 1987)
onshore
offshore
Co-
spec
trum
u:M
OB
1
Frequency Hz
However, other investigators have documented cases where offshore fluxes of sediment at
incident frequencies and vice-versa (Fig.s 2.5 & 2.6) (Osborne and Greenwood, 1992b;
Brander and Greenwood, 1993; Davidson et al., 1993; Aagaard and Greenwood, 1995).
Chapter 2: Literature review 11
Figure 2.5. Co-spectrum between cross-shore current velocity and suspended sediment
concentration, outside the surf zone under ebbing tide (from Davidson et al., 1993).
Chapter 2: Literature review 12
Figure 2.6. Temporal variability of the cross-shore velocity (z = 0.1 m; solid line) and
sediment concentration (z = 0.04 m; dashed line) spectra and the associated co-spectra from
the 85 m station under a range of wave conditions (from Osborne and Greenwood, 1992b)
These deviations were assumed to be due to various factors such as the presence of ripples
(Vincent et al., 1991; Osborne and Greenwood, 1992b; Brander and Greenwood, 1993;
Davidson et al., 1993; Osborne and Vincent, 1993, 1996), wave conditions (wave height to
water depth ratio) (Osborne and Greenwood, 1992a, b), varying tide level (Davidson et al.,
1993), and normalised velocity skewness (Russell and Huntley, 1999). The relative
magnitudes and directions of these different frequency components could vary with the
measurement position with respect to the breaker line (Osborne and Greenwood, 1992a;
Chapter 2: Literature review 13
Davidson et al., 1993; Aagaard and Greenwood, 1995; Russell and Huntley, 1999) as well
as the measurement height above the bed (Aagaard et al., 1998; Conley and Beach, 2003).
Some results indicated that cross-shore flux under low (infragravity) frequencies,
corresponding to wave groups, acted offshore outside the breaker zone and onshore inside
the breaker zone (Aagaard and Greenwood, 1995). The mean component of the sediment
flux was mainly offshore below the wave trough level because of the presence of undertow
(bed return flow) (Osborne and Greenwood, 1992b). The mean flow (zero frequency)
component, however, was not considered in the present study.
Wave height to water depth ratio (H/h)
Osborne and Greenwood (1992a, b) observed that the direction and magnitude of cross-
shore suspended sediment flux varied significantly with varying wave height to water depth
ratio (H/h) (Fig. 2.6). This was, however, observed at the same measurement location with
varying wave conditions as well as at different locations in the cross-shore direction
showing the variation in cross-shore sediment flux with the cross-shore location (Osborne
and Greenwood, 1992a, b).
Normalised velocity skewness (‹u3›⁄‹u2›3⁄2)
Russell and Huntley (1999) investigated the cross-shore sediment transport with an
energetic approach using cross-shore velocities. They observed a significant variation in
cross-shore transport with the location with respect to the breaker line, which was related to
the normalised velocity skewness (‹u3›⁄‹u2›3⁄2) (Russell and Huntley, 1999). Moreover,
based on their results, a ‘shape function’ representing spatial distribution of cross-shore
sediment transport was introduced for high energy beaches (Russell and Huntley, 1999).
Tidal cycle
Davidson (1993) investigated the cross-shore suspended sediment flux in the frequency
domain over a tidal cycle. The suspended sediment flux at the low frequencies remained
offshore throughout the cycle, but the flux due to incident waves was onshore during flood
Chapter 2: Literature review 14
tide and was offshore during the ebb tide (Fig. 2.5) (Davidson et al., 1993). Other
surrounding conditions also changed during this time and the possible presence of ripples
during the ebb tide was assumed to be a major cause for offshore flux observed (Davidson
et al., 1993).
Inside the surf zone
Inside the surf zone, the magnitude of suspended sediment flux at the incident wave band
reduced significantly as a result of energy dissipation due to wave breaking, but the
direction remained onshore (Osborne and Greenwood, 1992a, b; Aagaard and Greenwood,
1995). The relative magnitude of the sediment flux at the low frequencies increased inside
the surf zone (Osborne and Greenwood, 1992b) while the direction could alternate between
onshore and offshore depending upon the position of measurements (Fig. 2.7) (Aagaard and
Greenwood, 1995).
Chapter 2: Literature review 15
Figure 2.7. Co-spectra between cross-shore current velocity and suspended sediment
concentration at: a) 90 m; b) 111.5 m stations inside the surf zone (from Aagaard and
Greenwood, 1995)
2.4 Suspended sediment flux over rippled beds
Influence of ripples was considered as one of the most likely reasons for offshore
suspended sediment flux observed at the incident wave frequency band (Osborne and
Greenwood, 1992b; Brander and Greenwood, 1993; Davidson et al., 1993). The timing of
sediment suspension in relation to the cross-shore velocity can change significantly
depending on the ripple geometry and this can cause the direction of suspended sediment
transport at the incident frequency band to change and even to alternate between onshore
and offshore (Nielsen, 1979; Osborne and Vincent, 1993, 1996).
Chapter 2: Literature review 16
Inman and Bowen (1963) first described a mechanism for seaward suspended sediment flux
at the incident frequency band over a rippled bed. They described the suspension and
transport process over steep vortex ripples as follows: (1) when a skewed wave propagates
over vortex ripples, a vortex is formed on the leeside of the ripple during the relatively
strong onshore phase of flow, and remains trapped until the flow reverses; (2) during the
weaker offshore phase, the sand-laden vortex is released and ejected into the water column;
and (3) this sediment cloud is transported seaward by the offshore phase (Fig. 2.8).
Figure 2.8. Offshore suspended sediment transport due to incident waves over a rippled bed
(from Davidson et al., 1993)
During some studies, however, offshore sediment flux at the incident frequency band has
been observed over less steep post-vortex ripples (Osborne and Greenwood, 1992b;
Brander and Greenwood, 1993) and predominantly onshore flux has been measured over
steeper ripples (Osborne and Greenwood, 1992b). Davidson et al. (1993) noticed offshore
flux due to incident waves over a rippled bed, but the ripple geometry was not measured;
therefore it was unclear whether the ripples were vortex or post-vortex.
The above observations suggest that the direction of suspended sediment flux at the
incident frequency band could be a function of the ripple geometry and thus can vary over
Chapter 2: Literature review 17
different ripple types. Osborne and Vincent (1996) demonstrated the difference in
sediment suspension patterns over steeper vortex ripples and low steepness transitional
ripples and Osborne and Vincent (1993) observed that sediment suspension and transport
rates are highly sensitive to the ripple type. Sediment suspension over vortex ripples is
more a convective process (Lee and Hanes, 1996; Osborne and Vincent, 1996), whist the
suspension over low steepness ripples is diffusive (Osborne and Vincent, 1996).
Hay and Mudge (2005) studied the occurrence of five different bed states (flat bed and four
ripple types) using measurements in ~ 3m water depth during SandyDuck 97. However,
they did not present suspended sediment concentration data and sediment re-suspension or
cross-shore flux patterns were not discussed (Hay and Mudge, 2005).
2.4.1 Ripple classification
Several ripple classification schemes based on ripple geometry, near-bed orbital diameter,
boundary shear stress, shields parameter, and sediment suspension pattern can be found in
literature (Bagnold, 1946; Clifton, 1976; Grant and Madsen, 1982; Clifton and Dingler,
1984; Osborne and Vincent, 1993; Wiberg and Harris, 1994). In general, two dimensional
ripple geometry can be characterised by the ripple height (η), ripple length (λ), and ripple
steepness (η/λ) (Fig. 2.9).
η
λ
Figure 2.9. Ripple dimensions
Bagnold (1946), with his experiments, introduced a classification based on the pattern of
sediment movement over the ripples. Under low bed shear stresses sand grains moved back
and forth with the near-bed orbital velocity forming rather flat ripples. These ripples were
called pre-vortex or rolling grain ripples and the sediment transport is restricted to bed load.
Chapter 2: Literature review 18
As the bed shear stress increased ripples became steeper and vortices began to form in the
leeside of the ripples. Sediment was entrained in the vortices and ejected into the water
column. These ripples were called vortex. As the bed shear stress increased further, the
ripples began to erode and they became less steep and were called post-vortex. Finally, the
sea bed became flat when the bed shear stress was further increased corresponding to sheet
flow conditions (Fig. 2.10). When the steepness is less than 0.1, the ripples were called
post-vortex (Clifton and Dingler, 1984). Over post-vortex ripples, sediment suspension and
vortex shedding occur as irregular bursts (Osborne and Vincent, 1993).
pre-vortex or rolling
vortex (η/λ > 0.1)
Post-vortex (η/λ < 0.1) flat bed
Increasing bed shear stress
Figure 2.10. Ripple classification based on ripple geometry and sediment suspension
pattern in order of increasing bed shear stress
Osborne and Vincent (1993) introduced a classification scheme based on ripple size (η &
λ), sediment suspension pattern, number of crest dimensions (2-dimensional or 3-
dimensional), and profile shape (symmetric, asymmetric, and indeterminate). The ripple
classification scheme used in this study was formulated mainly based on Osborne and
Vincent’s (1993) classification and the classification explained in Fig. 2.10.
Ripple classification (used in this study)
In this study, the observed ripples were classified (according to their geometry and
sediment re-suspension patterns) into five categories: post-vortex ripples, 2D ripples,
2D/3D ripples, 3D ripples, and cross ripples.
Low amplitude ripples, where the ripple steepness was less than 0.1 (Clifton and Dingler,
1984), oriented parallel to the wave crests were classified as post-vortex ripples (Osborne
and Vincent, 1993). These ripples were not always present, as they were washed away
during larger waves of the wave groups and re-formed during smaller waves. Vortex-
Chapter 2: Literature review 19
shedding occurred at irregular intervals, and diffusive mixing seemed to be the major
mechanism for sediment re-suspension. During the field measurements in Broome (chapter
3), initially, the post-vortex ripples were not always present as they usually behave. But
with the rising tide level (reducing bed shear stress) the post-vortex ripples reached
equilibrium state and appeared to remain as permanent features. Therefore, the post-vortex
ripples observed in Broome were categorized as ephemeral post-vortex and permanent
post-vortex ripples.
Steep ripples with crests oriented parallel to the wave crests were termed 2D ripples (Fig.
2.11a). Clear vortex shedding was observed over these ripples. Ripples with smaller
heights and variable lengths, where no distinct linear crests were observed, were
categorized as 3D ripples (Fig. 2.11b). The distance between bifurcations was smaller (<
10 cm) over 3D ripples and sediment suspension occurred as discrete packages. Ripples
with geometry that fell in between the 2D and 3D classifications were called 2D/3D ripples.
The bifurcation density for 2D/3D ripples was greater than for 2D ripples but less than for
3D ripples. The ripple heights of 2D/3D ripples were greater than those of 3D ripples. The
sediment suspension process over 2D/3D ripples resembled that over 2D ripples.
The final ripple type, cross ripples, consisted of larger, primary ripples and smaller,
secondary ripples, which were orthogonal to each other (Fig. 2.11c). Independently, each
set of ripples could be considered 2D. The primary and secondary ripples were inclined to
the wave propagation direction by approximately ± 450. Cross ripples can be considered
vortex under the Osborne and Vincent’s (1993) classification.
Chapter 2: Literature review 20
(b)(a)
(c)
Figure 2.11. Schemetic diagrams of: a) 2D ripples; b) 3D ripples; and c) cross ripples (from
Osborne and Vincent, 1993)
2.5 Turbulence close to seabed under wave groups
Persistence and upward propagation of turbulence generated by a sequence of large waves
in a wave group is considered as a possible reason for the higher suspension events
observed under wave groups (Hanes and Huntley, 1986; Osborne and Greenwood, 1993;
Hay and Bowen, 1994a) (see section 2.2).
Measuring turbulent fluctuations close to the seabed in the field used to be fairly unyielding
until the recent developments of Acoustic/Laser Doppler Velocimeters (ADV/LDV),
Coherent Doppler Profiler (CDP), and hot film anemometers. Conley and Inman (1992)
Chapter 2: Literature review 21
used hot film anemometers to measure turbulent velocity fluctuations under near-breaking
waves to study the patterns and regimes involved in the development of fluid-granular
boundary layer. Trowbridge and Agrawal (1995) measured the vertical structure of
turbulent velocity inside the wave boundary layer over a sand beach using a profiling laser-
Doppler velocimeter. Coherent Doppler Profiler (CDP) was used by Smyth and Hay
(2003) to measure the turbulent vertical velocity component both inside and outside the
wave boundary layer.
Few studies can be found in the literature where simultaneous measurements of turbulent
velocities and suspended sediment concentration were obtained close to the seabed (Foster
et al., 2000; Smyth et al., 2002; Kos'yan et al., 2003; Aagaard and Hughes, 2006; Foster et
al., 2006). Kos’yan et al. (2003) used three component Acoustic Doppler Velocimeter
(Vector) to measure turbulent velocities close to the seabed simultaneously with suspended
sediment concentration to investigate mechanisms of sand suspension by irregular waves.
They found a close relation between turbulent kinetic energy (TKE) and suspended
sediment concentration (Kos'yan et al., 2003).
Smyth et al. (2002) observed near-bed peaks in suspended sediment flux following wave
phase reversal over low-energy rippled beds whilst no such features was observed over
high-energy flat beds. Foster et al. (2006) calculated the turbulent kinetic energy (TKE)
close to the seabed and found that TKE was largest under the wave crest, and decreased
during the deceleration phase until the flow turned offshore. Sediment suspension also was
observed to be biased toward the onshore decelerating phase (Foster et al., 2006).
However, no study could be found investigating the effect of TKE on the sediment
suspension due to wave groups.
2.5.1 Turbulent bursts
Intermittent coherent events of strong turbulence production and vertical transfer inside the
bottom boundary layer have been observed under different geophysical flow conditions:
mean flow in laboratory (Corino and Brodkey, 1969), tidal flow in the sea (Gordon, 1974;
Chapter 2: Literature review 22
Heathershaw, 1974), and over plowed fields (Merceret, 1972). This process of formation
of coherent turbulent structures was called “bursting phenomenon” (Gordon and Witting,
1977; Cantwell, 1981). These coherent events were studied based on Reynolds stress terms
(-ρu’w’) by dividing the motions into quadrants in u’-w’ space (e.g. Soulsby, 1983), where
u’ is the horizontal component of turbulent velocity and w’ is the vertical component.
Quadrants were named bursts (u’<0, w’>0), sweeps (u’>0, w’<0), up-accelerations (u’>0,
w’>0), and down-decelerations (u’<0, w’<0) (Soulsby, 1983).
Bursts and sweeps, which contribute to positive Reynolds stress, were stronger than up-
accelerations and down-decelerations (Soulsby, 1983; Heathershaw and Thorne, 1985).
Bursts, which consisted of low-speed upward momentum transfer and sweeps, which
consisted of high-speed downward momentum transfer have been observed suspending bed
sediments higher up into the water column (Sutherland, 1967; Jackson, 1976; Sumer and
Oguz, 1978; Sumer and Deigaard, 1981).
All these investigations involving “bursting phenomenon”, however, were conducted under
steady flows or slowly oscillating flow conditions with long periods (e.g. tides). The
difficulties involved in investigating “bursting phenomenon” under short period surface
waves were explained by Jackson (1976), Sleath (1970; 1974a; b). Under wind driven
surface waves the mean values of the flow parameters would not remain sensibly constant
during turbulent bursts and during the time scale of the largest turbulent eddies (Jackson,
1976). Further, fast oscillating flows would not provide ample time to make reasonable
measurements (Sleath, 1970; 1974a; b). These explanations were made quite sometime
before the development of modern instruments and therefore it is fair to assume these
measurements would be less hard-won at present. It should, however, be noted that no
studies could be found in literature investigating the “bursting phenomenon” under swell
waves. Moreover, Hay and Bowen (1994a) suggested that coherent structures in combined
flow turbulence as a possible cause for higher suspension events observed at wave group
time scales.
Chapter 2: Literature review 23
Nevertheless, sediment suspension due to incident waves have shown intermittent spikes
which did not correspond to wave orbital velocity (Jaffe et al., 1984; Huntley and Hanes,
1987; Hanes, 1988; Smyth and Hay, 2003) suggesting possible influence of turbulent bursts
generated at the seabed. In their measurements over shoaling, non-breaking waves, Foster
et al. (2006) observed a highly intermittent structure of turbulence production. Clarke et al.
(1982) also suggested that bursts of intense turbulence coherent with peak values of wave
orbital velocity caused greater suspension events.
2.6 Concluding remarks
This chapter presented the current knowledge in sediment re-suspension and cross-shore
flux in nearshore environments. It showed the complexity involved in sediment re-
suspension and cross-shore flux in this highly dynamic region and the need for further
investigations. The direction and magnitude of sediment flux in the frequency domain was
highly inconsistent and appeared to be influenced by many different parameters. Further
investigations on the influence of those parameters therefore would help evaluate the
relative importance of those parameters and improve the understanding of the processes.
Bed forms (ripples) are considered as one of the most influencing parameters and it has
been noted that different ripple types can alter the sediment re-suspension and cross-shore
flux markedly. However, there is only a limited number of field investigations conducted
exploring sediment re-suspension and flux over different ripple types and therefore more
investigations covering this scenario would be valuable to explain sediment transport
processes in nearshore.
Time series records of suspended sediment concentration have shown that the suspension
events occurred at wave group frequency were more pronounced than at the incident
frequency band. Persistence and upward propagation of turbulence during the larger waves
of wave groups is assumed to be a possible mechanism for these higher suspension events.
No studies, however, could be found examining the influence of turbulence production
close to seabed due to wave groups and therefore it would be interesting to observe the
variation in turbulence close to seabed as wave groups pass.
Chapter 2: Literature review 24
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
25
Chapter 3 Factors influencing cross-shore suspended
sediment flux in the frequency domain
3.1 Introduction
With rising global sea levels and rapidly increasing population densities along coastal
stretches, coastal stability has become a major issue for coastal communities and managers.
Accurate prediction of sediment transport in nearshore environments, however, is one of
the most complex challenges encountered by coastal researchers. Although nearshore
sediment transport mainly occurs in the alongshore direction, the cross-shore transport can
play a dominant role in determining seasonal shoreline evolution and beach morphology
(Masselink and Pattiaratchi, 1998). Further, it has been noted that longshore transport is
predominantly due to steady motions (Sternberg et al., 1989), whereas a range of mean
(tides and undertow) and oscillatory components (wind waves, swell, wave groups, and
infra-gravity oscillations) drives cross-shore transport. Each of these frequency
components uniquely influences the direction and magnitude of cross-shore sediment flux
under different conditions (Huntley and Hanes, 1987). Therefore, an improved
understanding of the processes of sediment re-suspension and flux due to the different
oscillatory components is essential to predict cross-shore sediment transport, and thus
coastal stability, accurately.
The majority of previous studies revealed that the suspension of sediment, and hence the
cross-shore sediment flux in nearshore regions, occurs in an event-like manner over a range
of timescales ranging from seconds (wind waves, swell) to minutes (wave groups or
infragravity waves) (Brenninkmeyer, 1976; Sternberg et al., 1984; Hanes and Huntley,
1986; Osborne and Greenwood, 1993). These studies further indicated that suspension
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
26
events that occurred at low frequencies (wave groups) were much more pronounced than
those at incident frequencies (wind waves, swell) (Hanes and Huntley, 1986; Huntley and
Hanes, 1987; Hanes, 1991; Vincent et al., 1991; Osborne and Greenwood, 1993; Williams
et al., 2002). This enhances the assumption that wave groups are more capable than
individual incident waves of suspending sediment particles from the bed. Vincent et al.
(1991) proposed that pronounced suspension events under low frequency oscillations (wave
groups) were due to changes in ripple geometry during the passage of wave groups.
However, higher suspension events at wave group frequencies have also been observed
under flat bed conditions (Davidson et al., 1993; Hay and Bowen, 1994). Osborne and
Greenwood (1993) and Hanes and Huntley (1986) explained that persistent turbulence
propagation caused by larger waves of wave groups could have pumped more sediments up
into the water column. From a series of experiments conducted in a large-scale wave
research flume over rippled beds, Villard and Osborne (2002) suggested that higher
suspension events that occurred at the group frequency following larger waves of the group
may be due to coupling between antecedent vortices created by larger waves and
developing vortices created by smaller waves which followed the larger ones.
Observations made under different conditions and at various locations worldwide have
revealed that the direction of cross-shore sediment flux under different frequency
components is variable. Huntley and Hanes (1987) originally found that for shoaling waves
outside the breaker zone, the cross-shore sediment flux was directed onshore at the incident
wave frequencies (wind waves, swell) and offshore at lower frequencies (wave groups,
infragravity waves). The shoreward sediment flux under incident waves as waves shoal
was attributed to the increasing velocity skewness in the propagation direction (Doering
and Bowen, 1988; Osborne and Greenwood, 1992a). The sediment suspended at wave
group (low) frequencies coupled with the offshore phase of the group bound long wave
(Longuet-Higgins and Stewart, 1964), resulting in a net offshore sediment transport at those
frequencies (Larsen, 1982; Shi and Larsen, 1984).
However, other investigators have documented cases where offshore fluxes of sediment at
incident frequencies and vice-versa (Osborne and Greenwood, 1992b; Davidson et al.,
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
27
1993; Aagaard and Greenwood, 1995). These deviations were assumed to be due to
various factors such as the presence of ripples (Vincent et al., 1991; Osborne and
Greenwood, 1992b; Davidson et al., 1993; Osborne and Vincent, 1993, 1996), wave energy
during a storm) (Osborne and Greenwood, 1992b), varying tide level (Davidson et al.,
1993), and grain size (Doucette, 2000). Further, the relative magnitudes and directions of
these different frequency components could vary with the location of the measurements
with respect to the breaker line (Osborne and Greenwood, 1992a; Davidson et al., 1993;
Aagaard and Greenwood, 1995; Russell and Huntley, 1999) as well as the measurement
height above the bed (Aagaard et al., 1998; Conley and Beach, 2003).
Some results indicated that cross-shore flux under low (infragravity) frequencies,
corresponding to wave groups, acted offshore outside the breaker zone and onshore inside
the breaker zone (Aagaard and Greenwood, 1995). The mean component of the sediment
flux was mainly offshore below the wave trough level because of the presence of undertow
(bed return flow). The mean flow (zero frequency) component, however, was not
considered in the present study.
Nonetheless, these observations emphasise the complexity involved in sediment transport
processes in this highly dynamic region and thus the need for a better understanding of the
factors influencing the magnitude and direction of cross-shore sediment transport. Further,
no studies could be found exploring many of these influencing factors at once. Evaluation
of the relative importance of these influencing factors is also of greater significance as most
of these factors act simultaneously.
This paper describes results obtained through a series of field measurements (water surface
elevation, horizontal current velocities, and suspended sediment concentration) undertaken
in different nearshore environments under various conditions, such as differing tide, grain
size, bed geometry, and cross-shore location. These results were then used to explore the
factors affecting cross-shore suspended sediment flux in the frequency domain. Note that
the suspended sediment concentration values presented in this paper were measured at 0.05
m from the seabed; hence the sediment flux discussed refers to the flux close to the seabed.
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
28
Perth
Fremantle
MullalooBeach
N
Broome
Perth
WESTERNAUSTRALIA
N
Mangrove PointGantheaumePoint
Cable Beach Club
Entrance Point
ROEBUCK BAY
GANTHEAUME BAY
BROOME
0 1 2 3 4 5km
INDIANOCEAN
Ca
ble
Bea
ch
Study Site
0 5 10 km
(a) (b)
(c)
study site
Figure 3.1: Location maps of study sites a) Mullaloo Beach, Perth, Western Australia; b)
Cable Beach, Broome, Western Australia; c) Ambakandawila Beach, Chilaw, Sri Lanka.
