Abldd Lecture 3 Web

7/30/2019 Abldd Lecture 3 Web

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Why is bed shear stress important? Provides an index of fluid force per unit

area on the stream bed, which has beenrelated to sediment mobilization andtransport in many theoretical and empiricaltreatments of sediment transport

Calculation of Bed Shear Stress


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Various methods based on

Reach-averaged relations

Theoretical assumptions about structureof turbulence

Direct measurements of turbulence

Calculation of Bed Shear Stress


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Reach-Averaged Method

Mean Bed Shear Stress

- force per unit areaexerted by a block ofwater on the channelboundary as it moves

downstream

F = WDXsin (N) [MLT-2)

RS (N m-2)

(downstream orientedcomponent of the weight ofthe block)


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Reach-Averaged

Method

Advantages Serves as an index of the totalresistance by ALL frictionalinfluences on the flow (particle-,

bedform-, bar-, and planform-scale effects)

Relatively easy to measure

Disadvantages

Does not provide information on spatial variation in resistance atsub-reach scale

Is not necessarily a good index of the competence of the stream

to move sediment


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Law of the Wall Method

Based on theassumption that thevelocity profile inthe lower portion(15-20%) of an openchannel flow has alogarithmicstructure:


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u = mean velocity (in vertical), u* = shear velocity, = von Karmans

constant, z = distance above bed, z0= roughness height (height above

bed where velocity goes to zero)


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Measure mean velocities (u) at various heightsabove bed in lower 15-20% of the flow

Regress the values of u against the logarithms

of z to get estimates of m and b

Calculate values of shear velocity, bed shearstress, and roughness height


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AdvantagesProvides local measure of shear stress

Can be used to map spatial patterns of shearstress and roughness height at subreach scale

Standard error of estimate of regression canprovide an estimate of error in u*

Disadvantages

Flow must conform with logarithmic velocityprofile

Errors in measurement of u and z can influence

results (least precise of law of wall methods)


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Variants on Law of the Wall

Advantage

requires only a single near-bed velocity reading in lower 20% offlow for estimate of u*

Disadvantage

requires information on the grain-size distribution of bed material

Applies to gravel-bed rivers only and assumes that empirical

relation z0 = (adp/30) applies to all such rivers

a = 3, p = 84 Whiting and Dietrich, 1990

a = 2.85, p = 90 Wilcock et al. 1996


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Variants on Law of the Wall

Advantage

Has less variability than other law of the wall methods

Disadvantage

requires measurement of velocity profile to determine mean [couldperhaps be used with a single measure of U (6/10th depth)]


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Evaluation of Law of the WallPrecision (Wilcock, 1996)

Lowest precision slopeof velocity profile

Highest precision depth-averaged velocity

Says nothing aboutaccuracy of the various

methods


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Direct Measurement:

Near-bed ReynoldsShear Stress

nfluctuatiovelocityverticalbed-near

nfluctuatiovelocitydownstreambed-near'

'

''

==

=t

b

b

bbb

w

u

wu


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Direct Measurement: Near-bedReynolds Shear Stress

Advantage

Direct measurement of turbulent shear stress nearthe bed

DisadvantageHow close to the bed do you need to be? (seems todepend on roughness characteristics and purpose ofmeasurement)

Many measurement devices cannot measure velocityfluctuations accurately close to the bed

Need 2-D measurements of turbulent fluctuations


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Turbulent Kinetic Energy Method

Alternative Formulation


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Turbulent Kinetic Energy Method

Advantages

No need to estimate roughness height

Single near-bed reading of 3-D velocitiesDisadvantages

How close to bed

3-D velocity measurements

Values of C1 and C2 not derived fromstreams or rivers (oceans)


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Is Bed Shear Stress the RightIndex?

Some recent studies have questionedwhether looking at turbulence fluxes orvelocity profiles is the right approach forunderstanding sediment transport

Instead look at actual sedimentmobilization and transport and relate itempirically to various velocity measures,

including instantaneous velocities

u = +u


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References

Bauer, B. O., D. J. Sherman, and J. F. Wolcott (1992), Sources of uncertainty in shear stressand roughness length estimates derived from velocity profiles, The ProfessionalGeographer, 44, 453-464.

