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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

REFERENCES

Abbott, J. E. & Francis, J. R. D. 1977 Saltation and suspension trajectories of solid grains in a water stream. Proc. R. Soc. Lond. 284, 225–254.Google Scholar
Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. National Bureau of Standards.Google Scholar
Ancey, C., Evesque, P. & Coussot, P. 1996 Motion of a single bead on a bead row: theoretical investigations. J. Phys. I 6, 725–751.Google Scholar
Ancey, C., Bigillon, F., Frey, P., Lanier, J. & Ducret, R. 2002 Saltating motion of a bead in a rapid water stream. Phys. Rev. E 66, 036306.Google Scholar
Ancey, C., Bigillon, F., Frey, P. & Ducret, R. 2003 Rolling motion of a single bead in a rapid shallow water stream down a steep channel. Phys. Rev. E 67, 011303.Google Scholar
Ancey, C., Böhm, T., Jodeau, M. & Frey, P. 2006 Statistical description of sediment transport experiments. Phys. Rev. E 74, 011302.Google ScholarPubMed
Armanini, A. & Gregoretti, C. 2005 Incipient sediment motion at high slopes in uniform flow condition. Water Resour. Res. 41, W12431.Google Scholar
Bagnold, R. A. 1966 An approach to the sediment transport problem from general physics. Professional paper 422-I. United States Geological Survey.Google Scholar
Bagnold, R. A. 1973 The nature of saltation and of ‘bed load’ transport in water. Proc. R. Soc. Lond. A 332, 473–504.Google Scholar
Balmforth, N. J. & Provenzale, A. 2001 Patterns of dirt. In Geomorphological Fluid Mechanics (ed. Balmforth, N. J. & Provenzale, A.), pp. 369–393. Springer.Google Scholar
Barry, J. J., Buffington, J. M. & King, J. G. 2004 A general power equation for predicting bed load transport rates in gravel bed rivers. Water Resour. Res. 40, W10401.CrossRefGoogle Scholar
Böhm, T., Ancey, C., Frey, P., Reboud, J.-L. & Duccotet, C. 2004 Fluctuations of the solid discharge of gravity-driven particle flows in a turbulent stream. Phys. Rev. E 69, 061307.Google Scholar
Böhm, T., Frey, P., Duccotet, C., Ancey, C., Jodeau, M. & Reboud, J.-L. 2006 Two-dimensional motion of a set of particles in a free surface flow with image processing. Exps. Fluids 41, 1–11.Google Scholar
Bunte, K. & Abt, S. 2005 Effect of sampling time on measured gravel bed load transport rates in a coarse-bedded stream. Water Resour. Res. 41, W11405.Google Scholar
Charru, F., Mouilleron, H. & Eiff, O. 2004 Erosion and deposition of particles on a bed sheared by a viscous flow. J. Fluid Mech. 519, 55–80.CrossRefGoogle Scholar
Cheng, N.-S. 2004 Analysis of bedload transport in laminar flows. Adv. Water Resour. 27, 937–942.CrossRefGoogle Scholar
Cheng, N.-S., Tang, H. & Zhu, L. 2004 Evaluation of bed load transport subject ot high shear stress fluctuations. Water Resour. Res. 40, W05601.Google Scholar
Cox, D. R. & Miller, H. D. 1965 The Theory of Stochastic Processes. Chapman & Hall.Google Scholar
Drake, T. G., Shreve, R. L., Dietrich, W. E. & Leopold, L. B. 1988 Bedload transport of fine gravel observed by motion-picture photography. J. Fluid Mech. 192, 193–217.CrossRefGoogle Scholar
Einstein, H. 1950 The bed-load function for sediment transportation in open channel flows. Tech. Rep. 1026. United States Department of Agriculture.Google Scholar
Ettema, R. & Mutel, C. 2004 Hans Albert Einstein: Innovation and compromise in formulating sediment transport by rivers. J. Hydraul. Engng ASCE 130, 477–487.Google Scholar