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
29
3.2 Methodology
3.2.1 Field sites
Field measurements providing the basis for the present study were undertaken at several
locations: Mullaloo Beach, south-western Australia (Fig. 3.1a); Cable Beach, Broome,
north-western Australia (Fig. 3.1b); and Chilaw, Sri Lanka (Fig. 3.1c). These locations
encompass a range of conditions.
South-western Australia, where Mullaloo Beach is located (Fig. 3.1a), experiences diurnal,
micro-tidal conditions, with a maximum tide range of 0.6 m (Pattiaratchi et al., 1997). The
wave climate can thus be divided into three regimes: (1) summer sea breezes; (2) winter
storms; and, (3) swell dominated periods between sea breezes (i.e. during the morning in
summer) and between the passage of frontal systems during winter (Pattiaratchi et al.,
1997; Masselink and Pattiaratchi, 2001). The latter regime is also dominated by the
presence of wave groups and is the focus of this paper.
Cable Beach, Broome, in north-western Australia (Fig. 3.1b), experiences a macro-tidal
regime, with a maximum spring range of 9.8 m; it is generally subject to low to medium
energy swell conditions, with significant wave heights of 0.5–1.5 m.
Ambakandawila Beach, located to the south of Chilaw, along the west coast of Sri Lanka
(Fig. 3.1c), experiences similar conditions to those of south-western Australia (Pattiaratchi
et al., 1999). The wave climate can also be divided into three regimes, similar to those of
south-western Australia.
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
30
0 20 40 60
−2
−1
0
1
2
Ele
vatio
n re
lativ
e to
MS
L (m
)
instrument station
MWL
(a)
0 50 100 150 200 2500
1
2
3
4
5
6
Ele
vatio
n re
lativ
e to
MS
L (m
)
instrument station
high tide level(b)
MWL
0 10 20 30 40 50
−1
0
1
2
3
Cross−shore distance (m)
Ele
vatio
n re
lativ
e to
MS
L (m
)
MWL
(c)
Figure 3.2: Beach slopes: a) Mullaloo Beach; b) Cable Beach; and c) Ambakandawila
Beach (thick solid line shows the range of instrument station location).
At all locations, the measurements were undertaken at long, straight, exposed beaches,
where waves were not refracted by nearshore reefs, islands or offshore/coastal structures.
The beaches had a plane form and were not barred. The beach profiles at the different
locations are presented in Fig. 3.2. At Mullaloo and Chilaw, the conditions can be
classified as reflective, since the beaches were relatively steep and the waves were seen
breaking almost on the beach face with a narrow surf zone. In contrast, Broome was
clearly dissipative with a mild slope and wider surf zone. Surging breakers were observed
at Mullaloo and Chilaw, whereas in Broome the breaker type was spilling. The sites
selected comprised a range of grain sizes: Mullaloo had medium to coarse sand with a
median grain size (d50) of 0.28 mm; at Chilaw, the median grain size was 0.15 mm; and in
Broome, the grains were very fine with a median grain size of 0.11 mm. At all the sites, the
grain size showed little variation in the cross-shore direction.
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
31
3.2.2 Field data collection
At each site, the water surface elevation, two-dimensional horizontal current velocities, and
suspended sand concentration data were collected with the S-probe—an instrument station
developed at the Centre for Water Research, University of Western Australia. The same
instrument station was used in previous nearshore dynamics experiments in Western
Australia (Pattiaratchi et al., 1997; Masselink and Pattiaratchi, 1998). The S-probe
comprised a Paroscientific Digiquartz pressure sensor and a Neil Brown ACM2 acoustic
current meter together with three D & A Instrument Company optical backscatter turbidity
sensors (OBS-3 model). The pressure sensor was located 0.35 m above the seabed and the
bottom pressure records were converted into sea surface elevation by using the shallow
water approximation. The current meter recorded the two-dimensional horizontal velocity
at 0.20 m, and the OBS sensors recorded the sediment concentration at 0.050, 0.125, and
0.275 m from the seabed. However, only the data from the OBS at 0.05 m were used in
this paper.
The cross-shore current velocity was measured at only one vertical point (0.20 m), as it is
widely considered (Huntley and Hanes, 1987; Aagaard and Greenwood, 1995; Foote et al.,
1998) that the velocities under oscillatory flow in shallow water remain constant over the
depth, except within the narrow bottom boundary layer.
The sampling frequency used at Chilaw was 2 Hz; at Mullaloo and Broome it was 5 Hz. A
lower sampling frequency was selected to record data over an extended period. At
Mullaloo, the measurements were conducted just offshore of the breaker zone, where the
presence of wave groups could be observed clearly; at Chilaw, the instrument station was
moved back and forth around the breaker line, with measurements obtained inside and
outside the breaker zone. In Broome, where the tidal range is very high, the instrument
station location varied with respect to the breaker line following the tidal movement. All
measurements from Broome presented in this paper were conducted around high tide
(morning and early afternoon) before the onset of the sea breeze. In Broome, visual
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
32
observations of the bed forms near the instrument station were also carried out at half-
hourly intervals using a snorkel and mask.
The majority of measurements were conducted during calm wind conditions (usually in the
morning before the onset of the sea breeze) because the waves were swell-dominated,
which is ideal for pronounced wave groups.
Seabed profiles were surveyed using a total station, and sediment samples, collected from
the field sites, were used to determine the median grain size and calibrate the OBSs.
Calibration of OBSs was undertaken following the method explained in Ludwig and Hanes
(1990). Additional details of the field measurements can be found in Masselink and
Pattiaratchi (2000; 2001), Pattiaratchi et al. (1997; 1999).
3.2.3 Data analysis techniques
All the time series records comprising of surface elevation, cross-shore current velocity,
and suspended sediment concentration were subjected to power and co-spectral analysis
through digital Fourier transforms (Bendat and Piersol, 1986). Each data record was
divided into a series comprising of 8192 data points (~27 mins at 5 Hz), and then each set
was divided into 16 equal segments for the segment average method (Bendat and Piersol,
1986). The number of degrees of freedom used was 32. Shorter data sets were used,
especially for Broome, to avoid the influence of the tidal cycle. The 95% confidence
interval calculated for all the spectra presented in this paper indicated that the upper and
lower confidence limits were 1.75 and 0.65 times the spectral estimates, respectively.
Time series records of the wave groupiness envelope, cross-shore current velocity, and
suspended sediment concentration were compared to investigate the effect of wave
groupiness on sediment re-suspension. The groupiness envelope was computed by low
pass-filtering the modulus of the cross-shore current record at 0.02 Hz (List, 1991).
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
33
3.2.4 Ripple classification
Two ripple types were observed during the measurement period in Broome: ephemeral
post-vortex and permanent post-vortex ripples. At around 1040, after the breaker line
migrated past the instrument station during the rising tide, two-dimensional ephemeral
ripples were observed in a mean water depth of approximately 2.5 m. The ripple lengths
(λ) were 0.06–0.08 m, and the ripple heights (η) were a few millimetres. The ripples were
called ephemeral because they were not always present; they were washed away during the
larger waves of the wave groups and re-formed by the smaller waves. Two-dimensional
permanent post-vortex ripples, with ripple lengths similar to ephemeral ripples and ripple
heights of around 0.005 m, were observed between 1110 and 1310. Both ripple types were
called post-vortex because the ripple steepness (η⁄λ) was clearly less than 0.1 (Clifton and
Dingler, 1984).
3.3 Results
This chapter presents the results obtained though the field measurements conducted to
investigate sediment re-suspension and cross-shore flux in the frequency domain. Section
3.3.1 presents the relation between suspended sediment concentration and wave groups.
Analysis of cross-shore suspended sediment flux in the frequency domain is presented in
section 3.3.2.
3.3.1 Sediment re-suspension
Time series records of cross-shore current velocity (u) at 0.20 m and suspended sediment
concentration (c) at 0.05 m from the bed obtained from Mullaloo Beach showed a strong
correlation between the passing of wave groups and pronounced suspension events (Fig.
3.3). The measurements were conducted during a summer morning with calm, swell-
dominated sea conditions. The instrument station was placed just outside the breaker zone,
where the seabed was flat, corresponding to sheet flow conditions as a result of high bed
shear stress exerted by the flow field. Flat bed conditions observed in nearshore regions
often correspond to sheet flow.
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
34
−4
−2
0
2
4
u (m
/s)
(a)
8:20 8:30 8:40 8:500
10
20
30
Time (hrs)
c (g
/l)
(b)
Figure 3.3: Time series of: a) cross-shore current velocity u (z = 0.25 m; solid line) and
envelope function of u (thick dashed lines); and b) suspended sediment concentration c (z =
0.05m; solid line) and lowpass-filtered c (thick dashed line) (just outside the breaker line,
over a flat bed—Mullaloo Beach, Western Australia).
Similar time series records obtained around high tide in swell-dominated conditions in
Broome showed the same pattern: higher suspension events occurred as wave groups
passed (Fig. 3.4). The instrument station was ~110 m offshore of the moving breaker line;
the seabed was covered with two-dimensional permanent post-vortex ripples with ripple
heights of approximately 0.005 m and spacing of 0.06–0.08 m.
This trend of higher suspension events coinciding with passing wave groups was observed
at all sites (not shown) whenever pronounced wave groups were present, either in the
presence or absence of ripples.
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
35
−1
−0.5
0
0.5
1
u (m
/s)
(a)
11:30 11:45 12:00 12:150
0.5
1
1.5
Time (hrs)
c (g
/l)
(b)
Figure 3.4: Time series of: a) cross-shore current velocity u (z = 0.25 m; solid line) and
envelope function of u (thick dashed lines); and b) suspended sediment concentration c (z =
0.05 m; solid line) and lowpass-filtered c (thick dashed line) (shoaling waves over 2-D
permanent post-vortex ripples—Cable Beach, Broome, Western Australia).
3.3.2 Cross-shore sediment flux
Shoaling, non-breaking waves over a flat bed
Spectral analyses were undertaken to quantify the cross-shore sediment flux due to different
frequency components. The results obtained for the cross-shore current velocity (u) and
suspended sediment concentration (c) data records presented in Fig. 3.3 are shown in Fig.
3.5 (Mullaloo Beach). The instrument station was placed just outside the breaker zone,
where the seabed was flat. The mean water depth (h) was 1.14 m, with the significant wave
height (Hs) of 0.97 m leading to a very high Hs/h of 0.85.
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
36
0
5
10
15
20
25
u sp
ectr
um (
m2 /s
)
(a)
0
20
40
60
80
c sp
ectr
um (
g2 /l2 )
(b)
−0.06
−0.03
0
0.03
0.06
Co−
spec
trum
u−
c onshore
offshore
(c)
−180
−90
0
90
180
Pha
se
(d)
0 0.05 0.1 0.15 0.20
0.05
0.1
Frequency (Hz)
Cro
ss−
spec
trum
(e)
0 0.05 0.1 0.15 0.20
0.2
0.4
0.6
Frequency (Hz)
Coh
eren
ce
(f)
Figure 3.5: Results of spectral analysis between u and c: (a) auto-spectrum of u; (b) auto-
spectrum of c; (c) c-u co-spectrum in (gl-1)(ms-1)Hz-1; (d) c-u phase spectrum; (e) c-u cross
spectrum; (f) c-u coherence spectrum (just outside the breaker line, over a flat bed—
Mullaloo Beach, Western Australia).
The auto-spectra of the cross-shore current (u) and suspended sediment concentration (c)
(Figs 3.5a–b) were used to identify the dominant frequencies. The dominant peak for u was
approximately 0.075 Hz, which is corresponding to swell (~13 s). A secondary peak of
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
37
approximately 0.15 Hz (~7 s) was due to the first harmonic of the swell waves; a minor
peak was observed at a very low frequency of around 0.01 Hz (Fig. 3.5a). The c spectrum,
however, showed a low secondary peak at the swell frequency (~0.075 Hz) and a distinct
dominant peak at a very low frequency of 0.01 Hz (100 s) (Fig. 3.5b), which is
corresponding to wave groups, indicating more sediment was stirred at low frequencies
(wave groups).
The co-spectrum between the time series of u and c (suspended sediment flux in the
frequency domain) (Fig. 3.5c) demonstrated the original finding for shoaling waves outside
the breaker zone (Huntley and Hanes, 1987): the cross-shore sediment flux was onshore at
high frequencies (swell waves) and offshore at low frequencies (wave groups). A minor
onshore component was observed at the first harmonic of the swell waves. The same
pattern was observed in most of the measurements when the instrument station was
positioned just outside the breaker line under shoaling waves over a flat bed.
The phase lag between u and c (Fig. 3.5d) was a direct indicator of the direction of cross-
shore sediment flux. Flux is onshore if the phase lag is between ± 900 and offshore if the
phase lag is outside ± 900. At the swell and the first harmonic of the swell frequency band
the phase lag was less than 900, leading to onshore flux, whereas at low frequencies the
phase lag was greater than 900, resulting in offshore flux. The 95% confidence interval in
the phase spectrum at the major frequency components (Fig. 5.5d) was calculated using the
coherence estimates (Jenkins and Watts, 1968) to determine the statistical significance of
the major co-spectral peaks (Davidson et al., 1993; Aagaard and Greenwood, 1995). The
results showed the magnitude and direction of the co-spectral peaks at all three major
frequency components were statistically significant (Fig. 3.5d).
The cross-spectrum between u and c illustrated the gross sediment flux rates in the
frequency domain (Fig. 3.5e); strong coherence between u and c was observed at swell and
low frequencies as well as the first harmonic of the swell waves (Fig. 3.5f). Strong first
harmonic components have been observed under highly asymmetric, shallow water waves
(Thornton et al., 1976; Osborne and Greenwood, 1992b).
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
38
(a) Hs/h = 0.27
Flat bed
(b) Hs/h = 0.18
Flat bed
(c) Hs/h = 0.14 changing to ephemeral
ripples (d)
Hs/h = 0.14 changing to 2-D
post-vortex ripples
h = 1.15m
h = 1.93m
h = 2.50m
h = 2.76m
Bre
aker
line
a) Flood tide
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
39
(e) Hs/h = 0.13 2-D post-
vortex ripples + subdued cross-
ripples
h = 2.72m
h = 1.43m
h = 2.37m
h = 1.80m
h = 0.65m
(f) Hs/h = 0.13 2-D post-
vortex ripples + subdued cross-
ripples
(g) Hs/h = 0.16 2-D post-
vortex ripples + subdued cross-
ripples
(h) Hs/h = 0.20
2-D post-vortex ripples getting
Bre
aker
line
(i) Hs/h = 0.26
Flat bed
eroded
b) Ebb tide
Figure 3.6: Schematic diagram of beach face and the positioning of the instrument station
with respect to the varying water level due to the tidal cycle—Cable Beach, Broome,
Western Australia (Instrument station was maintained at one place while the water level
changed due to tide).
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
40
Temporal variability: tidal cycle
At Cable Beach (Broome), data collection began during the flood tide (at approximately
0940) with the instrument station positioned inside the surf zone, and was completed before
the onset of the sea breeze (at approximately 1400) when the instrument station was again
inside the surf zone during the ebb tide. The breaker line migrated past the instrument
station during the flood tide (at around 1005) and back again during the ebb tide (at around
1330). The spectral analysis was conducted for nine time series records of 8192 data
points, covering different flow and bed conditions. The positioning of the instrument
station with respect to the breaker line for each data set is presented in Fig. 3.6, which
includes details of the prevailing conditions for the flood (Fig. 3.6a) and ebb (Fig. 3.6b)
tide. Hs/h values at this site (Broome) were significantly smaller than the other locations
reported in this chapter because the conditions in Broome were clearly dissipative while at
other locations it was reflective.
Spectral analysis results for data sets when the instrument station was just outside the
breaker line (h = 1.93 m), farther outside the breaker line (~110 m, h = 2.72 m), and back
inside the surf zone (h = 0.65 m) are presented in Figs 3.7a, b, and c, respectively. Cross-
shore current velocity (u) peaked at the swell wave frequency throughout the measurement
period, with minor peaks at low frequencies and the first harmonic of the swell waves (Figs
3.7a1, b1, and c1). When the instrument station was farther offshore of the moving
shoreline, however, the low frequency component disappeared (Fig. 3.7b1). The suspended
sediment concentration (c) was dominant at low frequencies (Figs 3.7a1, b1, and c1),
suggesting wave groups suspended more sediments than swell waves.
The suspended sediment flux due to swell waves was onshore just outside the surf zone
(Fig. 3.7a2), offshore when the instrument station was farther offshore of the breaker line
(Fig. 3.7b2), and onshore again inside the surf zone (Fig. 3.7c2). At low frequencies, the
sediment flux was offshore outside the surf zone (stronger closer to the breaker line) and
onshore inside the surf zone. The cross-shore sediment flux values were greater during the
ebb tide, especially when the instrument station was inside the surf zone. Note the scales
are different in the y-axis. Masselink and Pattiaratchi (2000), with the same data set,
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
41
showed the suspended sediment concentration was greater during the ebb tide than flood;
Davidson et al. (1993) also observed this in their study. The statistical significance tests
based on the 95% confidence interval in the phase spectrum (Davidson et al., 1993) were
conducted for each data set, as shown in Fig. 3.5d; the tests revealed that spectral peaks
observed at both low and swell frequencies were statistically significant (not shown).
0
2
4
6
8
(a1)
0
0.5
1
1.5
2
−2
−1
0
1
onshore
offshore
(a2)
x10−3
0
2
4
6
(b1)
u sp
ectr
um (
m2 /s
)
c sp
ectr
um (
g2 .s/l2 )
0
0.25
0.5
0.75
−10
−5
0
5
onshore
offshore
(b2)
x10−4
co−
spec
trum
u−
c
0 0.05 0.1 0.15 0.20
4
8
(c1)
0
6
12
Frequency (Hz)0 0.05 0.1 0.15 0.2
−5
0
5
10
onshore
offshore
(c2)
x10−3
Frequency (Hz)
Figure 3.7: Auto spectra of u (solid line); c (dashed line); and co-spectrum between u and c
for time series records starting at: (a) 10:15 h (just outside the surf zone during flood tide,
over a flat bed—hm = 1.93 m); (b) 11:45 h (~ 110 m offshore of breaker line, over
permanent post-vortex ripples—hm = 2.72 m); (c) 13:30 h (inside the surf zone during ebb
tide, over a flat bed—hm = 0.65 m)—Cable Beach, Broome, Western Australia.
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
42
0
1
2
3
h mea
n (m
)
(a)
surf
zon
e
surf
zon
e
shoa
ling
wav
es
−1
−0.5
0
0.5
1
norm
. sed
i. flu
x
(b)onshore
offshoreflat bedephe. post−vort. ripplesperm. post−vort. ripples
9:00 10:00 11:00 12:00 13:00 14:000
0.25
0.5
0.75
1
<u3 >
/(<
u2 >(3
/2) )
Hsi
g/h
(c)
0.1
0.2
0.3
Time (hrs)
Figure 3.8: Variation of: (a) mean water depth; (b) normalised net cross-shore suspended
sediment flux due to swell waves; (c) normalized velocity skewness (+) and ratio of
significant wave height to water depth (*) with time—Cable Beach, Broome, Western
Australia.
The net cross-shore suspended sediment flux at the swell frequency band (0.04 Hz <
frequency < 0.1 Hz) was estimated and normalised by the total (absolute) cross-shore flux
within the same frequency range. These values were obtained from the area under the co-
spectrum; the frequency range was chosen using the spectral valleys observed in the
corresponding u spectrum. The variation of normalised net cross-shore sediment flux with
the mean water depth (tide level) (Fig. 3.8a) is presented in Fig. 3.8b. Net sediment flux
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
43
due to swell waves was onshore inside and just outside the surf zone and offshore farther
outside the surf zone. Moreover, when the seabed was flat, the sediment flux was observed
onshore, whereas it reversed to offshore over rippled beds. The net sediment flux was
onshore over a rippled bed only for the data set starting at 1245. At this point, however, the
co-spectrum between u and c was bi-directional; the ripples began to wash away with the
lowering tide. It should be noted that other surrounding conditions also changed during this
time. The ratio of significant wave height to mean water depth (Hs/h) was greater close to
the breaker line; net sediment flux due to swell waves was onshore under greater Hs/h and
offshore under lower Hs/h (Fig. 3.8c).
The normalised velocity skewness (‹u3›⁄‹u2›3⁄2) for the swell frequency band (frequency >
0.04 Hz) was calculated for each data set, as Russell and Huntley (1999) explained, and
plotted with the varying tide level in Fig. 3.8c (velocity skewness is considered positive in
the onshore direction and negative in the offshore direction). The suspended sediment flux
at the swell frequency band was onshore when the normalised velocity skewness was high
and offshore when the skewness was low, but still positive (Figs 3.8b–c).
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
44
−1
−0.5
0
0.5
1uc
−no
rmlo
w
onshore
offshore
(a)
surf
zon
e
surf
zon
e
shoa
ling
wav
es
9:00 10:00 11:00 12:00 13:00 14:000.3
0.35
0.4
0.45
0.5
time (hrs)
GF
U
(b)
Figure 3.9: Variation of: (a) normalised net suspended sediment flux due to low frequency
waves; (b) wave groupiness factor (based on cross-shore current velocity) with time—
Cable Beach, Broome, Western Australia.
The normalised net cross-shore sediment flux calculated for the low frequency band (< 0.03
Hz) was offshore outside the surf zone and onshore inside the surf zone (Fig. 3.9a).
Aagaard and Greenwood (1995) obtained similar results. The wave groupiness factor for
cross-shore current velocity was computed as explained by (List, 1991); it was greater
when the instrument station was farther outside the breaker zone and relatively less inside
the surf zone, as the group structure was destroyed during wave breaking (Osborne and
Greenwood, 1992b).
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
45
Spatial variability: inside and outside the surf zone
The data obtained from a series of field measurements undertaken at Ambakandawila
Beach (Chilaw) (Fig. 3.1c) were analyzed to investigate the variation in cross-shore
sediment flux in the frequency domain. The measurements at this location were obtained
around the breaker line, where the waves broke almost on the beach face with a very
narrow surf zone. The breaking waves were observed to be surging/plunging, which was
proven by the calculations of Iribarren number. The seabed remained flat throughout.
Spectral analysis results were obtained for two data sets (just under and 2m inside the
breaker line), which produced fairly different outcomes (Figs 3.10a–b). The cross-shore
current velocity (u) spectrum showed a dominant peak at the swell frequency band, with
almost no low frequency oscillations in either data set (Figs 3.10a1–b1); however, the wave
energy reduced during the wave breaking (Figs 3.10a1–b1). The suspended sediment
concentration (c) showed dominant peaks at low frequencies for both data sets. At the
swell frequency band, a considerable peak was observed under the breaking waves (Fig.
3.10a2), whereas no distinct peak could be observed inside the breaker line (Fig. 3.10b2).
Further, the suspended sediment concentration (c spectrum) reduced significantly during
the wave breaking (Figs 3.10a2–b2). The cross-shore suspended sediment flux under the
breaking waves showed a strong onshore component at the swell frequency band and a
weaker offshore component at low frequencies (Fig. 3.10a3), in agreement with Huntley
and Hanes’ (1987) original observations, whereas, just after the breaker line, the magnitude
of sediment flux reduced markedly, showing a smaller bi-directional component at the
swell frequency band and a negligible offshore component at low frequencies (Fig. 3.10b3).