Bergeron, N. E., and A. D. Abrahams (1992), Estimating shear velocity and roughnesslength from velocity profiles, Water Resources Research, 28, 2155-2158.

Biron, P. M., S. N. Lane, A. G. Roy, K. F. Bradbrook, and K. S. Richards (1998), Sensitivity ofbed shear stress estimated from vertical velocity profiles: the problem of samplingresolution, Earth Surface Processes and Landforms, 23, 133-139.

Biron, P. M., C. Robson, M. F. Lapointe, and S. J. Gaskin (2004), Comparing differentmethods of bed shear stress estimates in simple and complex flow fields, Earth Surface

Processes and Landforms, 29, 1403-1415.

Kim, S.-C., C. T. Friedrichs, J. P.-Y. Maa, and L. D. Wright (2000), Estimating bottomstresses in tidal boundary layer from acoustic doppler velocimeter data, Journal ofHydraulic Engineering, 126, 399-406.

Wilcock, P. R. (1996), Estimating local bed shear stress from velocity observations, Water

Resources Research, 32, 3361-3366.


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Turbulent boundary layer structure the influence of roughness

Th i fl f h


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Rough-wall

velocity profiles

(Bergstrom et

al., 2002)

The influence of roughnessa. Smooth

b. Perforated plate

c. Sand grain

d. Wire screen


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Rough-wall

velocity profiles:

scale by

freestreamvelocity (outer-

wall scaling)

(Bergstrom et

al., 2002)


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Rough-wall

velocity profiles:

scale by inner-

wall variables(Bergstrom et

al., 2002)

Still great debate on

scaling (inner/outer) and

also if roughness effects

can be collapsed


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Nowell and Church, JGR, 1979

The influence of roughness density

(plan area of elements: total area)

Region 1: TI decreases linearly to surface and

u* is good to collapse profiles

Region 2: TI approx. constant at approx. 2

Region 3: roughness density influential


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After Nowell and Church, JGR, 1979

The influence of roughness density


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Grass, 1971

The influence of roughness on turbulence intensity (Grass 1971)


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Grass, 1971


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Influence ofroughness on

turbulence

intensity

(Ligrani and

Moffat 1986)


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Model of smooth wall TBL structure (Smith, 1996)

Near-wall

Outer region


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Model of rough wall TBL structure (Smith, 1996)


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Links to Large-Scale-Motions (Falco, 1977) and seminars


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Links to Sediment Entrainment (Grass, 1971)


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References

Bergstrom, D.J., Kotey, N.A. and Tachie, M.F. (2002) The effects

of surface roughness on the mean velocity profile in a turbulent

boundary layer, Journal of Fluids Engineering, 124, 664-670.

Grass, A.J. (1971) Structural features of turbulent flow over

smooth & rough boundaries, J. Fluid Mechanics, 50, 233-255.Ligrani, P.M. and Moffat, R.J. (1986) Structure of transitionally

rough and fully rough turbulent boundary layers, J. FluidMechanics, 162, 69-98.Nowell, A.R.M. and Church, M. (1979) Flow in a depth-limited

boundary layer, J. Geophysical Research, 84, 4816-4824.

Smith, C.R. (1996) Coherent flow structures in smooth-wallturbulent boundary layers: Facts, mechanisms and speculation.

in Coherent Flow Structures in open channelsedited by P.J.Ashworth, S.J. Bennett, J.L. Best, and S.J. McLelland, pp. 1-39,

John Wiley and Sons.


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Research Projects

The flow dynamics of idealized interacting gravel particles (x2)

Turbulence in transitional flows: the influence of fine sediment on flows (x2)

Mean flow and turbulence over a dune field in the Missouri River

Flow over the ripple:dune transition turbulence and vorticity

Flow separation at confluences (x2)

The flow dynamics of bendway weirs (x2)Flow structure and turbulence within meander bends (x2)

Your possible ideas for projects?...we are very keen to encourage projects

with your own data or develop your own ideas for a topic, which can be

worked into this format.....

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Abldd Lecture 3 Web