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On the formation of ripples on an erodible bed

Published online by Cambridge University Press:  20 April 2006

B. Mutlu Sumer  and
Mehmet Bakioglu
B. Mutlu Sumer
Affiliation:
Technical University of Istanbul, Faculty of Civil Engineering, Taskisla, Taksim, Istanbul, Turkey Present address: Technical University of Denmark. Institute of Hydrodynamic and Hydraulic Engineering, 2800 Lynghy, Denmark
Mehmet Bakioglu
Affiliation:
Technical University of Istanbul, Faculty of Civil Engineering, Taskisla, Taksim, Istanbul, Turkey
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Abstract

A linear stability analysis is presented of both hydraulically smooth and transitional flows over an erodible bed. The present theory is developed to account for the formation of ripples. It is essentially an extension of the theory of Richards (1980) to include the effect of viscosity upon the bed wave stability. The theory takes into consideration that the formation of ripples does not depend on flow depths, and that only the bed-load transport is involved in the formation of ripples. The effect of gravity is included in the analysis through the local inclination of the wavy bed surface. The results show that the bed is unstable (i.e. ripples exist) when the grain Reynolds number is less than a certain value. The limiting values of the grain Reynolds number for ripple existence obtained through present analysis are found to be in good agreement with observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 144 , July 1984 , pp. 177 - 190
Copyright
© 1984 Cambridge University Press

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