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Resonant flow of a stratified fluid over topography

Published online by Cambridge University Press:  21 April 2006

R. H. J. Grimshaw  and
N. Smyth
R. H. J. Grimshaw
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia Current address: School of Mathematics, University of N.S.W., P.O. Box 1, Kensington, N.S.W. 2033, Australia.
N. Smyth
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia Current address: School of Mathematics, University of N.S.W., P.O. Box 1, Kensington, N.S.W. 2033, Australia.
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Abstract

The flow of a stratified fluid over topography is considered in the long-wavelength weakly nonlinear limit for the case when the flow is near resonance; that is, the basic flow speed is close to a linear long-wave phase speed for one of the long-wave modes. It is shown that the amplitude of this mode is governed by a forced Korteweg-de Vries equation. This equation is discussed both analytically and numerically for a variety of different cases, covering subcritical and supercritical flow, resonant or non-resonant, and for localized forcing that has either the same, or opposite, polarity to the solitary waves that would exist in the absence of forcing. In many cases a significant upstream disturbance is generated which consists of a train of solitary waves. The usefulness of internal hydraulic theory in interpreting the results is also demonstrated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 169 , August 1986 , pp. 429 - 464
Copyright
© 1986 Cambridge University Press

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