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The formation of ripples and dunes on an erodible bed

Published online by Cambridge University Press:  19 April 2006

Kelvin J. Richards
Kelvin J. Richards
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
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Abstract

A two-dimensional stability analysis is presented of flow of low Froude number over an erodible bed. Particular regard is given to the modelling of the turbulent flow close to the bed. In contrast to previous theories that use a constant eddy-viscosity approach the present theory predicts the occurrence of two separate modes of instability, with wavelengths related to the roughness of the bed and the depth of the flow. It is postulated that these two modes correspond to the formation of ripples and dunes respectively. The results are strongly dependent on the two parameters z0, the roughness length of the bed, and β, the effect of the local bed slope on the bed-load transport. Using physically plausible estimates for these parameters the results of the analysis are in good agreement with observations for both ripples and dunes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 99 , Issue 3 , 14 August 1980 , pp. 597 - 618
Copyright
© 1980 Cambridge University Press

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