J Austral Math Soc Ser B 38 pp316--324, 1997.

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

Anna S. Dostovalova and Sergey T. Simakov

Abstract

The paper is concerned with formation of singularities in a density stratified fluid subject to a monochromatic point source of frequency s. 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 t^2/3 exp{i(s t + p/2)} as t ® ¥, whereas its large time behaviour at the other points of the surface is given by t^1/2 exp{i(s t + p/2 ± p/4)}.

Browse the article

Authors

Anna S. Dostovalova

Sergey T. Simakov

Applied Mathematics Department, University of Adelaide, Australia 5005.