The net suspended sediment flux at the swell frequency band, however, was offshore.
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
46
0
5
10
15
20
u sp
ectr
um (
m2 /s
)
(a1)
0
5
10
15
20
25
c sp
ectr
um (
g2 .s/l2 ) (a2)
0 0.05 0.1 0.15 0.2−1
0
1
2
3
4
Frequency (Hz)
co−
spec
tral
den
sity
x10−2
(a3)
onshore
offshore
(b1)
(b2)
0 0.05 0.1 0.15 0.2Frequency (Hz)
(b3)
onshore
offshore
Figure 3.10: Results of spectral analysis between u and c at: (a) just under the
surging/plunging breaker line; (b) 2 m shoreward of the breaker line; 1. u spectrum, 2. c
spectrum, 3. c-u co-spectrum—Ambakandawila Beach, Chilaw, Sri Lanka.
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
47
Variation with the Dean number (Dean, 1973)
The variation of normalised cross-shore suspended sediment flux due to swell waves with
the Dean number (Dean and Dalrymple, 2002) is presented in Fig. 3.11. The Dean number
(D) is given by
ps
s
TwHD β
= (3.1)
where Hs is the significant wave height, ws is the particle settling velocity, Tp is the peak
period obtained from the spectrum of cross-shore current velocity, and β is a constant (≈
0.3). Dean and Dalrymple (2002) showed that the suspended sediment transport is onshore
when
β21
<D (3.2)
This suggests the sediment flux should be onshore when D < 1.67 and offshore when D >
1.67. The results obtained from the present study, where sediment flux was mainly onshore
when D < 1.67 and offshore when D > 1.67 (Fig. 3.11), were in good agreement with this.
A few points were not in agreement; however, at those points, the normalised sediment flux
was close to zero, where the sediment flux component at the swell band was bi-directional
(e.g. Fig. 3.9b3).
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
48
0.5 1 1.5 2
−1
−0.5
0
0.5
1
βHs/(w
sT
p)
norm
alis
ed s
edim
ent f
lux
1.67
onshore
offshore
BroomeChilawMullaloo
Figure 3.11: Variation of normalized net cross-shore suspended sediment flux with the
Dean number (βHs/(ws.Tp)).
3.4 Discussion
A series of field measurements, covering different hydrodynamic and morphological
conditions, was conducted to investigate the factors influencing the magnitude and
direction of cross-shore suspended sediment flux, close to the seabed (0.05 m), in nearshore
environments.
The results from all the measurement sites indicated a significant relationship between
wave groups and the suspended sediment concentration. This affirms the well-established
assumption that wave groups are more capable than individual swell waves of stirring
sediments and retaining them in suspension (Hanes and Huntley, 1986; Vincent et al.,
1991; Osborne and Greenwood, 1993). This phenomenon was observed in the presence
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
49
and absence of ripples during this study. This suggests that even though the presence of
ripples can cause higher suspension events (Nielsen, 1984; Vincent et al., 1991; Villard and
Osborne, 2002), hydrodynamics within the wave groups alone caused increased suspension
events (Davidson et al., 1993; Hay and Bowen, 1994). Vincent et al. (1991), Osborne and
Greenwood (1993), and Villard and Osborne (2002) are among the researchers who
proposed explanations for this phenomenon.
The direction and magnitude of cross-shore sediment flux in the frequency domain
appeared to vary significantly at different locations under various conditions. Following
are descriptions of the identified features.
3.4.1 Cross-shore location
For most of the measurements obtained just outside the surf zone over a flat bed, the
suspended sediment flux was onshore at swell wave frequencies (swell, wind waves) and
offshore at lower frequencies (corresponding to wave groups), which was in agreement
with the Huntley and Hanes’ (1987) widely accepted finding. Increased velocity skewness
towards the wave propagation direction as waves shoal might have forced the suspended
sediment onshore (Doering and Bowen, 1988; Osborne and Greenwood, 1992b). Further, it
has been found that under near-breaking and breaking waves, large fluid accelerations,
skewed towards shore, suspend more sediments (Hanes and Huntley, 1986; Nielsen, 1992;
Osborne and Greenwood, 1993; Hay and Bowen, 1994), which coincides with the onshore
phase of the cross-shore velocity, causing onshore sediment flux (Elgar et al., 1988; 2001).
Moreover, the large waves in groups suspend more sediment, which in turn coincides with
the trough of the group bound long wave (Longuet-Higgins and Stewart, 1964) moving
sediment offshore at low frequencies (Larsen, 1982; Shi and Larsen, 1984).
Inside the surf zone, similar to shoaling waves just outside, the sediment flux at the swell
band was usually towards shore, although the low frequency component varied (Aagaard
and Greenwood, 1995). This might have been due to the fact that wave groups were
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
50
destroyed and then the group bound long wave was released during the wave breaking
(Osborne and Greenwood, 1992b).
In some cases (e.g. Chilaw—Fig 3.10), however, the magnitude of the suspended sediment
flux just inside the breaker line reduced significantly (by order of magnitude) relative to the
flux just under the breaking waves. The breaker type was surging/plunging. In contrast, in
Broome the sediment flux increased inside the breaker zone, where spilling breakers were
evident. The strong sediment flux just under the breaker line (Fig. 3.10a3) might have been
due to turbulence vortices generated by wave breakers; those vortices might not have
reached 2 m inside the plunge point. The increased uniformity in suspended sediment
concentration after the wave breaking, as the wave structure was destroyed because of
surging/plunging, might have caused the bi-directionality in the co-spectrum (Osborne and
Greenwood, 1992b).
In Broome, where the large tidal range caused the instrument station position to move
markedly with respect to the moving breaker line, the direction and magnitude of cross-
shore suspended sediment flux varied significantly. When the instrument station was inside
and just outside the surf zone, with a flat bed, the suspended sediment flux due to swell
waves was onshore, as was observed throughout the study. Conversely, when the
instrument station was farther offshore, the suspended sediment flux was predominantly
offshore (Fig. 3.8b). However, other factors, such as bed forms, velocity skewness, etc.,
which also changed along with the location with respect to the moving breaker line, could
well have influenced the suspended sediment flux.
3.4.2 Bed ripples
In Broome, with the varying tide level, the seabed configuration also changed significantly.
The seabed was flat when the instrument station was inside and just outside the surf zone
during the rising tide. Ephemeral post-vortex and permanent post-vortex ripples were
present while the instrument station was farther offshore of the breaker line (around high
tide). The seabed was flat again when the instrument station was back in the surf zone
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
51
during the ebb tide (Fig. 3.8b). The suspended sediment flux due to swell waves followed
this pattern; it was onshore when the seabed was flat and predominantly offshore when the
bed was rippled (Fig. 3.8b).
Inman and Bowen (1963) first proposed an explanation for sediment moving against the
direction of wave propagation over a rippled bed: when a skewed wave propagates over
vortex ripples, during the relatively strong onshore phase, a vortex is formed on the leeside
of the ripple and remains trapped until the flow reverses; during the weaker offshore phase,
the vortex shoots up into the water column, carrying a cloud of sediment. Simultaneously,
the offshore phase moves this sediment cloud back. This breakdown was explained for
vortex ripples, whereas the ripples observed during this study were clearly post-vortex
(steepness less than 0.1) (Clifton and Dingler, 1984).
The offshore sediment flux due to swell waves over less steep post-vortex ripples, however,
has been observed in the past (Osborne and Greenwood, 1992b; Brander and Greenwood,
1993). Davidson et al. (1993) also observed offshore flux at the swell band over ripples,
but the ripple geometry was not measured, so it was uncertain whether the ripples were
vortex or post-vortex.
No clear difference in the direction of suspended sediment flux due to swell waves could be
identified between ephemeral post-vortex and permanent post-vortex ripples, as the
sediment flux was predominantly offshore over both types.
3.4.3 Velocity skewness (‹u3›⁄‹u2›3⁄2)
The normalised velocity skewness due to swell waves varied with the measurement
location in the cross-shore direction under the varying tide (Fig. 3.8c). The normalised net
sediment flux was onshore when the velocity skewness was high, whereas offshore flux
was observed under lower skewness values, even though the skewness had been positive
throughout. Russell and Huntley (1999) predicted onshore transport associated with swell
wave skewness under high energy conditions both inside and outside the surf zone where
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
52
the seabed was flat. Increased velocity skewness in the wave propagation direction as
waves shoal could force the suspended sediment onshore (Doering and Bowen, 1988;
Osborne and Greenwood, 1992b). Russell and Huntley (1999) further suggested that under
low energy conditions (e.g. in the presence of ripples), the velocity skewness might not
predict the direction of cross-shore sediment transport. The results of the present study
were in agreement with this, as offshore sediment flux was observed under low energy
conditions in the presence of ripples when the velocity skewness was still positive (Figs
3.8b–c).
3.4.4 Dean number (D)
The variation in the direction of cross-shore suspended sediment flux due to swell waves
with the Dean number was in good agreement with Dean and Dalrymple’s (2002)
explanation: it was onshore when D < 1.67 and offshore when D > 1.67 (Fig. 3.11). This is
interesting, given that Dean and Dalrymple’s explanation did not account for parameters,
such as ripples or velocity skewness; it was based on whether the sediment particles,
suspended by each wave, would settle before or after the flow reversal and hence transport
onshore or offshore.
Further investigations of the changes in the above-discussed parameters would enable a
better understanding of cross-shore suspended sediment transport in nearshore
environments. A detailed study of the direction and magnitude of the cross-shore
suspended sediment flux over different ripple types would be particularly interesting. A
numerical model that accommodates all these factors could be an excellent tool to
investigate the influence of these factors independently.
3.5 Concluding remarks
A series of field measurements of hydrodynamics and sediment suspension together with
bed topography was collected at several nearshore locations to investigate the factors
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
53
influencing cross-shore suspended sediment flux close to the bed. The following features
were identified:
a) A significant correlation between wave groups and suspended sediment
concentration was observed at all the measurement sites, confirming the well-
established assumption that wave groups are more capable than incident swell
waves of equal amplitude of suspending sediments. This was observed both in the
presence and absence of ripples.
b) The direction and magnitude of suspended sediment flux varied significantly
depending on the measurement location with respect to the breaker line; however,
other parameters, such as bed ripples, velocity skewness, etc., could influence this.
c) At low frequencies, the suspended sediment flux was mainly offshore outside the
surf zone (due to the combined action of wave groups and the group bound long
wave), while it varied considerably inside the surf zone. Wave groupiness factor
was greater farther offshore of the surf zone and was relatively low inside the surf
zone.
d) The direction and magnitude of the suspended sediment flux inside the breaker line
changed with the breaker type.
e) Offshore suspended sediment flux due to swell waves was observed over low
steepness post-vortex ripples.
f) At the swell frequency band, onshore sediment flux was observed when the
normalised velocity skewness was high; offshore flux was observed when the
skewness was lower but still positive, suggesting the influence of other parameters,
such as ripples, grain size, etc. (Russell and Huntley, 1999).
g) Suspended sediment flux due to swell waves was predominantly onshore when the
Dean number was less than 1.67 and offshore when the Dean number was greater
than 1.67. Interestingly, this was in agreement with the simple hypothesis by Dean
and Dalrymple (2002) even though it did not account for the influence of bed
ripples or wave asymmetry.
Chapter 3: Factors influencing cross-shore suspended sediment flux in the frequency domain
54
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
55
Chapter 4 A numerical study of cross-shore
suspended sediment flux in the frequency
domain
It was noticed that the cross-shore suspended sediment flux in the frequency domain can be
influenced by many different factors (chapter 3). With field measurements, however, it is
difficult to investigate those factors independently as they are not mutually independent.
This chapter presents the results of a numerical study conducted to examine the separate
influence of some of the factors influencing cross-shore suspended sediment flux over a flat
bed.
4.1 Introduction
Predicting sediment transport in nearshore regions is one of the most complex challenges
faced by coastal researchers in designing coastal structures or beach nourishment schemes.
Even though longshore transport is the dominant sediment transport mode in nearshore
regions, cross-shore transport can be a contributing factor in determining seasonal shoreline
evolution and beach morphology (Masselink and Pattiaratchi, 1998). Cross-shore sediment
transport results from a range of many different frequency components such as swell, wind
waves, wave groups, and low frequency oscillations (group bound long wave, leaky waves,
edge waves, etc.).
Many researchers have investigated the cross-shore suspended sediment flux in the
frequency domain with the help of field measurements. Huntley and Hanes (1987) first
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
56
found that for shoaling, non-breaking, waves over a flat bed, the suspended sediment flux
was onshore due to incident waves and offshore due to low frequency waves. This pattern,
however, changed significantly under different conditions at different locations (Osborne
and Greenwood, 1992b; Brander and Greenwood, 1993; Davidson et al., 1993; Aagaard
and Greenwood, 1995). This variation in the direction and magnitude of cross-shore
suspended sediment flux in the frequency domain at different locations was attributed to
many different parameters: cross-shore location with respect to the breaker line (Osborne
and Greenwood, 1992a, b; Aagaard and Greenwood, 1995; Russell and Huntley, 1999);
varying tide level (Davidson et al., 1993; chapter 3); bed forms (Osborne and Greenwood,
1992b; Brander and Greenwood, 1993; Davidson et al., 1993; chapter 3); wave/velocity
skewness (Russell and Huntley, 1999; chapter 3); grain size (Deigaard, 1999).
From field studies, however, it is not possible to investigate these parameters separately as
they are not mutually exclusive. This study attempts to model the suspended sediment flux
due to shoaling waves in nearshore regions numerically to explore some of the governing
parameters in detail. The objective is to investigate the influence of these factors
independently and hence estimate the relative importance of those parameters. Note that
only oscillatory flow components were investigated; mean flow components were not
considered and this study focused only on suspended sediment transport close the seabed (~
0.05 m).
In the present study, only flat bed conditions were explored in detail. Detailed modelling
of rippled beds, which should take into account the flow structure generated due to the
presence of ripples (vortex formation) such as those undertaken by (Davies and Villaret,
1999; Zedler and Street, 2001; Barr et al., 2004; Davies and Thorne, 2005; Eidsvik, 2006),
however, is beyond the scope of this study.
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
57
4.2 Numerical model
The numerical model included a modified version of FUNWAVE 1D (an open source
distribution from the Centre for Applied Coastal Research, University of Delaware,
described in Kennedy et al. (2000)) to simulate wave shoaling and a simple wave boundary
layer model to predict the instantaneous bed shear stress. The bed shear stress is
subsequently used to calculate the vertical distribution of suspended sediment concentration
by solving turbulent diffusion equation (Deigaard et al., 1999).
4.2.1 Wave model
Wave shoaling was simulated using a modified version of FUNWAVE 1D (Kennedy et al.,
2000), which was developed based on the fully non-linear time domain Boussinesq model
of Wei et al. (1995). The Wei et al. (1995) model included additional dispersive terms to
accommodate intermediate water depths and was able to simulate wave propagation with
strong non-linearity. Initially the beach profile, based on the field observations, was
specified. A directional spectra or a time series record of surface elevation, at an offshore
location, was used as the input signal to the model using a source function method (Wei et
al., 1999). Sponge layers were located at both seaward and landward boundaries to absorb
reflected waves. The run-up at the shoreline was modelled using a slot technique, which
assumed the bed as semi-permeable. Wave breaking was introduced with an artificial eddy
viscosity term and the bottom friction was specified using the quadratic law. FUNWAVE
has been extensively tested and validated (Kennedy et al., 2000; Chen et al., 2002; Johnson
and Pattiaratchi, 2006)
The model output included the time series records of surface elevation and cross-shore
(horizontal) velocity at defined locations in the model domain (i.e. cross-shore). Several
gages (locations) were introduced at desired cross-shore locations to obtain output data.
The output cross-shore current velocity time series was at a reference elevation of zα (α = -
0.531h) where h is still water depth. The vertical coordinate, z, is measured from the still
water level. The bottom orbital velocity (ub) was assumed to be equivalent to the output of
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
58
FUNWAVE (uα) and was used to drive the wave boundary layer model. The cross-shore
current velocity in shallow water was assumed uniform over the water depth except inside
the narrow bottom boundary layer (Huntley and Hanes, 1987; Foote et al., 1998). Wave
boundary layer model estimated the time series of bed shear stress.
4.2.2 Wave Boundary Layer model
The near bed flow field was modeled using wave boundary layer equations. For two-
dimensional horizontal flow in xz-plane (x – horizontal axis in the cross-shore direction, z –
vertical axis), the linearised boundary layer equation is
zxp
tu
∂∂
+∂∂
−=∂∂ τρ (4.1)
where ρ is the density of water, u is the velocity in x-direction, p is the pressure, τ is the
shear stress, and t is time.
Shear stress was modeled based on turbulent eddy viscosity as
zu
t ∂∂
= ρυτ (4.2)
where υt is the turbulent eddy viscosity and was described by
zut *κυ = (4.3)
where u* is the shear velocity, κ is the von Karman’s constant (~ 0.4)
)/ln(),()(*
nkztzutu κ= (4.4)
where kn is the equivalent Nikuradse bottom roughness (= 30z0). Assuming logarithmic
vertical velocity distribution where u = 0 when z = z0. Over flat, moving bed conditions, kn
is assumed equal to 2.5d50 (Nielsen, 1992).
The boundary layer equations were solved numerically using a finite difference scheme in
space and time to obtain the instantaneous bottom shear stress (τb(t)), 2
* )()( tutb ρτ = (4.5)
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
59
4.2.3 Sediment suspension model
Only the suspended sediment flux was investigated in this study; the vertical distribution of
suspended sediment concentration (c) was calculated by solving a simple turbulent
diffusion equation
zcw
zc
ztc
ss ∂∂
+⎟⎠⎞
⎜⎝⎛
∂∂
∂∂
=∂∂ ε (4.6)
where εs is the sediment diffusion coefficient and ws is the settling velocity of the sediment.
Advection terms and horizontal turbulent diffusion terms were neglected. Lee and Hanes
(1996) found diffusion based models performed well over flat beds under high wave
conditions. Sediment diffusion coefficient (εs) was assumed to be equal to the turbulent
eddy viscosity (υt) (eq. 3) (Fredsoe and Deigaard, 1992; Rakha et al., 1997; Rakha, 1998;
Deigaard et al., 1999).
The bottom boundary condition was given at the level z = 2d50, where d50 is the median
grain diameter. Reference sediment concentration at the bottom boundary (cb) was
calculated as a function of the instantaneous Shields parameter (θ) using an empirical
formulation proposed by Zyserman and Fredsoe (1994),
( )( ) 75.1
75.1
331.01
331.0
cm
cb
C
cθθ
θθ
−+
−= (4.7)
where Shields parameter (θ) was defined as:
( ) 501 gdsb
−=
τθ (4.8)
θc is the critical Shields parameter, s is the specific gravity of sediment (~ 2.65), and g is
the gravitational acceleration (~ 9.81 m/s2). The maximum concentration, Cm is was used
as 0.32 (Zyserman and Fredsoe, 1994).
At the top boundary (z = h), the vertical flux of sediment was assumed to be zero:
cwzc
ss −=∂∂ε (4.9)
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
60
Rakha et al. (1997), Rakha (1998), and Deigaard et al. (1999) used this method to model
suspended sediment concentrations under oscillatory flow.
4.3 Field measurements
Field measurements to drive and to test the model were collected at Leighton Beach, and
City Beach, Perth, Western Australia. Field measurements included time series records of
the incoming wave signal at an offshore location to drive the model and cross-shore current
velocity (u) at 0.2 m from the seabed and suspended sediment concentration (c) at 0.05 m
from the seabed to compare with the model results at desired locations. An InterOcean
S4DW current meter equipped with a pressure sensor was used to obtain the incoming
offshore wave signal. The cross-shore current velocity and suspended sediment
concentration were measured with the ‘S’ probe―an instrument station developed at the
University of Western Australia. The ‘S’ probe consisted a Neil Brown ACM2 acoustic
current meter to measure the cross-shore current velocity and a D & A Instrument
Company optical backscatter (OBS–3 model) turbidity sensor to measure the suspended
sediment concentration. A schematic diagram of instrument positioning is presented in Fig.
4.1.
Both Leighton and City Beach had similar characteristics. Beach slope was around 1:20
and the median grain size (d50) was 0.28 mm and 0.2 mm respectively. South-western
Australia, where both beaches are located, experiences diurnal, micro-tidal conditions, with
a maximum tidal range of 0.6 m. At Leighton beach the S4 probe was deployed around
100 m from the shoreline in a water depth of 3.2 m. The S probe was deployed at a mean
water depth of 1.15 m where the significant wave height (Hs) was 0.8 m. At City Beach,
the S4 probe was deployed around 100 m from the shoreline where the mean water depth
was 3 m and the S probe was deployed at a mean water depth of 1 m with significant wave
height of 0.45 m.
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
61
S4DW
S probe
MWL
Figure 4.1: Instrument positioning along the beach slope
4.4 Model tests
The model was tested for different conditions by comparing output with field data obtained
at Leighton Beach, and City Beach, Perth, Western Australia.
4.4.1 Model domain
The model domain for all the model tests consisted of a constant slope as shown in Fig. 4.2
and the slopes closely represented the field sites. The grid spacing in the cross-shore
direction (Δx) and the time step (Δt) for the wave model (FUNWAVE) were 0.5 m and 0.2
s, respectively (the model time step was always tested based on CFL criterion for numerical
stability). The model was forced with the incoming wave signal at an offshore location and
the gages introduced at desired locations (e.g. gage 1—Fig. 4.2) provided output time series
of surface elevation and cross-shore current velocity (uα). The boundary layer model was
used to calculate the bed shear stress (τb) and the sediment suspension model was used to
calculate the suspended sediment concentration (c) as explained in sections 4.2.2 and 4.2.3.
The vertical length scale or resolution (Δz) was 0.00125 m for the boundary layer model
and 0.0125 m for the sediment suspension model. The time step (Δt) for both models was
0.2 s.
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
62
0 50 100 150 200 250−4
−3
−2
−1
0
1
2
x (m)
z (m
)
MWL
wav
e si
gnal
gage
1
slot re
gion
Figure 4.2. Wave model layout.
Co-spectral analysis
The co-spectrum between cross-shore current velocity (u) and suspended sediment
concentration (c) close to the seabed was determined to obtain the variation in cross-shore
suspended sediment flux in the frequency domain (Huntley and Hanes, 1987). Spectral
analysis was conducted through digital Fourier transforms (Bendat and Piersol, 1986) with
data records comprising 8192 data points (~27 mins at 5 Hz). Each data set was divided
into 16 equal segments for the segment average method (Bendat and Piersol, 1986). The
number of degrees of freedom used was 32. The 95% confidence interval calculated for all
the spectra presented in this paper indicated that the upper and lower confidence limits
were 1.75 and 0.65 times the spectral estimates, respectively.
4.4.2 Shoaling waves over a flat bed
The model was driven by a time series record of incoming wave signal measured at
approximately 100 m from the shore at Leighton Beach, Perth, Western Australia. The
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
63
layout of the model domain was presented in Fig. 4.2. The median grain size (d50) was
0.28 mm.
A model output gage (gage 1) was introduced at water depth of 1.15 m, which is assumed
to be outside the breaker line (based on field observations). The model output time series
of cross-shore current velocity (u) (Fig. 4.3a) and suspended sediment concentration (c)
(Fig. 4.3b) at 0.05 m from the bed for gage 1 showed pronounced suspension events with
paasage of wave groups (Vincent et al., 1991; Osborne and Greenwood, 1993; Villard and
Osborne, 2002). There was a good correspondence between the predicted and measured
wave groups and the associated suspended sediment concentration.
