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Three-dimensional wave instability near a critical level

Published online by Cambridge University Press:  26 April 2006

K. B. Winters  and
E. A. D’Asaro
K. B. Winters
Affiliation:
Department of Applied Mathematics and Applied Physics Laboratory, University of Washington, Seattle, WA 98105, USA
E. A. D’Asaro
Affiliation:
Department of Oceanography and Applied Physics Laboratory, University of Washington, Seattle, WA 98105, USA
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Abstract

The behaviour of internal gravity wave packets approaching a critical level is investigated through numerical simulation. Initial-value problems are formulated for both small- and large-amplitude wave packets. Wave propagation and the early stages of interaction with the mean shear are two-dimensional and result in the trapping of wave energy near a critical level. The subsequent dynamics of wave instability, however, are fundamentally different for two- and three-dimensional calculations. Three-dimensionality develops by transverse convective instability of the two-dimensional wave. The initialy two-dimensional flow eventually collapses into quasi-horizontal vortical structures. A detailed energy balance is presented. Of the initial wave energy, roughly one third reflects, one third results in mean flow acceleration and the remainder cascades to small scales where it is dissipated. The detailed budget depends on the wave amplitude, the amount of wave reflection being particularly sensitive.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 272 , 10 August 1994 , pp. 255 - 284
Copyright
Copyright © Cambridge University Press 1994

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