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Sediment dynamics. Part 1. Bed-load transport by laminar shearing flows

Published online by Cambridge University Press:  25 September 2009

MALIKA OURIEMI ,
PASCALE AUSSILLOUS  and
ÉLISABETH GUAZZELLI
MALIKA OURIEMI
Affiliation:
IUSTI CNRS UMR 6595 – Polytech'Marseille – Aix-Marseille Université (U1) 5 rue Enrico Fermi, 13453 Marseille Cedex 13, France
PASCALE AUSSILLOUS
Affiliation:
IUSTI CNRS UMR 6595 – Polytech'Marseille – Aix-Marseille Université (U1) 5 rue Enrico Fermi, 13453 Marseille Cedex 13, France
ÉLISABETH GUAZZELLI*
Affiliation:
IUSTI CNRS UMR 6595 – Polytech'Marseille – Aix-Marseille Université (U1) 5 rue Enrico Fermi, 13453 Marseille Cedex 13, France
*
‡Email address for correspondence: [email protected]
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Abstract

We propose a two-phase model having a Newtonian rheology for the fluid phase and friction for the particle phase to describe bed-load transport in the laminar viscous regime. We have applied this continuum model to sediment transport by viscous shearing flows. The equations are shown to reduce to the momentum equation for the mixture and the Brinkman equation for the fluid velocity. This modelling is able to provide a description of the flow of the mobile granular layer. At some distance from threshold of particle motion, where the continuum approach is more realistic as the mobile layer is larger than one particle diameter, there is very little slip between the two phases and the velocities inside the mobile bed have approximately a parabolic profile. When the Poiseuille (or Couette) flow is not significantly perturbed, simple analytical results of the particle flux varying cubically with the Shields number and of the bed-load thickness varying linearly with it can then be obtained. These predictions compare favourably with experimental observations of bed-load transport in pipe flows.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 636 , 10 October 2009 , pp. 295 - 319
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

†

Present address: IFP-Lyon, Rond-Point de I'échangeur de Solaize, BP3, 69360 Solaize, France.

References

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