10.9 11 11.1 11.2
−2
−1
0
1
2
u (m
/s)
(a)
10.9 11 11.1 11.20
10
20
30
40
Time (s)
c (g
/l)
(b)
Figure 4.3: Model output at gage 1. Time series of: a) cross-shore current velocity u (solid
line) and envelope function of u (thick dashed lines); and b) suspended sediment
concentration c (solid line) and lowpass-filtered c (thick dashed line) at 0.05 m from the
seabed.
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
64
The vertical distribution of cross-shore velocity (u) and suspended sediment concentration
(c) during a single wave cycle (~10s) obtained at gage 1 is presented in Fig. 4.4.
Logarithmic velocity distribution (Fig. 4.4a) and the exponential decay in suspended
sediment concentration (Fig. 4.4b) with the distance away from the bed is clearly visible.
−1.5 −1 −0.5 0 0.5 1 1.50
0.1
0.2
0.3
u (m/s)
z (m
)
(a)
024 6 810
0 10 20 30 40 500
0.1
0.2
0.3
c (g/l)
(b)
0
2
4
68
10
Figure 4.4: Model output at gage 1. Vertical distribution of: a) cross-shore current velocity;
b) suspended sediment concentration during one wave cycle.
The model results at gage 1 was compared with a data set (cross-shore velocity, u and
suspended sediment concentration, c) collected in the field (same water depth, h = 1.15m),
just outside the surf zone under shoaling waves, simultaneously with the input wave record
used to drive the model. A comparison of co-spectrum between u and c for field
measurements and model results is presented in Fig. 4.5. The model predictions were in
good agreement with the field results. The suspended sediment flux at the incident
frequency band was onshore, possibly due to the increasing velocity skewness as waves
shoal (Doering and Bowen, 1988; Osborne and Greenwood, 1992b); suspended sediment
flux was offshore at low frequencies due to the combined action of wave groups and the
group bound long wave (Larsen, 1982; Shi and Larsen, 1984). Huntley and Hanes (1987)
first noticed this pattern of suspended sediment flux in the frequency domain under
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
65
shoaling, non-breaking waves. The model results were always in good agreement with the
field results for shoaling waves over a flat bed.
0 0.05 0.1 0.15 0.2−0.04
−0.02
0
0.02
0.04
0.06
Frequency (Hz)
co−
spec
trum
u−
c
onshore
offshore
FIELD
(a)
0 0.05 0.1 0.15 0.2Frequency (Hz)
onshore
offshore
MODEL
(b)
Figure 4.5: Co-spectrum between cross-shore current velocity (u) and suspended sediment
concentration (c) at 0.05 m from the seabed for shoaling waves outside the surf zone over a
flat bed; a) measured at Leighton Beach, Perth, Western Australia; b) model prediction for
the same location.
4.4.3 Inside the surf zone
A similar comparison was performed for a data set collected just inside the surf zone at
City Beach, Perth, Western Australia. The mean grain size (d50) was 0.2 mm and the mean
water depth was 1.0 m. The model performed reasonably well at the incident frequency
band but the comparison was poor at low frequencies (Fig. 4.6). A comparison of the auto-
spectra for the cross-shore current velocity between the field measurements and the model
output showed that the model did not simulate the measured low frequency oscillations
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
66
inside the surf zone (Fig. 4.7). Spectral energy was not observed at the low frequency band
and energy at the incident frequency band was also relatively low compared to the field
results. This is most likey to be due to the model configuration (1-D in the cross-shore
direction) and therefore does not include the 2D alongshore effects which generate the low
frequency energy subsequent to wave breaking (e.g. Symonds et al., 1982).
0 0.05 0.1 0.15 0.2−0.002
−0.001
0
0.001
0.002
Frequency (Hz)
Co−
spec
trum
u−
c
onshore
offshore
FIELD (a)
0 0.05 0.1 0.15 0.2Frequency (Hz)
onshore
offshore
MODEL (b)
Figure 4.6: Co-spectrum between cross-shore current velocity (u) and suspended sediment
concentration (c) at 0.05 m from the seabed inside the surf zone over a flat bed; a)
measured at City Beach, Perth, Western Australia; b) model prediction for the same
location.
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
67
0 0.05 0.1 0.15 0.20
2
4
6
8
10
Aut
o−sp
ectr
um u
Frequency (Hz)
(a)
0 0.05 0.1 0.15 0.2Frequency (Hz)
(b)
Figure 4.7: Auto-spectrum of cross-shore current velocity (u) at 0.05 m from the seabed,
inside the surf zone over a flat bed; a) measured at City Beach, Perth, Western Australia; b)
model prediction for the same location.
4.5 Results and Discussion
The model was used to investigate the influence of factors such as mean grain size (d50),
ratio of significant wave height to water depth (Hs/h), cross-shore location with respect to
the breaker line, and bed roughness (Kn) on the direction and magnitude of cross-shore
suspended sediment flux in the frequency domain. Note that sediment flux discussed in
this paper is always the flux close to the bed (~ 0.05 m from the bed) and outside the
breaker zone.
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
68
4.5.1 Mean grain size (d50)
Grain size can influence the cross-shore suspended sediment flux by changing the settling
time of suspended particles and hence altering the phase lag between the horizontal
velocity (u) and suspended sediment concentration (c) (Deigaard et al., 1999). However, it
is not certain whether the influence of grain size alone is sufficiently large to influence the
direction of suspended sediment flux under shoaling waves over a flat bed.
The model was driven by the same incoming signal as used in Fig. 4.2 (Leighton Beach,
Perth); the cross-shore current velocity (u) and suspended sediment concentration (c) at
0.05 m from the seabed was obtained for shoaling, non-breaking waves at a water depth of
1.3 m. The significant wave height (Hs) was 0.55 m. Five model runs were conducted for
median sand grain sizes of 0.065, 0.15, 0.25, 0.35, and 0.45 mm. Calculations using
Madsen (1993) suggested the seabed was flat for all the grain sizes tested. The co-
spectrum between u and c was calculated for all the grain sizes and was plotted in Fig. 4.8.
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
69
0 0.05 0.1 0.15 0.2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
1.2
Frequency (Hz)
co−
spec
trum
u−
c
onshore
offshore
D50
= 0.065 mmD
50 = 0.15 mm
D50
= 0.25 mmD
50 = 0.35 mm
D50
= 0.45 mm
Figure 4.8: Variation of the co-spectrum between cross-shore current velocity (u) and
suspended sediment concentration (c) at 0.05 m from the seabed with the mean grain size
(d50).
The direction of the suspended sediment flux in the frequency domain for all grain sizes
was in agreement with the original finding by Huntley and Hanes (1987) for shoaling
waves over a flat bed: onshore flux at the incident frequency band and offshore flux at low
frequencies. The magnitude of the suspended sediment flux at all major frequency
components (incident waves, the first harmonic of the incident waves, and low frequencies)
was larger when the grains were finer and reduced significantly for coarser grains (Fig.
4.8). Even the finest sand grains (d50 = 0.065 mm), corresponding to a settling velocity of
0.0036 m/s, did not remain in suspension until the flow reversed to cause offshore flux at
the swell frequency band. Shorter period (~ 7 s) first harmonic of the incident waves,
however, resulted in offshore flux when the grain size was very fine (0.065 – 0.15 mm): i.e.
here, the sediment remained in suspension until the flow reversal (Fig. 4.8).
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
70
The magnitude of suspended sediment flux was higher for finer grains possibly because
more grains were suspended (smaller critical shields parameter) and remained in
suspension for longer than coarser grains. Even for the finest grains, however, the direction
remained onshore at the swell frequency band. This suggested that the grain size alone
may not be sufficient to result a change in the direction of suspended sediment flux under
shoaling waves over a flat bed, outside the breaker zone.
4.5.2 Cross-shore location (Hs/h)
The influence of cross-shore location or Hs/h on cross-shore suspended sediment flux in the
frequency domain was also investigated using the numerical model. Five output gages
were introduced along the sloping beach (Fig. 4.9) to obtain the cross-shore current
velocity (u) and suspended sediment concentration (c) at 0.05 m from the bed. Gages were
placed at 20, 35, 50, 65, and 80 m from the shoreline in 0.57, 1.0, 1.44, 1.9, and 2.3 m
water depths, respectively. Corresponding Hs/h values were 0.80, 0.61, 0.44, 0.31, and
0.23. The ratio of significant wave height (Hs) to water depth (h) varied with the cross-
shore location with respect to the breaker line; Hs/h was larger close to the shoreline and
smaller farther offshore. The seabed was flat throughout.
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
71
0 50 100 150 200 250−4
−3
−2
−1
0
1
2
x (m)
z (m
)
MWL
wav
e si
gnal
gage
1
2345
slot re
gion
Figure 4.9: Model layout for testing the variation with the cross-shore location.
The cross-shore suspended sediment flux in the frequency domain is in agreement with the
Huntley and Hanes’s (1987) original finding: onshore due to incident waves and offshore
due to low frequency oscillations (Fig. 4.10). The direction of suspended sediment flux
remained the same irrespective of the cross-shore location or Hs/h even though the
magnitude reduced significantly away from the shoreline (Fig. 4.10). Therefore, the cross-
shore location or Hs/h alone may not also be a contributing factor to influence the direction
of cross-shore suspended sediment flux.
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
72
0 0.05 0.1 0.15 0.2−0.06
−0.04
−0.02
0
0.02
0.04
0.06
Frequency (Hz)
Co−
spec
tral
den
sity onshore
offshore
Hs/h = 0.80
Hs/h = 0.61
Hs/h = 0.44
Hs/h = 0.31
Hs/h = 0.23
Figure 4.10: Variation of the co-spectrum between cross-shore current velocity (u) and
suspended sediment concentration (c) at 0.05 m from the seabed with the ratio of
significant wave height to water depth (Hs/h) or the cross-shore location.
The normalised velocity skewness (‹u3›⁄‹u2›3⁄2) was calculated for the incident frequency
band at five output gages as explained in chapter 3. Those values, however, indicated a
random variation with the cross-shore location as well as cross-shore suspended sediment
flux and hence were not investigated further.
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
73
4.5.3 Bed roughness (Kn)
Bed roughness has a major control in sediment suspension (Vincent et al., 1991) as well as
the flow close to the seabed (Grant and Madsen, 1979, 1982), influencing the suspended
sediment transport. In the model configuration adopted here, it is not possible to simulate
the effects of bed roughness as individual ripples but as a values which represented the bed
roughness on a flat bed. Nikuradse (1933), with his experiments on flow in a pipe, with
uniform sand particles glued to the walls, expressed the Nikuradse equivalent sand grain
roughness (Kn in eq. 4.4) as equivalent to the grain diameter (d50) (Schlichting, 1960). For
flows over moving beds, corresponding to effective sediment transporting stresses,
however, Kn is expressed as equivalent to 2.5d50 (Nielsen, 1992). Nielsen (1992) also
explained that, when the seabed is rippled, Kn is of the order of the ripple height (Kn ≈ η)
and further suggested that Kn may be represented by,
505.22 58 dKN θλη += (4.10)
where θ2.5 is the shields parameter corresponding to a grain roughness of 2.5d50.
The variation of the cross-shore suspended sediment flux in the frequency domain with
varying bed roughness (Kn) was tested while keeping other parameters constant. The same
input wave signal as in Fig. 4.2 was used to force the model; u and c records were obtained
as output at a water depth of 2.5 m. This forcing configuration, would result in a sea bed
roughness equivalent to having ripples of height (η) of 0.02 m and length (λ) of 0.15 m
(Nielsen, 1992) and can be classified as vortex ripples (Clifton and Dingler’s , 1984). The
mean grain size (d50) was 0.28 mm. The bed roughness (Kn) values tested were d50, 2.5 d50,
ripple height (η)(eqn. 4.10), and 5η, corresponding to a fixed bed, a moving bed and two
formulations for the bed roughness equivalent to ripples, and a hypothetical equivalent
ripple which is five times the calculated height, respectively. The latter condition was
introduced to observe the response to a roughness value corresponding to a large ripple.
The co-spectrum between u and c for varying Kn values are presented in Fig. 4.11. The
suspended sediment flux at the incident wave band increased with the increasing bed
roughness, but the direction was always onshore. Sediment flux at low frequencies,
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
74
however, did not change much with the changing bed roughness. Only at the first
harmonic of the incident frequency band the direction of suspended sediment flux changed
with increasing bed roughness: onshore for smaller Kn and offshore for larger Kn values
corresponding to ripples. Sediment remained sufficiently long in suspension to couple with
the offshore stroke of the short first harmonic waves. The largest sediment flux values
were observed when the bed roughness (Kn) was highest (Kn = 5η), which was
corresponding to the hypothetical equivalent ripple; the direction and magnitude of
suspended sediment flux was almost identical when Kn = η and Kn = eqn. 4.10. The change
in bed roughness by introducing an enhanced bed roughness value changed the magnitude
of sediment flux, but again did not change the direction at major frequency bands
corresponding to swell waves or wave groups.
0 0.05 0.1 0.15 0.2−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
Frequency (Hz)
co−
spec
trum
u−
c onshore
offshore
Kn = d
50K
n = 2.5d
50K
n = η
Kn = 5η
Kn − eqn. 4.10
Figure 4.11: Variation of the co-spectrum between cross-shore current velocity (u) and
suspended sediment concentration (c) at 0.05 m from the seabed with the bed roughness
(Kn).
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
75
4.5.4 Over equivalent ripples
An additional model run was performed with an incoming offshore signal measured at City
Beach, Perth, Western Australia. During the field measurements, cross-shore current
velocity (u) and the suspended sediment concentration (c) were measured at a point which
was approximately 50 m from the shoreline. The mean water depth was 2 m and the
seabed at this point was covered with ripples of 0.005 m ripple height (η) and 0.06 m ripple
length (λ). These ripples were classified as post-vortex according to the definition of
Clifton and Dingler (1984) and no vortex formation was observed.
During the model run an output gage was introduced at the same point as the u and c were
measured in the field (50 m from the shore in 2 m depth) and the model output of u and c
were obtained at 0.05 m from the seabed. Two model runs were conducted with different
bed roughness (Kn) values: 1) Kn = 2.5D50 ― moving flat bed; 2) Kn = eqn. 4.10 ―
enhanced roughness term by Nielsen (1992). Water surface elevation and the cross-shore
current velocity signals measured in the field were in good agreement with the model
output as it has been always for the measurements outside the surf zone.
The co-spectrum between u and c for field and model results (Fig. 4.12) indicated that, in
the field measurements (which were collected when the bed was covered with post-vortex
ripples) , the suspended sediment flux was directed offshore at both the incident and low
frequencies (Fig. 4.12a). In contrast, the model predictions indicated an onshore flux at the
incident frequency for both Kn values representing flat bed conditions (Fig. 4.12b).
Although the field and model predictions both included the same hydrodynamic and
sediment characteristics, contrasting results, in terms of the direction of cross-sediment
flux, were obtained. This is postulated to be due to the effect of the sea bed type – in the
field situation, post-vortex ripples were present whilst in the model flat bed conditions were
prescribed. This highlights the influence of ripples in governing the direction of cross-
shore sediment flux in the frequency domain (Osborne and Greenwood, 1992b; Davidson
et al., 1993).
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
76
0 0.05 0.1 0.15 0.2−5
−25
0
2.5
5
7.5
Frequency (Hz)
co−
spec
trum
u−
c
onshore
offshore
FIELD
(a)
x10−4
0 0.05 0.1 0.15 0.2Frequency (Hz)
onshore
offshore
MODEL
(b)
Kn = 2.5d
50K
n − eqn. 4.10
Figure 4.12: Co-spectrum between cross-shore current velocity (u) and suspended sediment
concentration (c) at 0.05 m from the seabed for shoaling waves over a rippled bed; a)
measured at City Beach, Perth, Western Australia; b) model prediction for the same
location.
From the above it is clear that using an enhanced bed roughness (Kn) is not sufficient to
represent the presence of ripples as it does not replicate the flow structure close to the
seabed such as vortex formation and ejection (see also Davies and Villaret, 2003).
4.6 Implications
Factors such as cross-shore location with respect to the breaker line, significant wave
height to water depth ratio (Hs/h), bed ripples, grain size, normalised velocity skewness
(‹u3›⁄‹u2›3⁄2), bed roughness, tidal variation were identified as potential factors to influence
the direction and magnitude of suspended sediment flux in nearshore regions (Vincent et
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
77
al., 1991; Osborne and Greenwood, 1992a, b; Brander and Greenwood, 1993; Davidson et
al., 1993; Aagaard and Greenwood, 1995; Russell and Huntley, 1999). This was confirmed
during the first phase of this study (chapter 3), with a series of field measurements.
However, it is difficult to estimate the influence of these factors separately in the field as
they are not mutually exclusive. This study investigated the influence of some of those
factors independently using a numerical model. Varying grain size, cross-shore location,
Hs/h, ‹u3›⁄‹u2›3⁄2, and bed roughness introduced with an enhanced roughness term were all
found not to influence the change in the direction of suspended sediment flux at the
incident frequency band. These results isolated ripples as the most likely cause for
changing the direction of suspended sediment flux due to incident waves. Detailed
modelling of rippled beds, which should take into account the flow structure generated due
to the presence of ripples (vortex formation) such as those undertaken by (Davies and
Villaret, 1999; Zedler and Street, 2001; Barr et al., 2004; Davies and Thorne, 2005;
Eidsvik, 2006), however, was beyond the scope of this study.
4.7 Concluding remarks
A simple numerical model was developed to investigate some of the potential factors
influencing the direction and magnitude of cross-shore suspended sediment flux due to
different frequency components such as incident waves and low frequency oscillations
(wave groups) over a flat bed.
The model performed well for shoaling waves outside the surf zone. Inside the surf zone,
the model under-predicted the sediment flux values at the incident frequency band and did
not capture the low frequency oscillations.
The model results showed that the varying factors such as the median grain size (d50),
cross-shore location with respect to the breaker line, the ratio of significant wave height to
water depth (Hs/h), and bed roughness (Kn) changed the magnitude of the cross-shore
suspended sediment flux; however, the direction remained unchanged: onshore at incident
Chapter 4: A numerical study of cross-shore suspended sediment flux in the frequency domain
78
frequency band and offshore at low frequencies. It appeared that each of the above factors
alone may not be sufficient to change the direction of suspended sediment flux. This
finding together with the observations made in Chapter 3 suggested that bed ripples can be
the most important factor controlling the direction of the suspended sediment flux at the
incident frequency band over shoaling non-breaking waves.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
79
Chapter 5 The role of ripple types on cross-shore
suspended sediment flux
Bed forms (ripples) appeared to be the major contributing factor in changing the direction
of suspended sediment flux under swell waves (Chapters 3 & 4). The numerical model
presented in Chapter 4, however, did not simulate the presence of ripples and the primary
aim of the work presented in this Chapter is to investigate the suspended sediment flux over
ripples. Further, in the past it has been noticed that the direction and magnitude of
suspended sediment flux can vary depending upon the ripple type with a limited number of
studies covering few different types of ripples. Therefore this Chapter presents results
obtained through a series of measurements conducted over both flat beds and different
ripple types.
5.1 Introduction
The presence of wave-induced ripples on the seabed has a significant impact on sediment
re-suspension and transport in nearshore environments (Osborne and Greenwood, 1992;
Brander and Greenwood, 1993; Davidson et al., 1993; Osborne and Vincent, 1993, 1996;
Masselink and Pattiaratchi, 2000; Chapter 3). Although bed load transport is the dominant
transport mode over a flat bed (sheet flow), the suspended load transport may be considered
dominant over rippled beds (Brenninkmeyer, 1976; Bailard and Inman, 1979; Nielsen et al.,
1979; Hanes, 1988; Sternberg et al., 1989).
Over a flat bed, sediment re-suspension mainly occurs as a diffusive process; over ripples,
it is more convective, with sand-laden separation vortices formed in the leeside of ripples
being ejected upward into the water column as waves pass (Lee and Hanes, 1996). These
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
80
vortices, however, do not always occur with the presence of ripples, as the vortex formation
strongly depends on the ripple geometry. Vortex formation can be seen over steeper ripples
at regular intervals when the ratio between ripple height (η) and ripple length (λ)—ripple
steepness (η⁄λ)—is greater than 0.1. These ripples are named vortex ripples (Clifton and
Dingler, 1984). Consistent vortex formation has been not observed over ripples when the
steepness is < 0.1; these ripples are called post-vortex ripples (Clifton and Dingler, 1984).
Increased suspended sediment concentrations have been observed higher in the water
column when vortex ripples are present (Vincent et al., 1991; Osborne and Greenwood,
1993; Osborne and Vincent, 1996) because the vortices ejected sand upward into the water
column. The vertical length scale of the suspended sediment concentration profiles is a
strong function of the ripple height (Nielsen, 1984).
Cross-shore suspended sediment flux over a flat bed under shoaling, non-breaking, incident
(swell, wind) waves has often been observed to be directed onshore (Osborne and
Greenwood, 1992; Davidson et al., 1993). Huntley and Hanes (1987) first highlighted this
and attributed it to the increased velocity skewness as waves shoal (Osborne and
Greenwood, 1992). Many researchers have also observed offshore suspended sediment
flux at the swell frequency band (Osborne and Greenwood, 1992; Davidson et al., 1993;
Masselink and Pattiaratchi, 2000; Chapter 3); the presence of ripples is considered the most
likely reason for this reversal in the direction of suspended sediment flux (Osborne and
Greenwood, 1992; Davidson et al., 1993).
The timing of sediment suspension in relation to cross-shore velocity can change
significantly depending on the ripple geometry (Osborne and Vincent, 1993, 1996). This
can cause the direction of suspended sediment transport at the incident frequency band to
alternate between onshore and offshore. Inman and Bowen (1963) first described a
mechanism for seaward suspended sediment flux at the incident frequency band over a
rippled bed. They described the re-suspension and transport process over steep vortex
ripples as follows: (1) when a skewed wave propagates over vortex ripples, a vortex is
formed on the leeside of the ripple during the relatively strong onshore phase of flow, and
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
81
remains trapped until the flow reverses; (2) during the weaker offshore phase, the sand-
laden vortex is released and ejected into the water column; and (3) this sediment cloud is
transported seaward by the offshore phase.
During some studies, however, offshore sediment flux at the incident frequency band has
been observed over less steep post-vortex ripples (Osborne and Greenwood, 1992; Brander
and Greenwood, 1993; Chapter 3) and predominantly onshore flux has been measured over
steeper ripples (Osborne and Greenwood, 1992). Davidson et al. (1993) noticed offshore
flux due to swell waves over a rippled bed, but the ripple geometry was not measured;
therefore it was unclear whether the ripples were vortex or post-vortex.
The above observations suggest that the direction of suspended sediment flux at the
incident frequency band could be a function of the ripple geometry and thus can vary over
different ripple types. Few detailed studies of cross-shore sediment flux over different
ripple types have been undertaken (Brander and Greenwood, 1993; Osborne and Vincent,
1993, 1996), yet they are essential to gain a thorough understanding of sediment re-
suspension and transport processes in nearshore environments. Further, past studies have
not included many different ripple types which could be observed in nearshore
environments.
