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The phase lead of shear stress in shallow-water flow over a perturbed bottom

Published online by Cambridge University Press:  06 December 2010

PAOLO LUCHINI
Affiliation:
Dipartimento di Ingegneria Meccanica, Università di Salerno, 84084 Fisciano (SA), Italy
FRANÇOIS CHARRU
Affiliation:
Institut de Mécanique des Fluides de Toulouse, CNRS–Université de Toulouse, 31400 Toulouse, France
Corresponding
E-mail address:

Abstract

The analysis of flow over a slowly perturbed bottom (when perturbations have a typical length scale much larger than channel height) is often based on the shallow-water (or Saint-Venant) equations with the addition of a wall-friction term which is a local function of the mean velocity. By this choice, small sinusoidal disturbances of wall stress and mean velocity are bound to be in phase with each other. In contrast, studies of shorter-scale disturbances have long established that a phase lead develops between wall stress and mean velocity, with a crucial destabilizing effect on sediment transport along an erodible bed. The purpose of this paper is to calculate the wall-shear stress under large length-scale conditions and provide corrections to the Saint-Venant model.

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Copyright © Cambridge University Press 2010

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