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Instability of a stratified boundary layer and its coupling with internal gravity waves. Part 2. Coupling with internal gravity waves via topography

Published online by Cambridge University Press:  08 January 2008

XUESONG WU  and
JING ZHANG
XUESONG WU
Affiliation:
Department of Mathematics, Imperial College London London SW7 2AZ, UK Department of Mechanics, Tianjin University, China
JING ZHANG
Affiliation:
Department of Mechanics, Tianjin University, China
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Abstract

The aim of this paper is to show that the viscous shear instability identified in Part 1 is intrinsically coupled with internal gravity waves when a localized surface topography is present within a boundary layer. The coupling involves two aspects: receptivity and radiation. The former refers to excitation of shear instability modes by gravity waves, and the latter to emission of gravity waves by instability modes. Both physical processes are studied using triple-deck theory. In particular, the radiated gravity waves are found to produce a leading-order back action on the source, and this feedback effect, completely ignored in the acoustic analogy type of approach, is naturally taken into account by the triple-deck formalism. A by-product is that for certain incident angles, gravity waves are over-reflected by the boundary layer, i.e. the reflected waves are stronger than the incident waves.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 595 , 25 January 2008 , pp. 409 - 433
Copyright
Copyright © Cambridge University Press 2008

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