This paper presents a series of measurements (water surface elevation, cross-shore current
velocity, and suspended sediment concentration) collected under shoaling waves over
different bed configurations (flat bed and different ripple types) at low energy, micro-tidal
beaches in southwestern Australia. The data were first presented in Doucette (2000) which
concentrated on the ripple geometry. This paper explores the effect of ripples on cross-
shore suspended sediment flux in more detail. The changes in bed morphology were also
observed concurrently with the measurements of ripple geometry. The cross-shore
suspended sediment flux in the frequency domain for each data set was investigated to
identify any trends with the ripple types. The results of further cross-spectral and cross-
correlation analyses are then presented with the aim of exploring factors governing changes
in the direction and magnitude of suspended sediment flux over different bed types.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
82
5.2 Methodology
5.2.1 Field sites
Measurements were conducted at 15 micro-tidal, low energy, sandy beaches in
southwestern Australia between 31/10/97 and 2/4/98 (Fig. 5.1). The measurements were
obtained at discrete cross-shore locations in the nearshore at each field site, to give a total
of 60 data sets. The grain sizes (d50) of the sand present at the measurement locations
varied between 0.14 mm and 0.54 mm.
Figure 5.1: Locations of field measurements in south-western Australia
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
83
5.2.2 Data collection
The instrumentation for data collection included a Marsh-McBirney Inc. 511
electromagnetic current meter, two D & A optical backscatterance sensors (OBS), and a
pressure sensor to measure horizontal components of the cross-shore current velocity,
suspended sediment concentration, and water surface elevation, respectively. These
instruments were mounted on a portable frame (Fig. 5.2), with the current meter 0.25 m
above the bed, the OBS at 0.05 m and 0.13 m above the bed, and the pressure sensor 0.05
m above the bed. The length of each measurement deployment was at least 17 mins (4096
data points at a frequency of 4 Hz). During each deployment, a free diver measured ripple
height (η) and length (λ) with a ruler.
Figure 5.2: Data collection
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
84
5.2.3 Data analysis
Spectral analysis
The co-spectrum between the cross-shore current velocity (u) and the suspended sediment
concentration (c) at 0.05 m from the bed was calculated for each data set to determine the
direction and magnitude of the cross-shore suspended sediment flux close to the bed (0.05
m) under different frequency components (swell waves, wind waves, and low frequency
oscillations, such as wave groups and the group bound long wave). Co-spectral analysis
was conducted through digital Fourier transforms, with each data set of 4096 points divided
into eight equal segments for the segment average method (Bendat and Piersol, 1986). The
number of degrees of freedom used was 16. Calculations of the 95% confidence interval
showed that the lower and upper values of these spectra were 0.55 and 2.31 times the
spectral estimates.
Net suspended sediment flux
The cross-shore suspended sediment flux at low frequencies was offshore at most locations,
possibly due to the combined action of wave groups and the group bound long wave (Shi
and Larsen, 1984). At the swell frequency band, however, the direction of suspended
sediment flux varied considerably over different bed conditions.
Therefore the main focus of this study was on swell waves. For all the data sets, the auto-
spectrum of u showed that most of the incident swell wave energy converged within
approximately 0.05 Hz and 0.11 Hz (i.e between 9s and 20s). Integrating the area under the
co-spectrum at this frequency band yielded the net cross-shore sediment flux due to swell
waves. The net sediment flux values were then normalised by the absolute value of the
area under the co-spectrum at the same frequency band to obtain normalised net cross-shore
sediment flux.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
85
5.2.4 Ripple classification
The observed ripples were classified (according to their geometry and sediment
resuspension patterns) into five categories: post-vortex ripples, 2D ripples, 2D/3D ripples,
3D ripples, and cross ripples.
Low amplitude ripples, where the ripple steepness was less than 0.1 (Clifton and Dingler,
1984), oriented parallel to the wave crests were classified as post-vortex ripples (Osborne
and Vincent, 1993). These ripples were not always present, as they were washed away
during larger waves of the wave groups and re-formed during smaller waves. Vortex-
shedding was observed at irregular intervals, and diffusive mixing appeared to be the major
mechanism for sediment re-suspension.
Steeper ripples with crests oriented parallel to the wave crests were termed 2D ripples.
Vortex shedding was clearly observed over these ripples. Ripples with smaller heights and
variable lengths, where no distinct linear crests were observed, were categorized as 3D
ripples. The distance between bifurcations was smaller (< 10 cm) over 3D ripples and
sediment suspension occurred as discrete packages. Ripples with geometry that was
between the 2D and 3D classifications were called 2D/3D ripples. The bifurcation density
for 2D/3D ripples was greater than for 2D ripples but less than for 3D ripples. The ripple
heights of 2D/3D ripples were greater than those of 3D ripples. The sediment suspension
process over 2D/3D ripples resembled that over 2D ripples.
The final ripple type, cross ripples, consisted of larger, primary ripples and smaller,
secondary ripples, which were orthogonal to each other. Independently, each set of ripples
could be considered to be 2D. The primary and secondary ripples were inclined to the
wave propagation direction by approximately ± 450. Cross ripples can be considered vortex
under the Osborne and Vincent’s (1993) classification. More details on ripple classification
can be found in Chapter 2 (Literature review).
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
86
5.3 Results and Discussion
Six different bed types (flat bed, post-vortex ripples, 2D ripples, 2D/3D ripples, 3D ripples,
and cross ripples) were studied during a series of field measurements conducted at low
energy, micro-tidal beaches in southwestern Australia to investigate sediment re-suspension
and cross-shore suspended sediment transport close to the seabed.
5.3.1 Ripple geometry
The mean values of ripple height and steepness for different ripple types are plotted in Figs
5.1a and 5.1b. Cross ripples showed the highest mean ripple height (about 5 cm) owing to
the larger, primary ripples. 2D ripples showed the second-highest ripple height, followed
by 2D/3D, 3D, and post-vortex ripples (Fig. 5.3a). The post-vortex ripple heights were
relatively small with a mean value of ~0.6 cm.
2D/3D and 3D ripples had greater ripple steepness (η⁄λ) values, due to shorter ripple lengths
(Fig. 5.3b). 2D and cross ripples were relatively less steep, as the ripple lengths were
greater for these types. Post-vortex ripples had the smallest mean steepness value of
approximately 0.08. The mean ripple steepness, however, was greater than 0.1 for all the
ripple types except for post-vortex.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
87
0
1
2
3
4
5
6
7
(a)η
(cm
)
0
0.05
0.1
0.15
0.2
0.25(b)
flatbed
post−vortexripples
2Dripples
2D/3Dripples
3Dripples
crossripples
η/λ
Figure 5.3: a) Mean ripple height and b) mean ripple steepness for different ripple types.
Error bars denote standard error around the mean values.
5.3.2 Ripple patterns
It has been shown that ripple type can depend on the mobility number (ψ1/10) as well as
grain size (represented by the median grain diameter, d50) (Lofquist, 1978; O'Donoghue and
Clubb, 2001; O'Donoghue et al., in press). Mobility number here was calculated with u1/10,
for comparison with (O'Donoghue et al., in press) and is given by,
( ) 50
2
101
101 1 gds
u
−=ψ (5.1)
where 2
101u is the mean of the highest one-tenth of the cross-shore velocity, s is the specific
gravity of sediment (2.65 for quartz sand), g is gravitational acceleration, and d50 is the
median grain diameter.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
88
O’Donogue et al. (in press) observed flat bed conditions under higher mobility numbers
(ψ1/10 > 190), and 2D or 3D ripples were present when the ψ1/10 was lower, although no
statistically significant difference in ψ was observed between 2D and 3D ripples. Further,
2D ripples have been observed in much coarser sediments than 3D ripples (Lofquist, 1978;
O'Donoghue and Clubb, 2001; O'Donoghue et al., in press).
0.1 0.2 0.3 0.4 0.5 0.60
50
100
150
200
250
D50
(mm)
ψ1/
10
flat bedpost−vortex ripplescross ripples2D/3D ripples2D ripples3D ripples
Figure 5.4: Change in ripple type with mobility number and median grain diameter.
In this study, flat bed conditions were observed under the highest mobility numbers (>
100), corresponding to higher bed shear stresses (Fig. 5.4). Post-vortex ripples were
observed under mobility numbers ranging from ~50 to 140, whereas no clear difference
could be identified between cross, 2D, 2D/3D, and 3D ripples (< 50). O’Donoghue et al.
(in press) also noticed a similar trend even though the limiting values were different.
2D ripples were composed of coarse grains (d50 > 0.35 mm), and other ripple types were
composed of finer grains (Fig. 5.4). No significant difference in d50 was found between flat
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
89
bed, post-vortex, cross, 2D/3D, and 3D ripples. This was in agreement with O’Donoghue
et al. (in press) and complies with the concept that 3D ripples form in the presence of fine
sand and field scale orbital diameters (Lofquist, 1978; O'Donoghue and Clubb, 2001).
Hay and Mudge (2005) investigated five bed states with measurements conducted at ~ 3m
water depth during SandyDuck 97 and suggested that occurrence of different bed states
depended primarily on rms wave orbital velocity. This was not observed under this study
and could possibly be due to the low energy conditions.
5.3.3 Suspended sediment concentration
The mean value of the highest one-third suspended sediment concentration (Csig) at 0.05 m
above the seabed is plotted against the ripple steepness in Fig. 5.5. Strong sediment re-
suspension events were always noticed over ripples with greater steepness, (η⁄λ > 0.15)
(solid circles). This observation supports the hypothesis that steeper ripples induce higher
suspension events—suspension enhanced by sand-laden separation vortices on the leeside
of ripples (Vincent et al., 1991; Osborne and Greenwood, 1993; Osborne and Vincent,
1996). Sediment suspension over low steepness ripples (η/λ < 0.15) was not as pronounced
as over steeper ripples because vortex formation was not as strong as over steeper ripples.
The sediment suspension was more diffusive over low steepness ripples (Osborne and
Vincent, 1996). Ripple geometry appeared to influence the sediment suspension pattern
significantly. This could influence the phase relationship between cross-shore current
velocity and the suspended sediment concentration, hence altering the direction of
suspended sediment flux.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
90
0.05 0.1 0.50
0.5
1
1.5
2
2.5
3
η/λ
c sig (
g/l)
steepness <= 0.15steepness > 0.15
Figure 5.5: Variation of suspended sediment concentration with ripple steepness.
5.3.4 Sediment suspension and wave groups
Simultaneous time series records of cross-shore current velocity (u) and suspended
sediment concentration (c) over a flat bed at Leighton Beach are shown in Figs 5.6a and
5.6b, respectively. The instrument station was deployed just outside the breaker line in a
mean water depth (h) of 0.52 m with a relatively high ratio of significant wave height to
water depth (Hs/h) of 0.94.
The envelope function calculated using the List (1991) method (Fig. 5.6a) highlighted the
presence of wave groups and higher suspension events coinciding with the passing of wave
groups (Fig. 5.6b). Wave groups causing higher suspension events have been observed in
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
91
−1.5
−1
−0.5
0
0.5
1
1.5
u (m
/s)
(a)
0 200 400 600 800 10000
10
20
30
Time (s)
c (g
/l)
(b)
Figure 5.6: Time series of a) cross-shore current velocity u (z = 0.25 m; solid line) and
envelope function of u calculated using List (1991) method (thick, dashed line) and b)
suspended sediment concentration c0.05 (z = 0.05 m; solid line) and lowpass-filtered c0.05
(thick, dashed line).
other studies and various explanations have been formulated: (1) Vincent et al. (1991)
proposed that alternative changes in ripple geometry during the passing of larger and
smaller waves of wave groups could cause higher suspension events, as larger waves meet
with steeper than expected ripples; (2) Villard and Osborne (2002) suggested the effect of
antecedent waves could lead to coupling between antecedent and developing vortices above
a rippled bed and hence cause higher suspension events. However, as shown in Fig. 5.6,
higher suspension events due to wave groups have also been observed over flat beds. (3)
Over a flat bed, larger waves of a wave group may produce persistent turbulence, which
can be a major factor influencing higher suspension events as wave groups pass (Hanes and
Huntley, 1986; Osborne and Greenwood, 1993). (4) Hay and Bowen (1994a) suggested
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
92
that higher suspension events observed at wave group frequency could be a results of more
than one action. They pointed at vortex shedding from megaripples, enhanced interaction
with the seabed during larger waves of the wave groups, perhaps via group bound long
wave, and coherent structures in combined flow turbulence as possible reasons (Hay and
Bowen, 1994a). (5) Bed forms, surface-injected vortices, and the sensor support structure
were mentioned as possible reasons by Hay and Bowen (1994b) for pumping up of
sediments observed at wave group frequency. Hay and Bowen (1994a), however,
suggested that keeping the sensors 5-10 diameters from the nearest support would minimise
the risk of supporting structure’s influence. Higher suspension events under wave groups
were observed over both flat and rippled beds during this study.
5.3.5 Cross-shore suspended sediment flux
The variation in the magnitude and direction of cross-shore suspended sediment flux over
six different bed types (flat bed, post-vortex ripples, 2D ripples, 2D/3D ripples, 3D ripples,
and cross ripples) was investigated using cross-spectral and cross-correlation analyses
between the time series records of u and c. Note that the suspended sediment concentration
was measured at only 0.05 m from the seabed; hence the sediment flux discussed here
refers to sediment flux at the same height.
The mean values of normalised net cross-shore suspended sediment flux at the swell
frequency band, calculated over different bed types, are shown in Fig. 5.7. Here, the
onshore flux was defined as positive and offshore flux was negative.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
93
−1
−0.75
−0.5
−0.25
0
0.25
0.5
0.75
1
norm
alis
ed m
ean
sedi
men
t flu
x (g
l−1 (m
s−1 ))
onshore
offshore
flatbed
post−vortexripples
2Dripples
2D/3Dripples
3Dripples
crossripples
Figure 5.7: Normalised net sediment flux over different ripple types.
Flat bed
Over a flat bed, the net sediment flux due to swell waves was predominantly onshore (Fig.
5.7), as Huntley and Hanes (1987) originally observed and many other researchers
(Osborne and Greenwood, 1992; Davidson et al., 1993; Chapter 3) observed later.
Results of the spectral analyses conducted for the two time series (u and c) presented in Fig.
4 are shown in Fig. 5.8. The location of the instrument station is shown in Fig. 5.8a
(Leighton Beach). The seabed was flat. The auto-spectrum of cross-shore current velocity
(u) showed a dominant peak at around 0.075 Hz (~13 s), corresponding to incoming swell
waves (Fig. 5.8b). The auto-spectrum of suspended sediment concentration (c) showed two
peaks corresponding to wave groups and swell waves, where the peak at wave group
frequency (< 0.025 Hz) dominated (Fig. 5.8c). Conditions were swell-dominated, and the
sediment concentration (c) spectrum indicates wave groups suspended more sediments.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
94
−20 −10 0 10 20 30 40 50−2
−1
0
1
Distance from shore (m)
Ele
vatio
n (m
)MSL
(a)
instrument station
Leighton Beach #1
Flat bed
0
2
4
6
8
10
u sp
ectr
um (
m2 /s
) (b)
0
200
400
c sp
ectr
um (
g2 /l2 ) (c)
−0.08
−0.04
0
0.04
0.08
Co−
spec
trum
u−
c
onshore
offshore
(d)
0
0.05
0.1
Cro
ss−
spec
trum
(e)
0 0.05 0.1 0.15 0.2−180
−90
0
90
180
Frequency (Hz)
Pha
se
(f)
0 0.05 0.1 0.15 0.20
0.3
0.6
Frequency (Hz)
Coh
eren
ce
(g)
Figure 5.8: a) Beach profile and the results of cross-spectral analysis between cross-shore
current velocity (u) and suspended sediment concentration (c0.05) for run 1 at Leighton
Beach (over a flat bed); b) u auto-spectrum; c) c auto-spectrum; d) u-c co-spectrum (dotted
lines show the frequency range chosen as the swell wave frequency band); e) u-c cross-
spectrum; f) u-c phase spectrum; g) u-c coherence spectrum.
The co-spectrum between u and c (Fig. 5.8d) indicate the usual trend observed over a flat
bed, where suspended sediment flux at the swell frequency band was onshore and the flux
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
95
at low frequencies was offshore (Huntley and Hanes, 1987). A smaller onshore component
was observed at the first harmonic of the swell waves. The cross-spectrum (Fig. 5.8e)
depicts the gross transport rates (addition of onshore and offshore transport) in the
frequency domain. Swell waves were the dominant transport component.
The phase lag between u and c (Fig. 5.8f) is a direct indicator of the direction of sediment
flux. Flux is onshore if the phase lag is between ± 900 because the peak in sediment
concentration occurs while the cross-shore current velocity is onshore. Flux is offshore if
the phase lag is outside ± 900 because the sediment concentration peaks during the offshore
mean. At this location, the phase lag was less than 900 at the swell frequency and first
harmonic bands, causing onshore flux, and greater than 900 out of phase at low frequencies,
resulting in offshore flux.
The 95% confidence interval for the phase spectrum (Davidson et al., 1993) at the dominant
frequency components was calculated using the coherence spectrum (Jenkins and Watts,
1968) to test the statistical significance of the dominant sediment flux components (Fig.
5.8f). The results showed the co-spectral peaks observed at all three major frequency bands
(low frequencies, swell band, and the first harmonics of the swell band) were statistically
significant (Fig. 5.8f). Strong coherence peaks between u and c at the swell and the first
harmonic of the swell bands were observed, whereas the coherence at low frequencies was
relatively low (Fig. 5.8g). This explains the higher suspended sediment flux observed
under swell waves compared with the low frequency waves (Fig. 5.8d). Similar results
were obtained when the seabed was flat.
The increasing velocity skewness as waves shoal was assumed to force the strong onshore
sediment flux at the swell band (Doering and Bowen, 1988, 1989; Osborne and
Greenwood, 1992). Flat bed conditions were generally observed close to the shore (or on
the seaward slope of a bar) where wave/velocity skewness was greatest. Moreover, it has
been observed that under near-breaking and breaking waves that large fluid accelerations
which are skewed towards shore, suspended more sediments (Hanes and Huntley, 1986;
Nielsen, 1992; Osborne and Greenwood, 1993). This coincided with the onshore mean of
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
96
the cross-shore velocity causing onshore sediment transport (Elgar et al., 1988; Elgar et al.,
2001).
−20 −10 0 10 20 30 40 50−2
−1
0
1
Distance from shore (m)
Ele
vatio
n (m
)
MSL
(a)
instrument station
Leighton Beach #3
Post−vortex
0
1
2
3
4
u sp
ectr
um (
m2 /s
) (b)
0
5
10
15
c sp
ectr
um (
g2 /l2 ) (c)
x10−3
−4
−2
0
2
Co−
spec
trum
u−
c onshore
offshore
(d)
x10−4
0
2
4
Cro
ss−
spec
trum
(e)
x10−4
0 0.05 0.1 0.15 0.2−180
−90
0
90
180
Frequency (Hz)
Pha
se
(f)
0 0.05 0.1 0.15 0.20
0.3
0.6
Frequency (Hz)
Coh
eren
ce
(g)
Figure 5.9: The results of cross-spectral analysis between cross-shore current velocity (u)
and suspended sediment concentration (c0.05) for run 3 at Leighton Beach (over post-vortex
ripples): a) beach profile b) u auto-spectrum (dotted lines show the frequency range chosen
as the swell wave frequency band); c) c auto-spectrum; d) u-c co-spectrum; e) u-c cross-
spectrum; f) u-c phase spectrum; g) u-c coherence spectrum.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
97
Post-vortex ripples
The net cross-shore sediment flux due to swell waves over post-vortex ripples was
predominantly offshore (Fig. 5.7). The results of spectral analysis between u and c at
Leighton Beach (Fig. 5.9a), where the seabed was covered with post-vortex ripples, are
presented in Figs 5.9b–g. This data set was collected at the same field site as the data set
presented in Fig. 5.8 except that this was collected from further offshore. Similar results as
these were obtained when the seabed was covered with post-vortex ripples.
The auto-spectra for u and c (Figs 5.9a–b) showed the same trend as in Figs 5.8a–b, with u
peaking at the swell frequency band and c peaking at the low frequency band. The co-
spectrum between u and c (Fig. 5.9c) deviated from what was observed over a flat bed at
this beach (Fig. 5.8c), with sediment flux at the swell band becoming offshore-directed
whilst the flux at the low frequency band remained offshore and the first harmonic of swell
band remained onshore. Inman and Bowen’s (1963) description for offshore sediment flux
observed over steep vortex ripples could not explain this, as the ripples were post-vortex
(steepness < 0.1), where no regular vortex formation was observed. Offshore sediment flux
over post-vortex or flat ripples has been observed in other studies (Osborne and
Greenwood, 1992; Brander and Greenwood, 1993; Masselink and Pattiaratchi, 2000;
Chapter 3). Davidson et al. (1993) also noted offshore sediment flux when ripples were
present, but as the ripple parameters were not measured, it was unclear whether the ripples
were vortex or post-vortex.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
98
−30 −20 −10 0 10 20 30−0.4
−0.2
0
0.2
0.4
Lag (s)
Cro
ss−
corr
elat
ion
(u−
c)
Figure 5.10: Cross-correlation between cross-shore current velocity (u) and suspended
sediment concentration (c0.05) for run 3 at Leighton Beach (over post-vortex ripples).
The cross-correlation between the cross-shore current velocity (u) and suspended sediment
concentration (c) was calculated to further investigate the offshore flux observed at the
swell band. The cross-correlation coefficient indicates a dominant, negative peak with a
lag of approximately 2 s; indicating the peak in suspended sediment concentration occurred
2 s after the wave trough passed (Fig. 5.10). Given the peak period of swell waves was ~14
s, this indicates that the maximum suspended sediment concentration coincided with the
offshore mean of the wave motion resulting in offshore flux.
Diffusive mixing has been identified as the major mechanism for sediment suspension over
post-vortex ripples where no vortex forms (Osborne and Vincent, 1996; Masselink and
Pattiaratchi, 2000). Osborne and Vincent (1996) found that over less steep ripples, during
the stronger onshore phase, relatively high sediment concentrations were generated very
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
99
close to the bed because of flow turbulence. These sediments moved (2–5 cm) up the water
column by diffusion during the offshore phase. The cross-correlation analysis (Fig. 5.10)
supports this finding by showing a peak in suspended sediment concentration at 0.05 m
from the bed during the offshore mean. Thus the suspended sediment flux close to the bed
due to swell waves over post-vortex ripples can be illustrated by Fig. 5.9. During the
stronger onshore phase, the sediment concentration increased very close to the bed because
of the strong, flow-generated turbulence (Fig. 5.11a). These sediments moved (2–5 cm) up
the water column during the offshore phase (Fig. 5.11b) resulting in net offshore sediment
flux at the swell frequency band close to the bed (Fig. 5.11c).
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
100
(a)
(b)
(c) Figure 5.11: Simple mechanism for offshore suspended sediment transport over post-vortex
ripples.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
101
2D ripples
The net cross-shore suspended sediment flux due to swell waves over 2D ripples was
onshore (Fig. 5.7). The seabed at all four measurement locations at South Beach (Fig.
5.12a) were covered with 2D ripples. The results of the spectral analysis between the time
series records of u and c, collected at the location closest to shore (Fig. 5.12a), are
presented in Figs 5.12b–g. Similar results were obtained throughout the study when the
seabed was covered with 2D ripples. The instrument station was deployed just outside the
breaker line, where the mean water depth (h) was 0.72 m.
The auto-spectra of u and c showed the same pattern as observed throughout the study:
swell waves dominated the u spectrum (Fig. 5.12b) and low frequency oscillations
dominated the sediment concentration (c) spectrum (Fig. 5.12c). The co-spectrum between
u and c showed onshore flux at the swell frequency band, whereas sediment flux was
negligible at low frequencies and the first harmonic of the swell wave frequency (Fig.