Fernandez Luque, R. & van Beek, R. 1976 Erosion and transport of bed-load sediment. J. Hydraul. Res. 14, 127–144.CrossRefGoogle Scholar
Frey, P. & Reboud, J.-L. 2001 Experimental study of narrow free-surface turbulent flows on steep slopes. In Advances in flow modeling and turbulence measurements (ed. Ninokata, H., Wada, A. & Tanaka, N.). World Scientific.Google Scholar
Frey, P., Dufresne, M., Böhm, T., Jodeau, M. & Ancey, C. 2006 Experimental study of bed load on steep slopes. In River Flow 2006 (ed. Ferreira, R. M. L., Alves, E. C. T. L., Leal, J. G. A. B. & Cardoso, A. H.), vol. 1, pp. 887–893. Taylor & Francis.Google Scholar
Gardiner, C. W. 1983 Handbook of Stochastic Methods. Springer.CrossRefGoogle Scholar
Gomez, B. & Church, M. 1989 An assessment of bed load sediment transport formulae for gravel bed rivers. Water Resour. Res. 25, 1161–1186.CrossRefGoogle Scholar
Gordon, R., Carmichael, J. B. & Isackson, F. J. 1972 Saltation of plastic balls in a one-dimensional flume. Water Resour. Res. 8, 444–459.Google Scholar
Graf, W. H. 1984 Hydraulics of Sediment Transport. Littleton.Google Scholar
Grant, G. E. 1997 Critical flow constrains flow hydraulics in mobile-bed streams: a new hypothesis. Water Resour. Res. 33, 349–358.Google Scholar
Iverson, R. M. 2003 How should mathematical models of geomorphic processes be judged? In Prediction in Geomorphology (ed. Wilcock, P. R. & Iverson, R. M.), pp. 83–94. American Geophysical Union.Google Scholar
Jenkins, J. T. & Hanes, H. M. 1998 Collisional sheet flows of sediment driven by a turbulent fluid. J. Fluid Mech. 370, 29–52.CrossRefGoogle Scholar
Julien, P.-Y. 1994 Erosion and Sedimentation. Cambridge University Press.Google Scholar
Kirchner, J., Dietrich, W., Iseya, F. & Ikeda, H. 1990 The variability of critical shear stress, friction angle, and grain protrusion in water-worked sediments. Sedimentology 37, 647–672.CrossRefGoogle Scholar
Kleinhans, M. & van Rijn, L. 2002 Stochastic prediction of sediment transport in sand-gravel bed rivers. J. Hydraul. Engng ASCE 128, 412–425.Google Scholar
Kovacs, A. & Parker, G. 1994 A new vectorial bedload formulation and its application to the time evolution of straight rivers. J. Fluid Mech. 267, 153–183.CrossRefGoogle Scholar
Kuhnle, R. A. & Southard, J. B. 1988 Bed load transport fluctuations in a gravel bed laboratory channel. Water Resour. Res. 24, 247–260.Google Scholar
Laursen, E. M. 1999 Discussion on ‘Pickup probability for sediment entrainment’. J. Hydraul. Engng ASCE 124, 786–787.Google Scholar
Lisle, I. G., Rose, C. W., Hogarth, W. L., Hairsine, P. B., Sander, G. & Parlange, J. Y. 1998 Stochastic sediment transport in soil erosion. J. Hydrol. 204, 217–230.Google Scholar
Lisle, T. E. 1989 Sediment transport and resulting deposition in spawning gravels, north coastal California. Water Resour. Res. 25, 1303–1319.Google Scholar
Lopez, F. & Garcìa, M. 2001 Risk of sediment erosion and suspension in turbulent flows. J. Hydraul. Engng ASCE 127, 231–235.Google Scholar
Martin, Y. 2003 Evaluation of bed load transport formulae using field evidence from the Vedder River, British Columbia. Geomorphology 53, 75–95.Google Scholar
Meyer-Peter, E. & Müller, R. 1948 Formulas for bed load transport. In 2nd meeting (ed. IAHR), Stockholm, Sweden, pp. 39–64.Google Scholar
Nelson, J. M., Shreve, R. L., McLean, S. R. & Drake, T. G. 1995 Role of near-bed turbulence structure in bed load transport and bed form mechanics. Water Resour. Res. 31, 2071–2086.CrossRefGoogle Scholar
