Factors influencing sediment re-suspension and cross-shore

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).


“A numerical study of cross-shore suspended sediment flux in the frequency domain”. To

be submitted to Journal of Coastal Research.


“The role of ripple types on cross-shore suspended sediment flux”. Submitted to Marine

Geology.


“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).


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


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


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).


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).


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)


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)


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.


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).


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).


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;


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


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).


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).


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


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.


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-


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.


(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)


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;


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.


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 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


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.,


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.


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.


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.


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.


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


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).


33


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.


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.


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.


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


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).


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


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-


ripples

(g) Hs/h = 0.16 2-D post-


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).


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,


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.


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


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).


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).


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.


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.


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).


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


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


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


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


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.


A series of field measurements of hydrodynamics and sediment suspension together with

bed topography was collected at several nearshore locations to investigate the factors


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.


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


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.


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


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)


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)


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.


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.


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


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.


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


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


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)


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.


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.


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.


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).


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.


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.


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


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.


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,


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


suspended sediment concentration (c) at 0.05 m from the seabed with the bed roughness

(Kn).


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).


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


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


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.


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


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


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


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.


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


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


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.


85


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).


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.


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.


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


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.


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


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


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.


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.


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


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


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


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.


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.


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


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).


100

(a)

(b)

(c) Figure 5.11: Simple mechanism for offshore suspended sediment transport over post-vortex

ripples.


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.


102

−10 −5 0 5 10 15 20−1.5

−1

−0.5

0

0.5

1


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)


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.


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)


sediment concentration (c0.05) for run 1 at South Beach (over 2D ripples).


104

(a)

(b)

(c) Figure 5.14: Simple mechanism for onshore suspended sediment transport over vortex

ripples.


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.


106

−10 0 10 20 30−1.2

−0.8

−0.4

0

0.4


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)


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.


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).


108

−10 0 10 20 30 40−1.5

−1

−0.5

0

0.5


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)


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.


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)


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


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.


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.


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.


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


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.


115


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


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


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).


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.


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


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).


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.


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.


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.


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’.


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).


−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,


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.


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).


−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.


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).


−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)




between 950 s and 1100 s.


−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)




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


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.


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.


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.


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


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


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.


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.

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Factors influencing sediment re-suspension and cross-shore