5.12d). This was observed throughout the study when the seabed was covered with 2D
ripples. Clear vortex formation was observed over 2D ripples; thus this outcome was not in
agreement with the explanation that suspended sediment flux over vortex ripples is offshore
(Inman and Bowen, 1963). Osborne and Greenwood (1992) and Brander and Greenwood
(1993), however, measured onshore flux over steeper ripples too.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
102
−10 −5 0 5 10 15 20−1.5
−1
−0.5
0
0.5
1
Distance from shore (m)
Ele
vatio
n (m
)MSL
(a)
instrument station
South Beach #1
2D
0
0.5
1
1.5
u sp
ectr
um (
m2 /s
) (b)
0
0.5
1
1.5
2
c sp
ectr
um (
g2 /l2 ) (c)
−2
0
2
4
Co−
spec
trum
u−
c
onshore
offshore
(d)
x10−3
0
2
4C
ross
−sp
ectr
um
(e)
x10−3
0 0.05 0.1 0.15 0.2−180
−90
0
90
180
Frequency (Hz)
Pha
se
(f)
0 0.05 0.1 0.15 0.20
0.3
0.6
Frequency (Hz)
Coh
eren
ce
(g)
Figure 5.12: The results of cross-spectral analysis between cross-shore current velocity (u)
and suspended sediment concentration (c0.05) for run 1 at South Beach (over 2D ripples): a)
beach profile; b) u auto-spectrum; c) c auto-spectrum (dotted lines show the frequency
range chosen as the swell wave frequency band); d) u-c co-spectrum; e) u-c cross-spectrum;
f) u-c phase spectrum; g) u-c coherence spectrum.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
103
The cross-correlation coefficient between u and c showed a positive peak with time lag of
approximately 1 s suggesting maximum suspended sediment concentration appeared 1 s
after the onshore velocity maxima (Fig. 5.13). This suggested the leeside vortices were
ejected just after the maxima in cross-shore velocity whilst the flow was still directed
onshore. A possible explanation for onshore suspended sediment flux observed over 2D
(vortex) ripples is depicted in Fig. 5.14. Leeside separation vortices form during the
stronger onshore phase (Fig. 5.14a) and those sand-laden vortices are ejected into the flow
while the flow is still onshore (Fig. 5.14b) resulting in onshore sediment flux close to the
bed (Fig. 5.14c).
−30 −20 −10 0 10 20 30−0.4
−0.2
0
0.2
0.4
Lag (s)
Cro
ss−
corr
elat
ion
(u−
c)
Figure 5.13: Cross-correlation between cross-shore current velocity (u) and suspended
sediment concentration (c0.05) for run 1 at South Beach (over 2D ripples).
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
104
(a)
(b)
(c) Figure 5.14: Simple mechanism for onshore suspended sediment transport over vortex
ripples.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
105
2D/3D ripples
The net suspended sediment flux due to swell waves over 2D/3D ripples was mainly
onshore (Fig. 5.7). The spectral analysis results obtained for a data set collected at South
Pinneroo Beach, are presented in Fig. 5.15 and are representative of 2D/3D ripples
observed in this study.
The instrument station was 25 m offshore in a water depth of 1.17 m (Fig. 5.15a). Similar
to most of the data sets examined in this study, the u spectrum peaked at the swell
frequency band (Fig. 5.15b), and the c spectrum peaked at low frequencies (Fig. 5.15c).
The co-spectrum between u and c was fairly similar to the trend observed over 2D ripples,
with a dominant onshore component at the swell band and a negligible offshore component
at low frequencies (Fig. 5.15d). Overall, the cross-spectral analysis results obtained over
2D/3D ripples were fairly similar to those of the 2D ripples. In situ observations further
suggested that the behaviour of 2D/3D ripples resembled 2D ripples. Thus the explanation
as illustrated by Fig. 5.14 for 2D ripples may be applied to the predominantly onshore
sediment flux observed over 2D/3D ripples.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
106
−10 0 10 20 30−1.2
−0.8
−0.4
0
0.4
Distance from shore (m)
Ele
vatio
n (m
) MSL
(a)
instrument station
South Pinneroo #3
2D/3D
0
0.5
1
u sp
ectr
um (
m2 /s
) (b)
0
0.5
1
1.5
c sp
ectr
um (
g2 /l2 ) (c)
−1
0
1
2
3
Co−
spec
trum
u−
c
onshore
offshore
(d)
x10−3
0
2
4C
ross
−sp
ectr
um
(e)
x10−3
0 0.05 0.1 0.15 0.2−180
−90
0
90
180
Frequency (Hz)
Pha
se
(f)
0 0.05 0.1 0.15 0.20
0.3
0.6
Frequency (Hz)
Coh
eren
ce
(g)
Figure 5.15: The results of cross-spectral analysis between cross-shore current velocity (u)
and suspended sediment concentration (c0.05) for run 3 at South Pinneroo (over 2D/3D
ripples): a) beach profile; b) u auto-spectrum; c) c auto-spectrum (dotted lines show the
frequency range chosen as the swell wave frequency band); d) u-c co-spectrum; e) u-c
cross-spectrum; f) u-c phase spectrum; g) u-c coherence spectrum.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
107
3D ripples
The net cross-shore sediment flux close to the seabed due to swell waves over 3D ripples
was generally offshore (Fig. 5.7). Results of the spectral analysis between u and c for a
location at Warnbro Sound (Fig. 5.16a), where the seabed was covered with 3D ripples, are
presented in Figs 5.16b–g. Similar results were always obtained when the ripples were 3D.
The instrument station was about 30 m from the shoreline in a mean water depth (h) of 0.8
m. The significant wave height to water depth ratio (Hs/h) was 0.182. The auto-spectra of
u and c showed the same pattern observed throughout this study, with a dominant swell
wave component in the u spectrum (Fig. 5.16b) and a dominant low frequency component
in the sediment concentration (c) spectrum (Fig. 5.16c). The co-spectrum between u and c
was similar to what was observed over post-vortex ripples, with a strong offshore sediment
flux component at the swell frequency band and a weaker offshore component at low
frequencies (Fig. 5.16d).
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
108
−10 0 10 20 30 40−1.5
−1
−0.5
0
0.5
Distance from shore (m)
Ele
vatio
n (m
)
MSL(a)
instrument station
Warnbro Sound #5
3D
0
0.4
0.8
u sp
ectr
um (
m2 /s
) (b)
0
0.1
0.2
0.3
0.4
c sp
ectr
um (
g2 /l2 ) (c)
−6
−4
−2
0
2
Co−
spec
trum
u−
c onshore
offshore
(d)
x10−4
0
2
4
6C
ross
−sp
ectr
um
(e)
x10−4
0 0.05 0.1 0.15 0.2−180
−90
0
90
180
Frequency (Hz)
Pha
se
(f)
0 0.05 0.1 0.15 0.20
0.3
0.6
Frequency (Hz)
Coh
eren
ce
(f)
Figure 5.16: The results of cross-spectral analysis between cross-shore current velocity (u)
and suspended sediment concentration (c0.05) for location no. 5 at Warnbro Sound (over 3D
ripples): a) beach profile; b) u auto-spectrum; c) c auto-spectrum (dotted lines show the
frequency range chosen as the swell wave frequency band); d) u-c co-spectrum; e) u-c
cross-spectrum; f) u-c phase spectrum; g) u-c coherence spectrum.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
109
The cross-correlation between the time series of u and c is presented in Fig. 5.17. A
negative correlation with approximately zero lag was observed, suggesting the peak in
offshore velocity coincided with the peak in suspended sediment concentration. The
sediment suspension pattern over 3D ripples, however, was completely different to that of
post-vortex ripples and therefore the same explanation was not applicable. 3D ripples
could be classified as vortex under Clifton and Dingler’s (1984) classification and the
sediment suspension occurred as discrete packages.
−30 −20 −10 0 10 20 30−0.4
−0.2
0
0.2
0.4
Lag (s)
Cro
ss−
corr
elat
ion
(u−
c)
Figure 5.17: Cross-correlation between cross-shore current velocity (u) and suspended
sediment concentration (c0.05) for location no. 5 at Warnbro Sound (over 3D ripples).
3D ripples, however, were always observed far away from the shoreline where the wave
asymmetry would be less. The distance from the shoreline, water depth, ripple type, and
the significant wave height to water depth ratio (Hs/h) at three locations where 3D ripples
were observed are presented in Table 5.1. 3D ripples were seen when the Hs/h was
relatively low where the shoaling waves were less asymmetric towards the shore. Hs/h
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
110
reduced with the increasing cross-shore distance from the shoreline except when a bar was
present. It could be speculated that this low wave asymmetry might be the reason for the
difference in timing of vortex ejection between 2D and 3D ripples. Further investigations
would, however, be needed to confirm this. Relatively small ripple heights of 3D ripples
compared to 2D or 2D/3D might also had an influence on this difference in timing of vortex
ejection.
Location Distance from
shore (m)
Water depth
(m) Ripple type Hs/h
6 0.25 Flat bed 0.75
9 0.54 Cross 0.36
18 0.95 3D 0.20
30 0.82 Cross 0.24
Eagle Bay
54 1.25 3D 0.16
8 0.46 Cross 0.29
10 0.55 2D 0.32
22 0.27 Post-vortex 0.68
25 0.51 Cross 0.35
Warnbro Sound
31 0.80 3D 0.18
5 0.26 Post-vortex 0.61
7 0.43 Cross 0.41
17 0.71 3D 0.19
25 0.60 3D 0.29
Safety Bay
35 0.99 3D 0.13
Table 5.1: Distance from the shoreline, mean water depth (h), ripple type, and significant
wave height to water depth ratio (Hs/h) at Eagle Bay, Warnbro Sound, and Safety Bay.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
111
Cross ripples
Although the mean value indicated net onshore sediment flux over cross ripples at the swell
frequency band (Fig. 5.7), both onshore and offshore net fluxes were experienced at
different locations. This was shown by the relatively large standard error.
The cross-shore sediment flux over cross ripples due to swell waves at different locations
varied between onshore and offshore. The co-spectra between u and c, calculated over
cross ripples at six locations, are presented in Fig. 5.18. Onshore sediment flux at the swell
frequency band is observable in Figs 5.18a, b, and f; predominantly offshore flux,
demonstrating the variability in the direction of suspended sediment flux, is apparent in
Figs 5.18c, d, and e.
The cross ripples consisted of large, primary and small, secondary ripples, which were
orthogonal to each other and oblique to the wave propagation direction by approximately ±
450 (Fig. 5.2). The ripple geometry of cross ripples is presented in Table 5.2. At most
locations, the ripple steepness was greater than 0.1 and hence could be considered vortex
(Osborne and Vincent, 1993). However, no trend could be found between the direction of
cross-shore sediment flux and the ripple parameters.
The combined effect of larger, primary ripples and smaller, secondary ripples could
possibly affect this high variability in the direction of cross-shore sediment flux. Further,
the positioning of the instruments relative to primary and secondary ripples that are
orthogonal to each other could also explain this high variability.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
112
−2
0
2
4
onshore
offshore
(a)x10−4
−1
0
1
2
onshore
offshore
(b)x10−3
−4
−2
0
2onshore
offshore
(c)x10−3
−12
−8
−4
0
4
Co−
spec
trum
u−
c (m
s−1 (g
l−1 ).
s)
onshore
offshore
(d)x10−4
−3
−2
−1
0
1onshore
offshore
(e)x10−3
0 0.05 0.1 0.15 0.2−8
−4
0
4
8
onshore
offshore
(f)
x10−4
Frequency (Hz) Figure 5.18: Co-spectrum between cross-shore current velocity (u) and suspended sediment
concentration (c0.05) at a) cross-shore location no. 2 at Port Beach1; b) location no. 4 at
Eagle Bay; c) location no. 1 at Warnbro Sound; d) location no. 2 at Safety Bay; e) location
no. 1 at Jurien Jetty; f) location no. 4 at South Pinneroo.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
113
Primary ripples Secondary ripples
Location η
(cm)λ (cm) η⁄λ
η
(cm)
λ
(cm) η⁄λ
Eagle Bay 2 11 57 0.19 4 15 0.27
Eagle Bay 4 8.5 50 0.17 4 15 0.27
Warnbro Sound 1 5.5 25 0.22 3.5 8 0.44
Warnbro Sound 4 8 26 0.31 3.5 13 0.27
Safety Bay 2 1.75 17.5 0.1 1.5 10 0.15
Port-2 2 5.5 45 0.12 3.5 8.5 0.41
North Boulanger point 3 4 17.5 0.23 2 8 0.25
Jurien Jetty 1 4 35 0.11 1 15 0.07
Table 5.2: Measurement location, ripple height (η), ripple length (λ), and ripple steepness
(η⁄λ) for primary and secondary ripples of cross ripples.
5.4 Implications
Sediment re-suspension and its relationship both temporally and spatially to the near bed
oscillatory flow significantly influenced by the type of ripples present (Nielsen, 1979;
Osborne and Vincent, 1993, 1996). This may result in the direction of suspended sediment
flux due to incident swell waves over different ripple types to change (Osborne and
Greenwood, 1992; Brander and Greenwood, 1993; Davidson et al., 1993). There is,
however, only a limited number of field observations which examined the sediment re-
suspension and flux over different ripple types (Brander and Greenwood, 1993; Osborne
and Vincent, 1993, 1996). This study investigated the sediment re-suspension and cross-
shore flux in the frequency domain over six different bed conditions in a low energy
environment. Ripples appeared to significantly alter both sediment suspension and flow
field close to the seabed. The direction of suspended sediment flux at the swell frequency
band showed a strong dependence on the ripple type. Here, the suspended sediment flux
was consistently onshore over flat beds, 2D and 2D/3D ripples whilst it was offshore over
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
114
post-vortex ripples and 3D ripples. In the case of cross ripples, the direction of transport
was inconsistent. This supports the speculation made in chapter 4 that ripples are the most
likely influence controlling the direction of cross-shore suspended sediment flux.
A summary of the variation in cross-shore sediment flux over different bed types and
possible reasoning is presented in Table 5.3.
Bed type Direction of sediment flux
due to swell waves
Process
Flat bed Onshore Increased velocity skewness
Post-vortex ripples Offshore Asymmetry in diffusive
suspension (see Fig. 5.11)
2D ripples Onshore Timing of flow and vortex
ejection (see Fig. 5.14)
2D/3D ripples Onshore Same as for 2D ripples
3D rippled Offshore Low wave asymmetry in
onshore direction
Cross ripples Onshore/offshore Combined effect of primary
and secondary ripples
Table 5.3. A summary of the direction of suspended sediment flux at swell frequency band
over different bed configurations and possible reasoning
The measurements presented in this study were conducted at low energy beaches. Low
energy conditions made the measurement process much easier and the different ripples
types could be observed in relatively shallow water. Under high energy conditions the
seabed would most probably be flat under similar water depths. Recent developments of
acoustic instruments, etc. (Hay and Mudge, 2005; Hay and Bowen, 1994a) would, however,
make the measurements less labourious and it is interesting to know these patterns (Table
5.3) would remain the same under high energy conditions.
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
115
5.5 Concluding remarks
The field measurements and numerical modeling studies conducted under Chapters 3 and 4
of this study suggested that bed ripples can be the most influencing factor in changing the
direction of suspended sediment flux due to incident swell waves. Thus this chapter
investigated the suspended sediment flux over number of different ripple types with the
help of a series of field experiments. The field experiments undertaken in low energy
beaches in south-western Australia in the presence of different bed conditions: flat bed,
post-vortex ripples, 2D ripples, 2D/3D ripples, 3D ripples, and cross ripples; revealed the
following:
• The mobility number (ψ1/10) based on highest one-tenth of orbital velocities can be
used to delineate between flat bed and post-vortex ripples. Flat bed conditions were
observed when the mobility number was ψ1/10 > 100 whilst post-vortex ripples were
present when 50 < ψ1/10 < 140. No clear boundaries in the mobility number were
observed when ψ1/10 < 50 and thus could not distinguish other ripple types
• 2D ripples were observed in the presence of coarser grains (d50 > 0.35 mm). All
other ripple types were observed when d50 < 0.35 mm but without any distinct
pattern.
• Higher suspended sediment concentration values were observed when the ripple
steepness was higher (η/λ > 0.15), possibly due to the ejection of sand by the
vortices formed in the leeside of the ripples. Suspended sediment concentration was
relatively low when η/λ < 0.15.
• The net cross-shore suspended sediment flux close to the seabed (~0.05 m) at the
swell frequency band varied depending on configuration of the sea bed. The
suspended sediment flux was consistently onshore over flat beds, 2D and 2D/3D
ripples whilst it was offshore over post-vortex ripples and 3D ripples. In the case of
cross ripples, the direction of sediment flux was inconsistent. Overall, the bed
Chapter 5: The role of ripple types on cross-shore suspended sediment flux
116
ripples appeared to have a significant influence in changing the direction of cross-
shore suspended sediment flux at the swell frequency band.
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 117
Chapter 6 Turbulent kinetic energy and sediment re-
suspension due to wave groups
6.1 Introduction
Sediment re- suspension due to shoaling waves in shallow water has been observed to occur
in an event-like manner corresponding to a range of time scales ranging from seconds (e.g.
swell, wind waves) to minutes (e.g. wave groups, infragravity waves) (Brenninkmeyer,
1976; Sternberg et al., 1984; Hanes and Huntley, 1986; Osborne and Greenwood, 1993). In
addition, sediment suspension events corresponding to wave groups caused higher
suspension events than at the incident wave frequency band (Clarke et al., 1982; Hanes and
Huntley, 1986; Huntley and Hanes, 1987; Hanes, 1991; Vincent et al., 1991; Osborne and
Greenwood, 1993; Williams et al., 2002). There have been a few explanations for the
higher suspension events observed under wave groups: (1) Vincent et al. (1991) attributed
this phenomenon to change in bed forms responding to the variability in the wave
conditions: Here, steeper ripples would be present on the sea bed when the smaller waves
of the wave group pass and these ripples would become less steep when the larger waves of
the group pass. Considering the lag in changing ripple geometry to the wave forcing, larger
waves of the wave groups would encounter steeper than expected ripples and hence cause
higher suspension events enhanced by sand-laden vortices formed in the leeside of the
ripples (Vincent et al., 1991); (2) Villard and Osborne (2002) suggested the effect of
antecedent waves could lead to coupling between antecedent and developing vortices above
a rippled bed and hence cause higher suspension events. Villard and Osborne (2002)
further noticed that these suspension events were more pronounced when smaller waves
followed larger waves; (3) Hanes and Huntley (1986) and Osborne and Greenwood (1993)
related the higher suspension events coinciding with wave groups which suspended
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 118
sediments higher in the water column to the persistence of turbulence. They suggested that
turbulence generated at the seabed by the larger waves of wave groups persisted longer and
caused higher suspension events. They did not, however, measure the turbulence
characteristics of the flow; (4) Hay and Bowen (1994a) suggested that higher suspension
events observed at wave group frequency could be a result of more than one action .i.e.
several mechanisms could be operating at the same time which are not mutually exclusive.
Hay and Bowen (1994a) proposed that vortex shedding from mega ripples, enhanced
interaction with the seabed during larger waves of the wave groups; perhaps via group
bound long wave, and coherent structures in combined flow turbulence as possible reasons;
and, (5) Hay and Bowen (1994b) suggested bed forms, surface-injected vortices, and the
sensor support structure as possible reasons for pumping up of sediments into the water
column observed at the wave group frequency. Hay and Bowen (1994a), however,
suggested that keeping the sensors 5-10 diameters from the nearest support would minimise
the risk of supporting structure’s influence.
Higher suspension events co-incident with the passing of wave groups, have been observed
both in the presence (Vincent et al., 1991; Osborne and Greenwood, 1993) and absence of
ripples (Hay and Bowen, 1994a; Chapter 3). Even though the turbulence generated during
the passing of wave groups can be considered one of the most likely reasons for higher
suspension events, field (or numerical) studies investigating the effect of turbulence on
higher suspension events observed under wave groups have not appeared in the literature.
6.1.1 Turbulent bursts
Sediment suspension due to incident waves have shown intermittent spikes which do not
correspond to wave orbital velocity (Jaffe et al., 1984; Huntley and Hanes, 1987; Hanes,
1988; Smyth and Hay, 2003) suggesting possible influence of turbulence generated at the
seabed. Intermittent coherent events of strong turbulence production and vertical transfer
inside the bottom boundary layer have been widely observed under different flow
conditions (Corino and Brodkey, 1969; Gordon, 1974; Heathershaw, 1974; Clarke et al.,
1982; Thorne et al., 1984; Smyth et al., 2002; Smyth and Hay, 2003; Foster et al., 2006).
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 119
This process of coherent turbulent structure formation is sometimes called “bursting
phenomenon” (Heathershaw, 1974; Gordon and Witting, 1977; Cantwell, 1981; Soulsby,
1983). These coherent events of turbulence were studied based on Reynolds stress term (-
ρu’w’) by dividing the motions into quadrants in u’-w’ space (e.g. Soulsby, 1983), where u’
is the horizontal component of turbulent velocity and w’ is the vertical component.
Quadrants were named bursts (u’<0, w’>0), sweeps (u’>0, w’<0), up-accelerations (u’>0,
w’>0), and down-decelerations (u’<0, w’<0) (Soulsby, 1983).
Bursts and sweeps, which contribute to positive Reynolds stress, were stronger than up-
accelerations and down-decelerations (Soulsby, 1983; Heathershaw and Thorne, 1985).
Bursts, which consisted of low-speed upward momentum transfer and sweeps, which
consisted of high-speed downward momentum transfer have been observed suspending bed
sediments higher up into the water column (Sutherland, 1967; Jackson, 1976; Sumer and
Oguz, 1978; Sumer and Deigaard, 1981).
All these investigations involving “bursting phenomenon”, however, were conducted with
steady flows or slowly oscillating flow conditions with longer periods (e.g. tides). The
difficulties involved in investigating “bursting phenomenon” under wind generated surface
waves were explained by Jackson (1976), Sleath (1970; 1974a; b). Under wind driven
surface waves the mean values of the flow parameters would not remain sensibly constant
during turbulent bursts and during the time scale of the largest turbulent eddies (Jackson,
1976). Further, high oscillating flows would not provide sufficient time to make reasonable
measurements, especially of vortex formation and sudden jets in laminar boundary layer
Sleath (1970; 1974a; b). These observations were made prior to the development of
modern instruments such as Acoustic/Laser Doppler Velocimeters (Kos'yan et al., 2003;
Aagaard and Hughes, 2006), hot film anemometers (Conley and Inman, 1992), Coherent
Doppler Profilers (Smyth and Hay, 2003). With the advent of these instrumentations,
turbulence measurements can be made on a more routine basis at present. It should,
however, be noted that authors are not aware of studies conducted investigating the
“bursting phenomenon” under swell waves.
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 120
Moreover, Madsen (1974) reported that “explosion” like events were observed on seabed
by divers. Hay and Bowen (1994a) suggested that coherent structures in combined flow
turbulence as a possible cause for higher suspension events observed at wave group time
scales. Clarke et al. (1982) also suggested that bursts of intense turbulence coherent with
peak values of wave orbital velocity caused higher suspension events. These observations
put forward the obvious presence of turbulent bursts at the seabed under swell waves and
therefore it is interesting to explore the possible presence of “bursting phenomenon” close
to the seabed.
