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Cnoidal waves and bores in uniform channels of arbitrary cross-section

Published online by Cambridge University Press:  29 March 2006

J. D. Fenton
J. D. Fenton
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge Present address: Department of Civil Engineering, Imperial College, London.
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Abstract

A steady nonlinear dispersive wave theory is developed in terms of three important invariants of channel flow: discharge, energy, and momentum flux. As such, the work is an extension of Benjamin & Lighthill's approach for rectangular channels.

Considering the differential equation obtained, we examine the behaviour of flows and wave systems in arbitrary channels for changes of energy and momentum. In particular, the bore problem is studied, and previous approaches to this problem, using linear wave theory, are seen to be invalid. The present theory describes several phenomena of open-channel flow, explains a scatter in previously obtained experimental results, and enables simple design recommendations to be made for channels in which stationary or moving bores are expected.

While this work does describe the variation of physical quantities across the channel section, there are some important three-dimensional phenomena, noted experimentally, which remain unexplained.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 58 , Issue 3 , 8 May 1973 , pp. 417 - 434
Copyright
© 1973 Cambridge University Press

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