Nelson, J. M., Schmeeckle, M. W. & Shreve, R. L. 2001 Turbulence and particle entrainment. In Gravel Bed Rivers (ed. Mosley, M.), pp. 221–248. Littleton.Google Scholar
Nezu, I. & Nakagawa, H. 1993 Turbulence in Open-Channel Flows. Balkema.Google Scholar
Niño, Y. & Garcìa, M. H. 1994 Gravel saltation 2. Modeling. Water Resour. Res. 30, 1915–1924.Google Scholar
Niño, Y. & Garcìa, M. H. 1998 Using Lagrangian particle saltation observations for bedload sediment transport modelling. Hydrolog. Process. 12, 1197–1218.Google Scholar
Niño, Y., Garcìa, M. H. & Ayala, L. 1994 Gravel saltation 1. Experiments. Water Resour. Res. 30, 1907–1914.Google Scholar
Nikora, V., Heald, J., Goring, D. & McEwan, I. 2001 Diffusion of saltating particles in unidirectional water flow over a rough granular bed. J. Phys. A: Math. Gen. 34, L743–L749.Google Scholar
Nikora, V., Habersack, H., Huber, T. & McEwan, I. 2002 On bed particle diffusion in gravel bed flows under weak bed load transport. Water Resour. Res. 38, WR000513.Google Scholar
Paintal, A. 1971 A stochastic model of bed load transport. J. Hydraul. Res. 9, 527–554.CrossRefGoogle Scholar
Papanicolaou, A., Diplas, P., Evaggelopoulos, N. & Fotopoulos, S. 2002 Stochastic incipient motion criterion for spheres under various bed packing conditions. J. Hydraul. Engng ASCE 128, 369–390.Google Scholar
Raudkivi, A. 1990 Loose Boundary Hydraulics. Pergamon.Google Scholar
Rickenmann, D. 2001 Comparison of bed load transport in torrents and gravel bed streams. Water Resour. Res. 37, 3295–3306.Google Scholar
van Rijn, L. 1985 Sediment transport, part I: bed load transport. J. Hydraul. Engng ASCE 110, 1431–1456.Google Scholar
Schmeeckle, M. W. & Nelson, J. M. 2003 Direct numerical simulation of bedload transport using a local, dynamic boundary condition. Sedimentology 50, 279–301.Google Scholar
Schmeeckle, M. W., Nelson, J. M., Pitlick, J. & Bennett, J. 2001 Interparticle collision of natural sediment grains in water. Water Resour. Res. 37, 2377–2391.Google Scholar
Schmeeckle, M., Nelson, J. M. & Shreve, R. 2007 Forces on stationary particles in near-bed turbulent flows. J. Geophys. Res. 112, F02003.Google Scholar
Seminara, G., Solari, L. & Parker, G. 2002 Bed load at low Shield stress on arbitrarilty sloping beds: failure of the Bagnold hypothesis. Water Resour. Res. 38, 1249.Google Scholar
Smart, G. & Jaeggi, M. 1983 Sedimenttransport in steilen Gerinnen. Tech. Rep. 64. Mitteilungen der Versuchanstalt für wasserbau, Hydrologie und Glaziologie.Google Scholar
Sornette, D. 2000 Critical Phenomena in Natural Sciences. Springer.Google Scholar
Wiberg, P. L. & Smith, J. D. 1985 A theoretical model for saltating grains in water. J. Geophys. Res. C 90, 7341–7354.CrossRefGoogle Scholar
Wiberg, P. L. & Smith, J. D. 1989 Model for calculating bedload transport of sediment. J. Hydraul. Engng ASCE 115, 101–123.Google Scholar
Wilcock, P. R. 2001 Toward a practical method for estimating sediment-transport rates in gravel bed-rivers. Earth Surf. Processes Landforms 26, 1395–1408.Google Scholar
Wong, M. & Parker, G. 2006 Reanalysis and correction of bed-load relation of Meyer-Peter and Müller using their own database. J. Hydraul. Engng ASCE 132, 1159–1168.Google Scholar

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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