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Transport relaxation time and length scales in turbulent suspensions

Published online by Cambridge University Press:  11 February 2011

PHILIPPE CLAUDIN*
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR 7636 ESPCI–CNRS, Université Paris Diderot–Université Pierre et Marie Curie, 10 rue Vauquelin, 75005 Paris, France
FRANÇOIS CHARRU
Affiliation:
Institut de Mécanique des Fluides de Toulouse–CNRS, Université de Toulouse, 31400 Toulouse, France
BRUNO ANDREOTTI
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR 7636 ESPCI–CNRS, Université Paris Diderot–Université Pierre et Marie Curie, 10 rue Vauquelin, 75005 Paris, France
*
Email address for correspondence: claudin@pmmh.espci.fr
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Abstract

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We show that in a turbulent flow transporting suspended sediment, the unsaturated sediment flux q(x, t) can be described by a first-order relaxation equation. From a mode analysis of the advection–diffusion equation for the particle concentration, the relaxation length and time scales of the dominant mode are shown to be the deposition length HU/Vfall and deposition time H/Vfall, where H is the flow depth, U the mean flow velocity and Vfall the sediment settling velocity. This result is expected to be particularly relevant for the case of sediment transport in slowly varying flows, where the flux is never far from saturation. Predictions are shown to be in quantitative agreement with flume experiments, for both net erosion and net deposition situations.

Type
Papers
Copyright
Copyright © Cambridge University Press 2011. The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution-NonCommercial-ShareAlike licence <http://creativecommons.org/licenses/by-nc-sa/2.5/>. The written permission of Cambridge University Press must be obtained for commercial re-use.

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