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Long nonlinear internal waves in channels of arbitrary cross-section

Published online by Cambridge University Press:  12 April 2006

R. H. J. Grimshaw
R. H. J. Grimshaw
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia
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Abstract

Using a two-layer fluid model, equations are developed which describe long internal waves propagating along a channel of arbitrary cross-section. Expressions for the phase speed of these waves are derived in terms of geometric properties of the cross-section. When weakly nonlinear effects are balanced by weak dispersion, a Korteweg-de Vries equation is derived to describe the waves. The effects of a slowly varying cross-section are included. Applications of the theory are made to recent observations of internal surges in lakes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 86 , Issue 3 , 14 June 1978 , pp. 415 - 431
Copyright
© 1978 Cambridge University Press

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