Date post: | 04-Apr-2018 |
Category: |
Documents |
Upload: | buddy-walker |
View: | 215 times |
Download: | 0 times |
of 33
7/30/2019 Abldd Lecture 3 Web
1/33
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
7/30/2019 Abldd Lecture 3 Web
2/33
Various methods based on
Reach-averaged relations
Theoretical assumptions about structureof turbulence
Direct measurements of turbulence
Calculation of Bed Shear Stress
7/30/2019 Abldd Lecture 3 Web
3/33
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)
7/30/2019 Abldd Lecture 3 Web
4/33
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
7/30/2019 Abldd Lecture 3 Web
5/33
Law of the Wall Method
Based on theassumption that thevelocity profile inthe lower portion(15-20%) of an openchannel flow has alogarithmicstructure:
7/30/2019 Abldd Lecture 3 Web
6/33
Law of the Wall Method
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)
7/30/2019 Abldd Lecture 3 Web
7/33
Law of the Wall Method
7/30/2019 Abldd Lecture 3 Web
8/33
Law of the Wall Method
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
7/30/2019 Abldd Lecture 3 Web
9/33
Law of the Wall Method
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)
7/30/2019 Abldd Lecture 3 Web
10/33
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
7/30/2019 Abldd Lecture 3 Web
11/33
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)]
7/30/2019 Abldd Lecture 3 Web
12/33
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
7/30/2019 Abldd Lecture 3 Web
13/33
Direct Measurement:
Near-bed ReynoldsShear Stress
nfluctuatiovelocityverticalbed-near
nfluctuatiovelocitydownstreambed-near'
'
''
==
=t
b
b
bbb
w
u
wu
7/30/2019 Abldd Lecture 3 Web
14/33
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
7/30/2019 Abldd Lecture 3 Web
15/33
Turbulent Kinetic Energy Method
Alternative Formulation
7/30/2019 Abldd Lecture 3 Web
16/33
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)
7/30/2019 Abldd Lecture 3 Web
17/33
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
7/30/2019 Abldd Lecture 3 Web
18/33
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.
7/30/2019 Abldd Lecture 3 Web
19/33
Turbulent boundary layer structure the influence of roughness
Th i fl f h
7/30/2019 Abldd Lecture 3 Web
20/33
Rough-wall
velocity profiles
(Bergstrom et
al., 2002)
The influence of roughnessa. Smooth
b. Perforated plate
c. Sand grain
d. Wire screen
7/30/2019 Abldd Lecture 3 Web
21/33
Rough-wall
velocity profiles:
scale by
freestreamvelocity (outer-
wall scaling)
(Bergstrom et
al., 2002)
7/30/2019 Abldd Lecture 3 Web
22/33
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
7/30/2019 Abldd Lecture 3 Web
23/33
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
7/30/2019 Abldd Lecture 3 Web
24/33
After Nowell and Church, JGR, 1979
The influence of roughness density
7/30/2019 Abldd Lecture 3 Web
25/33
Grass, 1971
The influence of roughness on turbulence intensity (Grass 1971)
7/30/2019 Abldd Lecture 3 Web
26/33
Grass, 1971
7/30/2019 Abldd Lecture 3 Web
27/33
Influence ofroughness on
turbulence
intensity
(Ligrani and
Moffat 1986)
7/30/2019 Abldd Lecture 3 Web
28/33
Model of smooth wall TBL structure (Smith, 1996)
Near-wall
Outer region
7/30/2019 Abldd Lecture 3 Web
29/33
Model of rough wall TBL structure (Smith, 1996)
7/30/2019 Abldd Lecture 3 Web
30/33
Links to Large-Scale-Motions (Falco, 1977) and seminars
7/30/2019 Abldd Lecture 3 Web
31/33
Links to Sediment Entrainment (Grass, 1971)
7/30/2019 Abldd Lecture 3 Web
32/33
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.
7/30/2019 Abldd Lecture 3 Web
33/33
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.....