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

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?

Erosion equation: 1

sb

qt C

Two-dimensional flow:

1 s

b

q

t C x

?sq Bed load or suspended load?

Early, fixed bed experiment- effects of acceleration

SShift relative to upstream ramp crest

Shift relative to reattachment

Shift relative to reattachment

Research Goal: predict bedform evolution• Predict transport rate (Nelson , et

al. tomorrow)• Measure transport rate• Measure near-bed velocity

statistics

• Determine effects of ripples

Experiments

•Goal: determine relationship between flow and transport

1) Characterize flow 2) Measure transport rate

Instrumentation:

•Acoustic Doppler Profiler Velocity along four beams (~1 mm

bin spacing) ~20 Hz sampling freq; not

simultaneous

Quad set-up

Streamwise velocity profile- no upstream ramp

Streamwise velocity profile- with upstream ramp

Reynolds stress- with upstream ramp

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)

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

Flat bed downstream of ramp

Time stack- no upstream ramp

Change in bed elevation- no upstream ramp

Time stack – with upstream ramp

Change in bed elevation- with upstream ramp

Stress and transport- no upstream ramp

Nondimensional transport- no upstream ramp

Stress and transport- with upstream ramp

Non-dimensional transport- with upstream ramp

Stress and transport with and without upstream ramp

Comparison with and without upstream ramp

Stress and transport with and without upstream ramp

Stress and transport with and without upstream ramp

Comparison between beginning and end of run

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

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

Erosion equation versus ripple migration