This paper presents a high frequency (16 Hz) turbulent velocity data set recorded
simultaneously with the water surface elevation, cross-shore current velocity, and
suspended sediment concentration close to the seabed (0.05 m), under shoaling, non-
breaking waves. Swell dominated conditions prevailed during the measurement period
where pronounced wave groups were present.
The primary objective of this study was to investigate the relationship between turbulent
kinetic energy and the increased sediment suspension events occurring under wave groups.
The turbulence measurements were analysed to investigate the intermittent nature of
turbulence generation and sediment suspension. Finally, an attempt was made to explore
the possible signs of “bursting phenomenon” under swell waves.
6.2 Methodology
6.2.1 Field site and conditions
Measurements were conducted at Floreat Beach, Perth, Western Australia (Fig. 6.1) on 16th
of December 2003. This area experiences diurnal, micro tidal conditions with a spring tidal
range of 0.6 m. Floreat Beach is a long straight exposed beach where waves were not
refracted by nearshore reefs or coastal/offshore structures. An offshore bar was not present.
The beach was relatively steep (Fig. 6.2) with reflective conditions where the waves were
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 121
breaking almost on the beach face leaving a narrow surf zone. The median grain diameter
(d50) at the measurement site was 0.2 mm.
10
Rottnest Island
20
20
10
30
20
10
10
20
20
20
10
20
0 5 10 km
30
20
Perth
Fremantle
NBroome
Perth
WESTERNAUSTRALIA
FloreatBeach
Figure 6.1: Location map (Floreat Beach, Perth, Western Australia).
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 122
0 5 10 15 20 25 30−1.5
−1
−0.5
0
0.5
1
1.5
Cross−shore distance (m)
Ele
vatio
n re
lativ
e to
MS
L (m
)
instrument station
MWL
Figure 6.2: Instrument deployment location and beach profile.
The instrument station was deployed just outside the breaker line at a mean water depth of
1.2 m (Fig. 6.2). The data recording was started at around 10:00 hrs under swell dominated
conditions (peak period = 14s) and was terminated around 11:15 hrs with the onset of sea
breeze (the sea breeze modified the narrow banded swell dominated conditions). The
significant wave height was 0.9 m with rms wave height of 0.65 m. The boundary layer
thickness estimated using Madsen (1993) method was 0.03 m suggesting that turbulent
velocity and suspended sediment concentration were measured just outside the wave
boundary layer (see below).
6.2.2 Instrumentation
Hydrodynamic and suspended sediment concentration measurements were collected using
an array of instruments mounted on a triangular frame (SW-probe) developed at the
University of Western Australia. Instruments included a Paroscientific Digiquartz pressure
sensor (0.35 m above the bed), a Marsh-McBirney (model 512 OEM) electromagnetic
water current meter (0.20 m above the bed), an optical backscatter (OBS-3) turbidity sensor
(0.05 m above the bed), and a NORTEK AS VECTOR Acoustic Doppler Velocimeter
(ADV, with the measurement volume at 0.05 m above the bed). The pressure sensor,
electromagnetic current meter, and OBS sensor measured water surface elevation, 2-D
horizontal current velocities, and suspended sediment concentration, respectively, at 2 Hz.
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 123
Where as the ADV measured three components of velocity fluctuations at a sampling
frequency of 16 Hz.
6.2.3 Data analysis techniques
A data set of duration 2048 s (~35 mins) was used for the analysis presented here. The
number of data points used from the ADV was 32768 and from the other instruments was
4096 each. The wave groupiness envelope was computed by low–pass filtering the
modulus of the cross-shore current velocity record at 0.02 Hz as explained by List (1991).
Spectral analysis was conducted using digital Fourier transforms (Bendat and Piersol,
1986). The data records were divided into 8 equal segments for the segment average
method with 50% overlapping (Bendat and Piersol, 1986). A cosine taper window was
applied and the number of degrees of freedom was 32. The 95% confidence interval
calculated for all the spectra presented in this paper indicated that the upper and lower
confidence limits were 1.75 and 0.65 times the spectral estimates, respectively.
Inertial subrange of turbulence
The high frequency (16 Hz) velocity measurements of the ADV were used to estimate
turbulent velocity fluctuations. Time series records of turbulent velocities were used to
obtain the frequency (f) spectra and the f spectra were then converted to wave number (k)
spectra following the Taylor’s hypothesis of “frozen turbulence” (Soulsby, 1983),
( ) ( ) ( )fEzUkEπ2
= (6.1)
where E(k) is the wave number spectra, U(z) is the mean velocity at z distance from the
seabed, and E(f) is the frequency spectra. This is assumed to be valid when k is equal or
larger than either 2π/z, or the highest significant incident wave number seen in the velocity
spectra (Huntley and Hazen, 1988). Inertial subrange corresponds to the range of wave
numbers where the spectral slope was -5/3.
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 124
10−1 100 101 102 10310−2
10−1
100
101
102
103
E(k
) (m
3 /s2 )
k (m−1)
(a)
95%
10−1 100 101 102 10310−3
10−2
10−1
100
101
102
k (m−1)
(b)
95%
Figure 6.3: Wave number spectra of: a) horizontal cross-shore velocity (u); b) vertical
velocity (w).
Turbulent energy corresponding to the inertial subrange were observed between
approximately 30 < k < 110 m-1 (Fig. 6.3). Beyond this range the signals appeared to
contain higher levels of noise and therefore were discarded. The spectral slope of the
inertial subrange was 1.63 (approximately -5/3) for u (Fig. 6.3a); it was 1.31 for w (Fig.
6.3b). The -5/3 spectral slope has not been generally found in measurements close to
seabed (Hino et al., 1983; George et al., 1994; Smyth et al., 2002; Smyth and Hay, 2003)
especially for the vertical component (Smyth et al., 2002). Turbulence generated by
irregular waves over a mobile bed may be anisotropic (Smyth and Hay, 2003).
Corresponding frequency spectra showed that inertial subrange lay between 0.5 Hz and 3
Hz.
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 125
For turbulence analysis the velocity signals were high-pass filtered with a cutoff frequency
of 0.5 Hz and low-pass filtered with a cutoff frequency of 3 Hz. Numerical filters were
designed using Fast Fourier Transform techniques (Bendat and Piersol, 1986). High-pass
cut-off frequency was much larger than the incident wave frequency (0.07 Hz) and
therefore the filtering process adopted during this study removed most of the incident wave
band energy from the original data record.
Turbulent Kinetic Energy (TKE)
Time series of TKE was estimated using the three components of turbulent velocity (u’ –
cross-shore, v’ – longshore, and w’ – vertical) at the inertial subrange,
( )2225.0 wvuTKE ′+′+′= (6.2)
Turbulent Reynolds stress
Turbulent Reynolds stress values were estimated by,
wu ′′−= ρτRe (6.3)
where ρ is the density of the fluid. Since, no quantitative analysis of Reynolds stress was
undertaken in this study, turbulent Reynolds stress was represented by the term u’w’.
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 126
6.3 Results and discussion
6.3.1 Sediment suspension under wave groups
The role of wave groupiness on sediment re-suspension was investigated by comparing
time series records of the wave groupiness envelope, cross-shore current velocity and
suspended sediment concentration. The time series records of cross-shore current velocity
(u) at 0.2 m from the seabed (Fig. 6.4a) and the suspended sediment concentration (c) at
0.05 m from the seabed (Fig. 6.4b) showed a significant correspondence between wave
groups and the suspended sediment concentration (Hanes and Huntley, 1986; Huntley and
Hanes, 1987; Hanes, 1991; Vincent et al., 1991; Osborne and Greenwood, 1993; Chapter
4).
6.3.2 Spectral analysis between u and c
The spectral analysis results for time series of u (0.2 m from the seabed) and c (0.05 m from
the seabed) is presented in Fig. 6.5. It is widely accepted that the horizontal velocities
under oscillatory flow in shallow water remain constant over the depth (Huntley and Hanes,
1987; Aagaard and Greenwood, 1995; Foote et al., 1998).
The auto-spectrum of u showed a dominant peak at 0.07 Hz (~14 s) showing swell
dominated conditions (Fig. 6.5a). Minor peaks were observed at the first harmonic of the
swell frequency band and at low frequencies. The auto-spectrum of c showed a dominant
peak at low frequencies confirming higher sediment concentrations due to wave groups
(Fig. 6.5b).
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 127
−3
−1.5
0
1.5
3
u (m
/s)
(a)
0
10
20
30
c (g
/l)
(b)
0 400 800 1200 1600 20000
0.1
0.2
0.3
0.4
TK
E (
m2 s−
2 )
(c)
time (s)
Figure 6.4: Time series records of: a) cross-shore current velocity (u); b) suspended
sediment concentration (c); and c) turbulent kinetic energy (TKE). Thick solid lines show
the envelope function of u (Fig. 6.4a), low-pass filtered c (Fig. 6.4b), and low-pass filtered
TKE (Fig. 6.4c), respectively.
The co-spectrum between u and c (Fig. 6.5c) was in agreement with the original findings by
Huntley and Hanes (1987) for shoaling, non-breaking waves in shallow water: onshore flux
at the incident frequency band and offshore flux at low frequencies corresponding to wave
groups. The onshore flux at the incident band was attributed to the increased wave/velocity
skewness towards the wave propagation direction (Doering and Bowen, 1988; Osborne and
Greenwood, 1992); offshore flux at low frequencies was due to the combined action of
wave groups and group bound long wave (Larsen, 1982; Shi and Larsen, 1984). Moreover,
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 128
a minor offshore sediment flux component was present at the first harmonic of the incident
frequency band.
0 0.05 0.1 0.15 0.20
1
2
3
Aut
o−sp
ectr
um (
u)
x104
(a)
0 0.05 0.1 0.15 0.20
2
4
6
Aut
o−sp
ectr
um (
c)
x105
(b)
0 0.05 0.1 0.15 0.2−0.08
−0.04
0
0.04
0.08
Co−
spec
tral
den
sity
onshore
offshore
(c)
Frequency (Hz)
Figure 6.5: Results of spectral analysis between u and c: a) auto-spectrum of u; b) auto-
spectrum of c; and c) u-c co-spectrum in (gl-1)(ms-1)Hz-1.
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 129
6.3.3 Turbulent Kinetic Energy (TKE)
Time series record of TKE is presented in Fig. 6.4c along with cross-shore current velocity
(Fig. 6.4a) and suspended sediment concentration, c (Fig. 6.4b). The data series indicate
that the TKE increased with the passing of wave groups together with the suspended
sediment concentration (c).
This was further investigated by calculating the cross-correlation between low-pass filtered
TKE (TKElow) and low-pass filtered clow (Fig. 6.6). The cutoff used for low-pass filtering
was 0.02 Hz. A strong positive correlation can be seen with clow lagging TKElow by
approximately 15s. i.e. the peak in suspended sediment concentration occurred
approximately one wave period after the peak in TKE.
−100 −75 −50 −25 0 25 50 75 100−0.4
−0.2
0
0.2
0.4
0.6
lag (s)
cros
s−co
rrel
atio
n (T
KE
low
− c
low
)
Figure 6.6: Cross-correlation between lowpass filtered turbulent kinetic energy (TKE) and
lowpass filtered suspended sediment concentration (c).
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 130
−1
−0.5
0
0.5
1
η (m
)
(a)
−0.1
−0.05
0
0.05
0.1
u’w
’ (m
2 s−2 ) (b)
0
0.1
0.2
0.3
0.4
TK
E (
m2 s−
2 ) (c)
600 700 800 9000
10
20
30(d)
c (g
/l)
time (s)
Figure 6.7: Time series records of: a) water surface elevation, η (solid line) and envelope
function of η (thick solid line); b) turbulent Reynolds stress (u’w’); c) turbulent kinetic
energy (TKE); and d) suspended sediment concentration (c) for a wave group observed
between 600 s and 900 s. Note: The setting of the maximum voltage for the OBS was not
sufficient to capture the maximum suspended sediment concentrations occurred between
700 and 730 s.
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 131
The relationship between turbulent kinetic energy (TKE) and sediment suspension during a
single wave group from 600 s to 900 s was examined in detail (Fig. 6.7). Variation of
water surface elevation (Fig. 6.7a), turbulent Reynolds stress term (Fig. 6.7b), TKE (Fig.
6.7c), and c0.05 (Fig. 6.7d) are presented. TKE was negligible at the beginning of the wave
group (Fig. 6.7b) and increased markedly as the wave group approached, especially when
the incident wave height was increasing (Fig.s 6.7b & c). Then the TKE reduced gradually
whilst the incident wave height remained almost constant. Similarly, towards the end of the
wave group, the TKE again showed an increase with a change in incident wave height.
Suspended sediment concentration followed the same pattern: increased suspended
sediment concentration values were observed with the increased turbulent intensity with a
lag of 1 – 2 wave cycles (Fig. 6.7d).
A similar pattern was observed for the wave group which spanned between 950 s and 1100
s (Fig. 6.8). At the beginning there was almost no TKE and no suspended sediments.
However, when the incident wave height started to increase as the wave group approached
(Fig. 6.8a), the TKE increased (Fig.s 6.8b & c) followed by the suspended sediment
concentration (Fig. 6.8d). The same trend was observed with the wave group observed
between 80 s and 240 s (Fig. 6.9) and other wave groups in the data record.
These observations suggested that changes in incident wave height (or energy) as wave
groups approached resulted in higher TKE and caused higher sediment suspension events.
TKE was higher when the incident wave height was changing (increasing) than when it was
constant irrespective of the magnitude of the wave height. Suspended sediment
concentration lagged the TKE by ~1 wave period. Note that the suspended sediment
concentration measurements were obtained 0.05 m from the seabed. It is not possible to
comment on the turbulence propagation or sediment suspension higher up in the water
column as both quantities were measured at a single height (0.05 m from the seabed).
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 132
−1
−0.5
0
0.5
1
η (m
)
(a)
−0.1
−0.05
0
0.05
0.1
u’w
’ (m
2 s−2 ) (b)
0
0.1
0.2
0.3
0.4
TK
E (
m2 s−
2 ) (c)
950 1000 1050 11000
10
20
30(d)
c (g
/l)
time (s)
Figure 6.8: Time series records of: a) water surface elevation, η (solid line) and envelope
function of η (thick solid line); b) turbulent Reynolds stress (u’w’); c) turbulent kinetic
energy (TKE); and d) suspended sediment concentration (c) for a wave group observed
between 950 s and 1100 s.
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 133
−1
−0.5
0
0.5
1
η (m
)
(a)
−0.1
−0.05
0
0.05
0.1
u’w
’ (m
2 s−2 ) (b)
0
0.1
0.2
0.3
0.4
TK
E (
m2 s−
2 ) (c)
80 120 160 200 2400
10
20
30(d)
c (g
/l)
time (s)
Figure 6.9: Time series records of: a) water surface elevation, η (solid line) and envelope
function of η (thick solid line); b) turbulent Reynolds stress (u’w’); c) turbulent kinetic
energy (TKE); and d) suspended sediment concentration (c) for a wave group observed
between 80 s and 240 s.
At the incident wave scale, turbulent Reynolds stress (u’w’) showed intermittent bursts
while these bursts sometimes appeared to coincide with the wave trough where the cross-
shore velocity was at offshore maximum (Fig.s 6.9b & 6.10b). Foster et al. (2006) also
observed highly intermittent generation of near-bed turbulence under shoaling non-
breaking waves in shallow water. In this study, the sediment suspension observations
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 134
indicated an intermittent structure coinciding with the onshore decelerating phase of the
flow (Fig. 6.8a & d) similar to that of Foster et al. (2006). Intermittent Reynolds stress
(u’w’) observed in this study, however, did not always result in suspension events (Fig.s 6.8
& 9).
−0.1
−0.05
0
0.05
0.1
u’w
’ (m
2 s−2 )
(a)
burstsweep
730 750 770 7900
10
20
30(b)
c (g
/l)
time (s) Figure 6.10: Time series records of: a) turbulent Reynolds stress (u’w’); and b) suspended
sediment concentration (c) between 730 s and 790 s.
6.3.4 Bursting phenomenon
A brief description of “bursting phenomenon” and the difficulties involved in its
measurements under swell waves was presented in the introduction (section 6.1.1). Results
of the present study showed the intermittent nature of the turbulent bursts, whilst higher
Reynolds shear stress values were observed under burst and sweep events (negative u’w’)
than under up-acceleration and down-deceleration events (positive u’w’) (Fig.s 6.7b, 6.8b,
& 6.9b). Time series records of u’w’ and suspended sediment concentration for a 60 s
period are presented in Fig. 6.10. Major burst and sweep events accounted for only 3 s out
of 60 s (5%) but they contributed for approximately 60% of the turbulence production.
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 135
Similar results have been observed under flow conditions which were different to swell
waves (Gordon, 1974; Heathershaw, 1974; Soulsby, 1983). It should, however, be
mentioned that in this study the turbulent velocity measurements were obtained just outside
the wave boundary layer.
Higher suspension events, however, were not always observed with bursting or sweeping
events associated with high Reynolds stresses (Fig. 6.10). It is possible that larger
Reynolds stresses did not necessarily cause higher suspension events.
6.4 Concluding remarks
A set of high frequency (16 Hz) turbulent velocity measurements obtained simultaneously
with suspended sediment concentration, cross-shore current velocity, and water surface
elevation at Floreat Beach (Perth, Western Australia) were analysed to investigate: effects
of turbulent kinetic energy on higher suspension events caused by wave groups;
intermittent nature of bottom turbulence production and sediment suspension; and the
“bursting phenomenon” (Heathershaw, 1974).
The field data indicated that the Turbulent kinetic energy (TKE) increased with the increase
in incident wave height associated with the passage of a wave group. The TKE was higher
when the incident wave height was increasing than when it was constant irrespective of the
magnitude of the wave height. The higher TKE also resulted in higher sediment suspension
events. It is concluded that the increase in TKE due to the changing wave heights
associated with wave groups results in increased sediment re-suspension.
Turbulent Reynolds stress (u’w’) indicated intermittent high bursts whilst sometimes they
appeared to coincide with the wave trough. The sediment suspension observations showed
an intermittent structure coinciding with the onshore decelerating phase of the flow.
Intermittent turbulent bursts, however, did not always caused higher suspension events
suggesting that larger Reynolds stresses did not necessarily cause higher suspension events.
Chapter 6: Turbulent kinetic energy and sediment re-suspension due to wave groups 136
Reynolds stress (u’w’) term was dominated by short but intense burst and sweep events
suggesting the presence of the “Bursting phenomenon”. Burst events, in the meantime,
resulted in higher suspension events more often than sweep events. More detailed
measurements, however, would be necessary to confirm this.
Chapter 7: Discussion and conclusions 137
Chapter 7 Discussion and conclusions
This thesis investigated sediment re-suspension and cross-shore suspended sediment flux
under different frequency components in nearshore regions through a series of field
measurements undertaken at different locations and a numerical model. Field
measurements were conducted at a variety of locations in Western Australia and Sri Lanka
under swell dominated conditions where pronounced wave groups were present.
Cross-shore sediment flux in the frequency domain
The direction and magnitude of suspended sediment flux close to the seabed in the
frequency domain was observed to be highly variable under different conditions. This
inconsistency was attributed to many different governing factors such as bed ripples, cross-
shore location with respect to the breaker line, median grain size, etc by the past
researchers. However, the relative significance of above mentioned factors is of great
interest as they all can influence cross-shore suspended sediment flux simultaneously.
Nonetheless, there was much to be investigated in terms of the processes. The primary
objective of this study was to investigate the factors governing the direction and magnitude
of cross-shore suspended sediment flux in the frequency domain; following conclusions
were drawn.
The suspended sediment flux under shoaling, non-breaking waves over a flat bed was
always in agreement with the original finding by Huntley and Hanes (1987): onshore under
incident waves and offshore under low frequency waves corresponding to wave groups.
However, under the presence of ripples the direction was found to be more variable.
Although many different factors such as cross-shore location with respect to the breaker
line, significant wave height to water depth ratio (Hs/h), normalised horizontal velocity
skewness (‹u3›⁄‹u2›3⁄2), grain size (d50), wave breaker type, and wave groupiness appeared to
Chapter 7: Discussion and conclusions 138
influence the cross-shore suspended sediment flux, it is concluded that bed ripple type to be
the major contributing factor in changing the direction of suspended sediment flux due to
swell waves. Suspended sediment flux at low frequencies corresponding to wave groups
was offshore outside the surf zone, but varied inside the surf zone.
Sediment re-suspension under wave groups
Sediment suspension events under wave groups have been observed to be more pronounced
than that under incident waves and this was observed throughout this study and in the past
over both rippled and flat beds. Persistence turbulence caused by the larger waves of the
wave groups has been attributed as a major contributor for this. However, no literature
could be found on field measurements investigating this phenomenon. Under this study a
set of high frequency velocity records were obtained close to the seabed to study the effect
of flow generated turbulent kinetic energy (TKE) on higher sediment suspension events
observed under wave groups. It was observed that higher TKE was generated at the seabed
by approaching wave groups and increased TKE caused higher suspension events.
In addition to the major findings described above, following conclusions were drawn from
this study;
The net cross-shore suspended sediment flux due to swell waves was onshore when the
Dean number was less than 1.67 and was offshore when the Dean number was greater than
1.67. This is interesting as the Dean number (Dean and Dalrymple, 2002) does not account
for the influence of ripples or wave asymmetry.
The mobility number (ψ1/10) based on highest one-tenth of orbital velocities appeared to
have a major control in determining the type of ripples present. Flat bed conditions were
observed when the mobility number was highest (ψ1/10 > 100) whilst post-vortex ripples
were observed when 50 < ψ1/10 < 140. No clear difference in mobility number was
observed over other ripple types (ψ1/10 < 50). 2D ripples were observed when the median
grain size (d50) was greater than 0. 35 mm; all other ripple types were observed when d50 <
0.35 mm but without any distinct pattern. Highest one-third of suspended sediment
Chapter 7: Discussion and conclusions 139
concentration (ssc) at 0.05 m from the seabed was greater over steeper ripples (ripple
steepness, η⁄λ > 0.15), possibly due to the ejection of sand-laden vortices in the leeside of
the ripples. Where as ssc was relatively low when η⁄λ < 0.15.
Both near bed turbulence and sediment suspension showed intermittent burst events.
Turbulent Reynolds stress (u’w’) term was dominated by fairly short but intense burst and
sweep events suggesting a possible presence of “Bursting phenomenon” (Heathershaw,
1974; Cantwell, 1981; Soulsby, 1983).
7.1 Future work
There are several avenues of research that would compliment the results described here.
The measurements presented in this thesis over different ripple types were mainly
conducted at low energy beaches. Low energy conditions made the measurements process
less demanding and different ripple types were present in relatively shallow water. Under
high energy conditions the seabed would often be flat under similar water depths. With
recent developments in acoustic instruments, etc (Hay and Bowen, 1994; Hay and Mudge,
2005), however, the measurements including bed topography records in relatively deep
waters are less hard-won. Therefore, it would be interesting to investigate whether the
trends observed under low energy conditions would remain the same under high energy
conditions.
At present, there are detailed numerical models developed to simulate flow and sediment
suspension patterns over rippled beds (Davies and Villaret, 1999; Zedler and Street, 2001;
Barr et al., 2004; Davies and Thorne, 2005; Eidsvik, 2006). Investigating the direction and
magnitude of suspended sediment flux with a numerical model which simulated the flow
deformation due to the presence of ripples would give further insight into the observations
made under this study. This could include the presence of different ripple types defined in
this thesis.
