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Dissipative effects on the resonant flow of a stratified fluid over topography

Published online by Cambridge University Press:  21 April 2006

N. F. Smyth
N. F. Smyth
Affiliation:
Department of Mathematics, University of Wollongong, P.O. Box 1144, Wollongong, NSW, 2500, Australia
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Abstract

The effect of dissipation on the flow of a stratified fluid over topography is considered in the weakly nonlinear, long-wave limit for the case when the flow is near resonance, i.e. the basic flow speed is close to a linear long-wave speed for one of the long-wave modes. The two types of dissipation considered are the dissipation due to viscosity acting in boundary layers and/or interfaces and the dissipation due to viscosity acting in the fluid as a whole. The effect of changing bottom topography on the flow produced by a force moving at a resonant velocity is also considered. In this case, the resonant condition is that the force velocity is close to a linear long-wave velocity for one of the long-wave modes. It is found that in most cases, these extra effects result in the formation of a steady state, in contrast to the flow without these effects, which remains unsteady for all time. The flow resulting under the action of boundary-layer dissipation is compared with recent experimental results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 192 , July 1988 , pp. 287 - 312
Copyright
© 1988 Cambridge University Press

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