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Sediment Transport over Ripples and Dunes
Stephen R McLean, UC Santa BarbaraJonathan Nelson, USGS, Denver, CO
Thanks to: Sandro Orlandi, University of Bologna
Lindsay Gary, UCSB
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Ultimate Goal: predict bedform evolution
System: • Response of flow to topography• Response of sediment to flow• Response of topography to sediment flux
divergence
What is the sediment flux over a dune?
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Erosion equation: 1
sb
qt C
Two-dimensional flow:
1 s
b
q
t C x
?sq Bed load or suspended load?
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Early, fixed bed experiment- effects of acceleration
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SShift relative to upstream ramp crest
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Shift relative to reattachment
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Shift relative to reattachment
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Research Goal: predict bedform evolution• Predict transport rate (Nelson , et
al. tomorrow)• Measure transport rate• Measure near-bed velocity
statistics
• Determine effects of ripples
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Experiments
•Goal: determine relationship between flow and transport
1) Characterize flow 2) Measure transport rate
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Instrumentation:
•Acoustic Doppler Profiler Velocity along four beams (~1 mm
bin spacing) ~20 Hz sampling freq; not
simultaneous
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Quad set-up
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Streamwise velocity profile- no upstream ramp
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Streamwise velocity profile- with upstream ramp
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Reynolds stress- with upstream ramp
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Instrumentation:
•Acoustic Doppler Profiler Velocity along four beams (~1 mm bin
spacing) ~20 Hz sampling freq; not simultaneous
•Multiple transducer array (MTA) 32 acoustic transducers (20mm
spacing)
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Estimating Transport rate• For two-dimensional flow
erosion equation yields:
0
0
0 0
where
is the bed elevation,
is the sediment volume concentration in the bed and
is the sediment flux at
x
s s b
x
b
s
q q C dxt
C
q x
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Flat bed downstream of ramp
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Time stack- no upstream ramp
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Change in bed elevation- no upstream ramp
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Time stack – with upstream ramp
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Change in bed elevation- with upstream ramp
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Stress and transport- no upstream ramp
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Nondimensional transport- no upstream ramp
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Stress and transport- with upstream ramp
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Non-dimensional transport- with upstream ramp
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Stress and transport with and without upstream ramp
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Comparison with and without upstream ramp
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Stress and transport with and without upstream ramp
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Stress and transport with and without upstream ramp
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Comparison between beginning and end of run
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General Observations• Flow/transport relation not strongly affected by
acceleration– Transport decreases as acceleration increases– Near-bed flow decreases as acceleration increases
also• Concept of critical shear stress plays no role in
lee of a separation zone • Ripples form almost immediately for the flat bed
case• Ripples form on steep slopes with no upstream
flow separation• Ripples do not form on steep slopes downstream
of flow separation• Ripples seem to enhance transport
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Transport rate from ripple migration rate
Assumptions:
Transport primarily as bed load Ripples are approximately triangular
1
2sq cH
where c is the propagation speed and H is the ripple height
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Erosion equation versus ripple migration