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Stability of bedforms in laminar flows with free surface: from bars to ripples

Published online by Cambridge University Press:  23 December 2009

O. DEVAUCHELLE ,
L. MALVERTI ,
É. LAJEUNESSE ,
P.-Y. LAGRÉE ,
C. JOSSERAND  and
K.-D. NGUYEN THU-LAM
O. DEVAUCHELLE*
Affiliation:
Institut de Physique du Globe, 4 place Jussieu, 75252 Paris cedex 05, France Earth, Atmospheric and Planetary Science, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA
L. MALVERTI
Affiliation:
Institut de Physique du Globe, 4 place Jussieu, 75252 Paris cedex 05, France
É. LAJEUNESSE
Affiliation:
Institut de Physique du Globe, 4 place Jussieu, 75252 Paris cedex 05, France
P.-Y. LAGRÉE
Affiliation:
Institut Jean le Rond d'Alembert, CNRS, Université Pierre et Marie Curie, Boîte 161–162, Tour 55–65, 4 Place Jussieu, 75252 Paris Cedex 05, France
C. JOSSERAND
Affiliation:
Institut Jean le Rond d'Alembert, CNRS, Université Pierre et Marie Curie, Boîte 161–162, Tour 55–65, 4 Place Jussieu, 75252 Paris Cedex 05, France
K.-D. NGUYEN THU-LAM
Affiliation:
Institut Jean le Rond d'Alembert, CNRS, Université Pierre et Marie Curie, Boîte 161–162, Tour 55–65, 4 Place Jussieu, 75252 Paris Cedex 05, France
*
†Email address for correspondence: devauche@mit.edu
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Abstract

The present paper is devoted to the formation of sand patterns by laminar flows. It focuses on the rhomboid beach pattern, formed during the backswash. A recent bedload transport model, based on a moving-grains balance, is generalized in three dimensions for viscous flows. The water flow is modelled by the full incompressible Navier–Stokes equations with a free surface. A linear stability analysis then shows the simultaneous existence of two distinct instabilities, namely ripples and bars. The comparison of the bar instability characteristics with laboratory rhomboid patterns indicates that the latter could result from the nonlinear evolution of unstable bars. This result, together with the sensibility of the stability analysis with respect to the parameters of the transport law, suggests that the rhomboid pattern could help improving sediment transport models, so critical to geomorphologists.

JFM classification

Geophysical and Geological Flows: Sediment transport
Type
Papers
Information
Journal of Fluid Mechanics , Volume 642 , 10 January 2010 , pp. 329 - 348
Copyright
Copyright © Cambridge University Press 2010

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References

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