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Internal wave—vortical mode interactions in strongly stratified flows

Published online by Cambridge University Press:  26 April 2006

M. -Pascale Lelong  and
James J. Riley
M. -Pascale Lelong
Affiliation:
University of Washington, Seattle WA, USA Present address: National Center for Atmospheric Research, Boulder CO 80307–3000, USA.
James J. Riley
Affiliation:
University of Washington, Seattle WA, USA
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Abstract

In this paper, weakly nonlinear interactions in a strongly-stratified, inviscid flow are re-examined, taking into account the presence of both internal waves and vortical modes. We use a multiple scale formulation, based on the two characteristic times of the problem. Ertel's potential vorticity motivates a splitting of the velocity into propagating (wave) and non-propagating (vortical) contributions. We focus on the three fundamental interactions: the wave/wave, wave/vortex and vortex/vortex interactions. The oft-studied wave/wave interaction illustrates the difference between potential and vertical vorticities. We then identify two additional resonances for the wave/vortex and vortex/vortex interactions respectively. The wave/vortex resonance provides a mechanism for redistributing energy in spectral space while the vortex/vortex interaction may give rise to an internal wave field.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 232 , November 1991 , pp. 1 - 19
Copyright
© 1991 Cambridge University Press

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