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Entrainment and motion of coarse particles in a shallow water stream down a steep slope

Published online by Cambridge University Press:  08 January 2008

C. ANCEY ,
A. C. DAVISON ,
T. BÖHM ,
M. JODEAU  and
P. FREY
C. ANCEY
Affiliation:
School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
A. C. DAVISON
Affiliation:
Institute of Mathematics, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
T. BÖHM
Affiliation:
Cemagref, Domaine Universitaire BP 76, 38402 Saint-Martin-d'Hères Cedex, France
M. JODEAU
Affiliation:
Cemagref, 3 bis quai Chauveau, 69336 Lyon, France
P. FREY
Affiliation:
Cemagref, Domaine Universitaire BP 76, 38402 Saint-Martin-d'Hères Cedex, France
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Abstract

We investigate the entrainment, deposition and motion of coarse spherical particles within a turbulent shallow water stream down a steep slope. This is an idealization of bed-load transport in mountain streams. Earlier investigations have described this kind of sediment transport using empirical correlations or concepts borrowed from continuum mechanics. The intermittent character of particle transport at low-water discharges led us to consider it as a random process. Sediment transport in this regime results from the imbalance between entrainment and deposition of particles rather than from momentum balance between water and particles. We develop a birth–death immigration–emigration Markov process to describe the particle exchanges between the bed and the water stream. A key feature of the model is its long autocorrelation times and wide, frequent fluctuations in the solid discharge, a phenomenon never previously explained despite its ubiquity in both nature and laboratory experiments. We present experimental data obtained using a nearly two-dimensional channel and glass beads as a substitute for sediment. Entrainment, trajectories, and deposition were monitored using a high-speed digital camera. The empirical probability distributions of the solid discharge and deposition frequency were properly described by the theoretical model. Experiments confirmed the existence of wide and frequent fluctuations of the solid discharge, and revealed the existence of long autocorrelation time, but theory overestimates the autocorrelation times by a factor of around three. Particle velocity was weakly dependent on the fluid velocity contrary to the predictions of the theoretical model, which performs well when a single particle is moving. For our experiments, the dependence of the solid discharge on the fluid velocity is entirely controlled by the number of moving particles rather than by their velocity. We also noted significant changes in the behaviour of particle transport when the bed slope or the water discharge was increased. The more vigorous the stream was, the more continuous the solid discharge became. Moreover, although 90% of the energy supplied by gravity to the stream is dissipated by turbulence for slopes lower than 10%, particles dissipate more and more energy when the bed slope is increased, but surprisingly, the dissipation rate is nearly independent of fluid velocity. A movie is available with the online version of the paper.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Geophysical and Geological Flows: Sediment transport
Type
Papers
Information
Journal of Fluid Mechanics , Volume 595 , 25 January 2008 , pp. 83 - 114
Copyright
Copyright © Cambridge University Press 2008

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References

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Ancey et al. supplementary movie

The movie shows a short sequence corresponding to run E10-8 (experiment g) (flume slope: 10%, time-averaged solid discharge: 8 beads/s). The flow was filmed from the sidewall using a high-speed video camera (130 Hz). The thin line represents the free surface of the water stream. The bed is made up of a rough bottom (corrugated bottom mimicking randomly distributed, stationary particles) and stationary particles, which can be entrained by the water stream. In the upper layer of the bed, we observe particles that are sporadically moving: once destabilized as a result of the water action or a collision with another particle, particles start to roll, then come to a halt. On some occasions, a few particles can start to jump (saltating motion). At each time, the position of each particle was recorded using particle-track techniques, which made it possible to measure the number of moving particles, entrainment and deposition rates, particles' velocity, and so on.

Download Ancey et al. supplementary movie(Video)
Video 2.2 MB

Ancey et al. supplementary movie

The movie shows a short sequence corresponding to run E10-8 (experiment g) (flume slope: 10%, time-averaged solid discharge: 8 beads/s). The flow was filmed from the sidewall using a high-speed video camera (130 Hz). The thin line represents the free surface of the water stream. The bed is made up of a rough bottom (corrugated bottom mimicking randomly distributed, stationary particles) and stationary particles, which can be entrained by the water stream. In the upper layer of the bed, we observe particles that are sporadically moving: once destabilized as a result of the water action or a collision with another particle, particles start to roll, then come to a halt. On some occasions, a few particles can start to jump (saltating motion). At each time, the position of each particle was recorded using particle-track techniques, which made it possible to measure the number of moving particles, entrainment and deposition rates, particles' velocity, and so on.

Download Ancey et al. supplementary movie(Video)
Video 2.3 MB
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