Chapter 7: Discussion and conclusions 140
No studies could be found in literature investigating “bursting phenomenon” under swell
waves. Even though this had been considered rather unyielding in the past (Sleath, 1970,
1974a, b; Jackson, 1976), recent development of acoustic Doppler instruments and hot film
anemometers (Conley and Inman, 1992; Foster et al., 2000; Smyth et al., 2002; Smyth and
Hay, 2003; Aagaard and Hughes, 2006; Foster et al., 2006), has made turbulent
measurements inside the wave boundary layer much less demanding and it would be
interesting to investigate whether the observations made during this study were indicating a
presence of “bursting phenomenon” under a range of wave (random) conditions.
References 141
References
Aagaard, T., and Greenwood, B. (1995). Suspended sediment transport and morphological
response on a dissipative beach. Continental Shelf Research, 15 (9): 1061-1086.
Aagaard, T., and Hughes, M.G. (2006). Sediment suspension and turbulence in the swash
zone of dissipative beaches. Marine Geology, 228: 117-135.
Aagaard, T., Nielsen, J., and Greenwood, B. (1998). Suspended sediment transport and
nearshore bar formation on a shallow intermediate-state beach. Marine Geology,
148: 203-225.
Bagnold, R.A. (1946). Motion of waves in shallow water. Interaction between waves and
sand bottoms. Proc. Royal Soc. London, A187: 1-15.
Bagnold, R.A. (1966). An approach to the sediment transport problem from general
physics. 422-I.
Bailard, J.A. (1981). An energetics total load sediment transport model for a plane sloping
beach. Journal of Geophysical Research, 86 (C11): 938-954.
Bailard, J.A., and Inman, D.L. (1979). A re-exmaination of Bagnold's granular-fluid model
and bedload transport equation. Journal of Geophysical Research, 84 (C12): 7827-
7833.
Barr, B.C., Slinn, D.N., Pierro, T., and Winters, K.B. (2004). Numerical simulation of
turbulent, oscillatory flow over sand ripples. Journal of Geophysical Research, 109
(C09009): doi: 10.1029/2002JC001709.
Bendat, J.S., and Piersol, A.G. (1986). Random Data: Analysis and measurement
procedures. Wiley-Interscience.
Brander, R.W., and Greenwood, B. (1993). Bedform roughness and the re-suspension and
transport of sand under shoaling and breaking waves: a field study. Proc. of
Canadian Coastal Conference: 587-599.
Brenninkmeyer, B.M. (1976). In situ measurements of rapidly fluctuating, high sediment
concentrations. Marine Geology, 20: 117-128.
Cantwell, B.J. (1981). Organised motion in the turbulent flow. Annual Review of Fluid
Mechanics, 13: 457-515.
References 142
Chen, Q., Dalrymple, R.A., Kirby, J.T., Kennedy, A.B., and Haller, M.C. (1999).
Boussinesq modeling of a rip current system. Journal of Geophysical Research,
104: 20,617-20,637.
Chen, Q. et al. (2000). Boussinesq modeling of waves and longshore currents under field
conditions.
Chen, Q., Kirby, J.T., Dalrymple, R.A., Shi, F., and Thornton, E.B. (2002). Boussinesq
modeling of waves and longshore currents under field conditions. Journal of
Geophysical Research, 108 (C11): doi: 10.1029/2002JC001308.
Clarke, T.L., Lesht, R.A., Young, R.A., Swift, D.J.P., and Freeland, G.L. (1982). Sediment
resuspension by surface-wave action: An examination of possible mechanisms.
Marine Geology, 49: 43-59.
Clifton, H.E. (1976). Wave-formed sedimentary structures - a conceptual model. In:
R.A.J.a.E. Davies, R.L. (Editor), Beach and nearshore sedimentation. SEPM Spec.
Publs., pp. 126-148.
Clifton, H.E., and Dingler, J.R. (1984). Wave-formed structures and paleoenvironmental
reconstruction. Marine Geology, 60: 165-198.
Conley, D.C., and Beach, R.A. (2003). Cross-shore sediment transport partitioning in the
nearshore during a storm event. Journal of Geophysical Research, 108 (C3).
Conley, D.C., and Inman, D.L. (1992). Field observations of the fluid-granular boundary
layer under near-breaking waves. Journal of Geophysical Research, 97 (C6): 9631-
9643.
Corino, E.R., and Brodkey, R.S. (1969). A visual investigation of the wall region in
turbulent flow. J. Fluid Mechanics, 37: 1-30.
Davidson, M.A., Russell, P.E., Huntley, A.H., and Hardisty, J. (1993). Tidal asymmetry in
suspended sand transport on a macrotidal intermediate beach. Marine Geology, 110:
333-353.
Davies, A.G., and Li, Z. (1997). Modelling sediment transport beneath regular symmetrical
and asymmetrical waves above a plane bed. Continental Shelf Research, 17 (5):
555-582.
References 143
Davies, A.G., and Thorne, P.D. (2005). Modeling and measurement of sediment transport
by waves in the vortex ripple regime. Journal of Geophysical Research, 110
(C05017): doi:10.1029/2004JC002468.
Davies, A.G., van Rijn, L.C., Damgaard, J.S., Graaff, v.d., and Ribberink, J.S. (2002).
Intercomparison of research and practical sand transport models. Coastal
Engineering, 46: 1-23.
Davies, A.G., and Villaret, C. (1999). Eulerian drift induced by progressive waves above
rippled and very rough beds. Journal of Geophysical Research, 104 (C1): 1465-
1488.
Davies, A.G., and Villaret, C. (2003). Sediment transport modelling for coastal
morphodynamics. Proc. of Coastal Sediments 03.
Dean, R.G. (1973). Heuristic models of sand transport in the surf zone. Proc. of Conference
on Engineering Dynamics in the surf zone: 208-214.
Dean, R.G., and Dalrymple, R.A. (2002). Coastal Processes with Engineering
Applications. Cambridge University Press, 475 pp.
Deigaard, R., Jakobsen, J.B., and Fredsoe, J. (1999). Net sediment transport under wave
groups and bound long waves. Journal of Geophysical Research, 104 (C6): 13,559-
13,575.
Doering, J.C., and Bowen, A.J. (1988). Wave-induced flow and nearshore suspended
sediment. Proc. of 21st Intl. Conf. of Coastal Engineering: 1452-1463.
Doucette, J.S. (2000). The distribution of nearshore bedforms and effects of sand
suspension on low-energy, micro-tidal beaches in Southwestern Australia. Marine
Geology, 165: 41-61.
Drake, T.G., and Calantoni, J. (2001). Discrete particle model for sheet flow sediment
transport in the nearshore. Journal of Geophysical Research, 106 (C9): 19,859-
19,868.
Eidsvik, K.J. (2006). Large scale modelling of ascillatory flows over a rippled bottom.
Continental Shelf Research, 26: 318-337.
Elgar, S., Gallagher, E.L., and Guza, R.T. (2001). Nearshore sandbar migration. Journal of
Geophysical Research, 106 (C6): 11,623-11,627.
References 144
Elgar, S., Guza, R.T., and Freilich, M.H. (1988). Eulerian measurements of horizontal
accelarations in shoaling gravity waves. Journal of Geophysical Research, 93 (C8):
9261-9269.
Foote, Y., Russell, P.E., Huntley, D.A., and Sims, P. (1998). Energetics prediction of
frequency-dependent suspended sand transport rates on a macrotidal beach. Earth
surface processes and landforms, 23: 927-941.
Foster, D.L., Beach, R.A., and Holman, R.A. (2000). Field observations of the wave
bottom boundary layer. Journal of Geophysical Research, 105 (C8): 19,631-19,647.
Foster, D.L., Beach, R.A., and Holman, R.A. (2006). Turbulence observations of the
nearshore wave bottom boundary layer. Journal of Geophysical Research, 111
(C04011): doi:10.1029/2004JC002838.
Fredsoe, J., and Deigaard, R. (1992). Mechanics of Coastal Sediment Transport. World
Scientific, Singapore, 369 pp.
George, R., Flick, R.E., and Guza, R.T. (1994). Observations of turbulence in the surf zone.
Journal of Geophysical Research, 99: 801-810.
Gordon, C.M. (1974). Intermittent momentum transport in geophysical boundary layer.
Nature, 248: 392-394.
Gordon, C.M., and Witting, J. (1977). Turbulent structure in a benthic boundary layer. In:
J.C.J. Nihoul (Editor), Bottom turbulence. Elsevier, Amsterdam.
Grant, W.D., and Madsen, O.S. (1979). Combined wave and current interactions with a
rough bottom. Journal of Geophysical Research, 84: 1797-1808.
Grant, W.D., and Madsen, O.S. (1982). Movable bed roughness in unsteady oscillatory
flow. Journal of Geophysical Research, 87 ((C1)): 469-481.
Hanes, D.M. (1988). The significance of intermittent sediment suspension in the nearshore
region. Marine Geology, 81: 175-183.
Hanes, D.M. (1991). Suspension of sand due to wave groups. Journal of Geophysical
Research, 96 (C5): 8911-8915.
Hanes, D.M., and Huntley, D.A. (1986). Continuous measurements of suspended sand
concentration in a wave dominated nearshore environment. Continental Shelf
Research, 6 (4): 585-596.
References 145
Hay, A.E., and Bowen, A.J. (1994a). Coherence scales of wave-induced suspended sand
concentration fluctuations. Journal of Geophysical Research, 99: 12749-12765.
Hay, A.E., and Bowen, A.J. (1994b). Space-time variability of sediment suspension in the
nearshore zone. Proc. of Coastal Dunamics '94: 962-975.
Hay, A.E., and Mudge, T. (2005). Principal bed states during SandyDuck97: Occurance,
spectral anisotropy, and the bed state storm cycle. Journal of Geophysical Research,
110 (C03013): doi: 10.1029/2004JC002451.
Heathershaw, A.D. (1974). "Bursting" phenomena in the sea. Nature, 248: 394-395.
Heathershaw, A.D., and Thorne, P.D. (1985). Sea-bed noises reveal role of turbulent
bursting phenomenon in sediment transport by tidal currents. Nature, 316 (No.
6026): 339-342.
Hino, M., Kashiwayanagi, M., and Hara, T. (1983). Experiments on the turbulent statistics
and the structure of reciprocating oscillatory flows. J. Fluid Mechanics, 131: 363-
400.
Holmedal, L.E., and Myrhaug, D. (2006). Boundary layer flow and net sediment transport
beneath asymmetric waves. Continental Shelf Research, 26: 252-268.
Huntley, D.A., and Hanes, D.M. (1987). Direct measurement of suspended sediment
transport. Coastal Sediments '87, ASCE: 723-737.
Huntley, D.A., and Hazen, D.G. (1988). Seabed stresses in combined wave and steady flow
conditions on the Nova Scotia continental shelf: field measurements and
predictions. Journal of Physical Oceanography, 18 (2): 347-362.
Inman, D.L., and Bowen, A.J. (1963). Flume experiments on sand transport by waves and
currents. Proc. of 8th Intl. Conf. of Coastal Eng.: 137-150.
Jackson, R.G. (1976). Sedimentological and fluid-dynamic implications of the turbulent
bursting phenomenon in geophysical flows. J. Fluid Mechanics, 77 (3): 531-560.
Jaffe, B.E., Sternberg, R.W., and Sallenger, A.H. (1984). The role of suspended sediment
in shore-normal beach profile changes. Proc. of 19th Intl. Conf. of Coastal Eng.
Jenkins, G.M., and Watts, D.G. (1968). Spectral analysis and its applications.
Holden_Day, San Francisco, 525 pp.
References 146
Karambas, K.V., and Koutitas, C. (2002). Surf and swash zone morphology evolution
induced by nonlinear waves. J. Waterway, Port, Coastal, and Coastal Engineering,
128: 102-113.
Kennedy, A.B., Chen, Q., Kirby, J.T., and Dalrymple, R.A. (2000). Boussinesq modelling
of wave transformation, breaking, and runup. I:1D. J. Waterway, Port, Coastal, and
Ocean Engineering, 126: 39-47.
Kos'yan, R., Kunz, H., Kuznetsov, S., Podymov, I., and Pykhov, N. (2003). Research of the
basic mechanism of sand suspension by irregular waves. Proc. of COPEDEC VI.
Kularatne, S.R., and Pattiaratchi, C. (in review). Factors influencing cross-shore sediment
flux in the frequency domain. Continental Shelf Research.
Larsen, L.H. (1982). A new mechanism for seaward dispersion of midshelf sediments.
Sedimentology, 29: 279-283.
Lee, T.H., and Hanes, D.M. (1996). Comparison of field observations of the vertical
distribution of suspended sand and its prediction by models. Journal of Geophysical
Research, 101 (C2): 3561-3572.
List, J.H. (1991). Wave groupiness variations in the nearshore. Coastal Engineering, 15:
475-496.
Lofquist, K.E.B. (1978). Sand ripple growth in an oscillatory-flow water tunnel, U.S. Army
Corps of Engineers, Coastal Engineering Research Centre.
Longuet-Higgins, M., and Stewart, R. (1962). Radiation stress and mass transport in gravity
waves, with application to 'surf beats'. J. Fluid Mechanics, 13: 481-504.
Longuet-Higgins, M., and Stewart, R. (1964). Radiation stresses in water waves: a physical
discussion, with applications. Deep Sea Research, 11: 529-562.
Ludwig, K., and Hanes, D.M. (1990). A laboratory evaluation of optical backscatterance
suspended solids sensors exposed to sand mud mixtures. Marine Geology, 94: 173-
179.
Madsen, O.S. (1974). Stability of a sand bed under breaking waves. Proc. of 14th Intl.
Conf. of Coastal Engineering: 776-794.
Madsen, O.S. (1993). Sediment transport on the shelf. Draft document, Ralph M. Parsons
Laboratory, Massachusetts Institute of Technology, Cambridge, M.A.
References 147
Madsen, P.A., Murray, R., and Sorenson, O.R. (1991). A new form of Boussinesq
equations with improved dispersion characteristics. Coastal Engineering, 15: 371-
388.
Masselink, G., and Pattiaratchi, C. (1998). The effect of sea breeze on beach morphology,
surf zone hydrodynamics and sediment resuspension. Marine Geology, 146 (1-4):
115-135.
Masselink, G., and Pattiaratchi, C. (2000). Tidal asymmetry in sediment resuspension on a
macrotidal beach in northwestern Australia. Marine Geology, 163: 257-274.
Masselink, G., and Pattiaratchi, C. (2001). Seasonal changes in beach morphology along
the sheltered coastline of Perth, Western Australia. Marine Geology, 172: 243-263.
Merceret, F.J. (1972). An experimental study of wind velocity profiles over a wavy surface,
College of Maritime Studies, Delaware University.
Munk, W.H. (1949). Surf beats. Trans. American Geophysical Union, 30: 849-854.
Nielsen, P. (1979). Some basic concepts of wave sediment transport. Series paper 20,
ISVA, Technical University of Denmark, Lyngby.
Nielsen, P. (1984). Field measurements of time-averaged suspended sediment
concentrations under waves. Coastal Engineering, 8: 51-72.
Nielsen, P. (1988). Three simple models of wave sediment transport. Coastal Engineering,
12: 43-62.
Nielsen, P. (1991). Combined convection and diffusion: a new framework for suspended
sediment modelling. Proc. of Coastal Sediments '91: 418-431.
Nielsen, P. (1992). Coastal Bottom Boundary Layers and Sediment Transport. World
Scientific, Singapore, 324 pp.
Nielsen, P., Svendsen, A., and Staub, C. (1979). Onshore-offshore sediment movement on
a beach. Proc. of 16th Intl. Conf. of Coastal Eng.,: 1475-1492.
Nielsen, P., van der Wal, K., and Gillan, L. (2002). Vertical fluxes of sediment in
oscillatory sheet flow. Coastal Engineering, 45: 61-68.
Nikuradse, J. (1933). Stromungsgesetze in rauhen Rohren. VDI Forschungsheft No. 361
(English translation NACA Technical Memorandum No. 1292).
Nwogu, O. (1993). An alternative form of the Boussinesq equations for nearshore wave
propagation. J. Waterway, Port, Coastal, and Coastal Engineering, 119: 618-638.
References 148
O'Donoghue, T., and Clubb, G.S. (2001). Sand ripples generated by regular oscillatory
flow. Coastal Engineering, 44: 101-115.
O'Donoghue, T., Doucette, J.S., van der Werf, J.J., and Ribberink, J.S. (2006). The
dimensions of sand ripples in full-scale oscillatory flows. Coastal Engineering.
Osborne, P.D., and Greenwood, B. (1992a). Frequency dependent cross-shore suspended
sediment transport. 1. A non-barred shoreface. Marine Geology, 106: 1-24.
Osborne, P.D., and Greenwood, B. (1992b). Frequency dependent cross-shore suspended
sediment transport. 2. A barred shoreface. Marine Geology, 106: 25-51.
Osborne, P.D., and Greenwood, B. (1993). Sediment suspension under waves and currents:
time scales and vertical structure. Sedimentology, 40: 599-622.
Osborne, P.D., and Vincent, C.E. (1993). Dynamics of large and small scale bedforms on a
macrotidal shoreface under shoaling and breaking waves. Marine Geology, 115:
207-226.
Osborne, P.D., and Vincent, C.E. (1996). Vertical and horizontal structure in suspended
sand concentrations and wave-induced fluxes over bedforms. Marine Geology, 131:
195-208.
Pattiaratchi, C., Hegge, B., Gould, J., and Eliot, I. (1997). Impact of sea-breeze activity on
nearshore and foreshore processes in southwestern Australia. Continental Shelf
Research, 17 (13): 1539-1560.
Pattiaratchi, C., Masselink, G., and Wikramanayake, N. (1999). Sea breeze effects on
coastal processes. Proc. of fifth international conference on Coastal and Port
Engineering in Developing Countries (COPEDEC V): 37-48.
Peregrine, D.H. (1967). Long waves on a beach. J. Fluid Mechanics, 27: 815-827.
Rakha, K.A. (1998). A Quasi-3D phase-resolving hydrodynamic and sediment transport
model. Coastal Engineering, 34: 277-311.
Rakha, K.A., Deigaard, R., and Broker, I. (1997). A phase-resolving cross-shore sediment
transport model for beach profile evolution. Coastal Engineering, 31: 231-261.
Ribberink, J.S., and Al-Salem, A.A. (1995). Sheet flow and suspension of sand in
oscillatory boundary layers. Coastal Engineering, 25: 205-225.
Russell, P.E., and Huntley, D.A. (1999). A cross-shore transport 'Shape function' for high
energy beaches. Journal of Coastal Research, 15 (1): 198-205.
References 149
Schlichting, H. (1960). Boundary layer theory. McGraw-Hill, New York.
Shi, N.C., and Larsen, L.H. (1984). Reverse sediment transport induced by amplitude-
modulated waves. Marine Geology, 54: 181-200.
Sleath, J.F.A. (1970). Velocity measurements close to the bed in a wave tank. J. Fluid
Mechanics, 42: 111-123.
Sleath, J.F.A. (1974a). Stability of laminar flow at seabed. J. Waterway, Port, Coastal, and
Coastal Engineering, 100: 105-122.
Sleath, J.F.A. (1974b). Velocities above bed in oscillatory flow. J. Waterway, Port,
Coastal, and Coastal Engineering, 100: 287-304.
Smyth, C., and Hay, A.E. (2003). Near-bed turbulence and bottom friction during
SandyDuck97. Journal of Geophysical Research, 108 (C6):
doi:10.1029/2001JC000952, 2003.
Smyth, C., Hay, A.E., and Zedel, L. (2002). Coherent Doppler Profiler measurements of
near-bed suspended sediment fluxes and the influence of bed forms. Journal of
Geophysical Research, 107 (C8): doi: 10.1029/2000jc000760.
Soulsby, R.L. (1983). The bottom boundary layer of shelf seas. In: B. Johns (Editor),
Physical oceanography of coastal and shelf seas. Elsevvier, Amsterdam, pp. 189-
266.
Sternberg, R.W., Shi, N.C., and Downing, J.P. (1984). Field investigations of suspended
sediment transport in the nearshore zone. Proc. of 19th Intl. Conf. of Coastal
Engineering: 1782-1798.
Sternberg, R.W., Shi, N.C., and Downing, J.P. (1989). Continuous measurement of
suspended sediment. In: R.J. Seymour (Editor), Nearshore Sediment Transport,
New York, pp. 231-259.
Sumer, B.M., and Deigaard, R. (1981). Particle motions near the bottom in turbulent flows
in an open channel, Part 2. J. Fluid Mechanics, 109: 311-337.
Sumer, B.M., and Oguz, B. (1978). Particle motions near the bottom in turbulent flow in an
open channel. J. Fluid Mechanics, 86: 109-127.
Sutherland, A.J. (1967). Proposed mechanism for sediment entrainment by turbulent flow.
Journal of Geophysical Research, 72: 191-198.
References 150
Symonds, G., Huntley, D.A., and Bowen, A.J. (1982). Two-dimensional surf beat long
wave generation by a time-varying breakpoint. Journal of Geophysical Research,
87 (C1): 492-499.
Thorne, P.D., Heathershaw, A.D., and Troiano, L. (1984). Acoustic detection of seabed
gravel movement in turbulent currents. Marine Geology, 54 (3-4): M43-M48.
Thornton, E.B., Galvin, J.J., Bub, F.L., and Richardson, D.P. (1976). Kinematics of
breaking waves. Proc. of 15th Intl. Conf. of Coastal Engineering: 461-476.
Trowbridge, J.H., and Agrawal, Y.C. (1995). Glimpses of a wave boundary layer. Journal
of Geophysical Research, 100 (C10): 20,729-20,743.
Tucker, M.J. (1950). Surf beats: sea waves of 1 to 5 minutes' period. Proc. Royal Soc.,
A207: 565-573.
Villard, P.V., and Osborne, P.D. (2002). Visualization of wave-induced suspension patterns
over two-dimensional bedforms. Sedimentology, 49: 363-378.
Villard, P.V., Osborne, P.D., and Vincent, C.E. (2000). Influence of wave groups on SSC
patterns over vortex ripples. Continental Shelf Research, 20: 2391-2410.
Vincent, C.E., Hanes, D.M., and Bowen, A.J. (1991). Acoustic measurements of suspended
sand on the shoreface and the control of concentration by bed roughness. Marine
Geology, 96: 1-18.
Wei, G., Kirby, J.T., Grilli, S.T., and Subramanya, R. (1995). A fullt nonlinear Boussinesq
model for surface waves: I. Highly nonlinear unsteady waves. Journal of Fluid
Mechanics, 294: 71-92.
Wei, G., Kirby, J.T., and Sinha, A. (1999). Generation of waves in Boussinesq models
using a source function method. Coastal Engineering, 36: 271-299.
Wiberg, P.L., and Harris, C.K. (1994). Ripple geometry in wave-dominated environments.
Journal of Geophysical Research, 99 (C1): 775-789.
Williams, J.J., Rose, C.P., and Thorne, P.D. (2002). Role of wave groups in resuspension of
sandy sediments. Marine Geology, 183 (1-4): 17-29.
Zedler, E.A., and Street, R.L. (2001). Large-eddy simulation of sediment transport: currents
over ripples. Journal of Hydraulic Engineering, ASCE, 127 (6): 444-452.
Zyserman, J.A., and Fredsoe, J. (1994). Data analysis of bed concentration of suspended
sediment. Journal of Hydraulic Engineering, ASCE, 120 (9): 1021-1042.