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Formation of singularities in a stratified fluid in the presence of a critical level

Published online by Cambridge University Press:  17 February 2009

Anna S. Dostovalova  and
Sergey T. Simakov
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Abstract

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The paper is concerned with formation of singularities in a density stratified fluid subject to a monochromatic point source of frequency σ. The frequency of the source is assumed to be such that the steady-oscillation equation is hyperbolic in the neighbourhood of the source and degenerates at a critical level. We obtain asymptotic formulae demonstrating how the solution diverges as t → ∞ on the characteristic surface emanating from the source. It is shown that, at points of the surface that belong to the critical level, the solution behaves as t⅔ exp {i(σt + π/2)} as t → ∞, whereas its large time behaviour at the other points of the surface is given by t½ exp {i(σt + π/2 ± π/4)}.

Type
Research Article
Information
The ANZIAM Journal , Volume 38 , Issue 3 , January 1997 , pp. 316 - 324
Copyright
Copyright © Australian Mathematical Society 1997

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