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Bedforms in a turbulent stream: ripples, chevrons and antidunes

Published online by Cambridge University Press:  28 November 2011

Bruno Andreotti ,
Philippe Claudin ,
Olivier Devauchelle ,
Orencio Durán  and
Antoine Fourrière
Bruno Andreotti*
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH UMR 7636 ESPCI – CNRS – Univ. Paris Diderot – Univ. P. M. Curie), 10 rue Vauquelin, 75231, Paris CEDEX 05, France
Philippe Claudin
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH UMR 7636 ESPCI – CNRS – Univ. Paris Diderot – Univ. P. M. Curie), 10 rue Vauquelin, 75231, Paris CEDEX 05, France
Olivier Devauchelle
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH UMR 7636 ESPCI – CNRS – Univ. Paris Diderot – Univ. P. M. Curie), 10 rue Vauquelin, 75231, Paris CEDEX 05, France Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA
Orencio Durán
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH UMR 7636 ESPCI – CNRS – Univ. Paris Diderot – Univ. P. M. Curie), 10 rue Vauquelin, 75231, Paris CEDEX 05, France
Antoine Fourrière
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH UMR 7636 ESPCI – CNRS – Univ. Paris Diderot – Univ. P. M. Curie), 10 rue Vauquelin, 75231, Paris CEDEX 05, France
*
†Email address for correspondence: andreotti@pmmh.espci.fr
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Abstract

The interaction between a turbulent flow and a granular bed via sediment transport produces various bedforms associated with distinct hydrodynamical regimes. In this paper, we compare ripples (downstream-propagating transverse bedforms), chevrons and bars (bedforms inclined with respect to the flow direction) and antidunes (upstream-propagating bedforms), focusing on the mechanisms involved in the early stages of their formation. Performing the linear stability analysis of a flat bed, we study the asymptotic behaviours of the dispersion relation with respect to the physical parameters of the problem. In the subcritical regime (Froude number smaller than unity), we show that the same instability produces ripples or chevrons depending on the influence of the free surface. The transition from transverse to inclined bedforms is controlled by the ratio of the saturation length , which encodes the stabilizing effect of sediment transport, to the flow depth , which determines the hydrodynamical regime. These results suggest that alternate bars form in rivers during flooding events, when suspended load dominates over bedload. In the supercritical regime , the transition from ripples to antidunes is also controlled by the ratio . Antidunes appear around resonant conditions for free surface waves, a situation for which the sediment transport saturation becomes destabilizing. This resonance turns out to be fundamentally different from the inviscid prediction. Their wavelength selected by linear instability mostly scales on the flow depth , which is in agreement with existing experimental data. Our results also predict the emergence, at large Froude numbers, of ‘antichevrons’ or ‘antibars’, i.e. bedforms inclined with respect to the flow and propagating upstream.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Nonlinear Dynamical Systems: Pattern formation Geophysical and Geological Flows: River dynamics

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Papers
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Journal of Fluid Mechanics , Volume 690 , 10 January 2012 , pp. 94 - 128
Copyright
Copyright © Cambridge University Press 2011

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