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Purely erosional cyclic and solitary steps created by flow over a cohesive bed

Published online by Cambridge University Press:  20 October 2000

GARY PARKER  and
NORIHIRO IZUMI
GARY PARKER
Affiliation:
St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55414, USA
NORIHIRO IZUMI
Affiliation:
Department of Civil Engineering, Tohoku University, Sendai, 980–8579, Japan Present address: School of Civil Engineering, Asian Institute of Technology, Pathumthani 12120, Thailand.
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Abstract

An erodible surface exposed to supercritical flow often devolves into a series of steps that migrate slowly upstream. Each step delineates a headcut with an associated hydraulic jump. These steps can form in a bed of cohesive material which, once eroded, is carried downstream as washload without redeposition. Here the case of purely erosional, one-dimensional periodic, or cyclic steps in cohesive material is considered. The St. Venant shallow-water equations combined with a formulation for sediment erosion are used to construct a complete theory of the erosional case. The solution allows wavelength, wave height, migration speed and bed and water surface profiles to be determined as functions of imposed parameters. The analysis also admits a solution for a solitary step, or single headcut of self-preserving form.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 419 , 25 September 2000 , pp. 203 - 238
Copyright
© 2000 Cambridge University Press

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