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On the stability of large-amplitude vortices in a continuously stratified fluid on the f-plane

Published online by Cambridge University Press:  25 January 1998

E. S. BENILOV ,
D. BROUTMAN  and
E. P. KUZNETSOVA
E. S. BENILOV
Affiliation:
Department of Mathematics, University of Tasmania, PO Box 1214, Launceston 7250, Australia Present address: Department of Mathematics, University of Warwick, Coventry CV4 7AL, UK.
D. BROUTMAN
Affiliation:
School of Mathematics, University of New South Wales, Sydney 2052, Australia
E. P. KUZNETSOVA
Affiliation:
Department of Mathematics, University of Tasmania, PO Box 1214, Launceston 7250, Australia
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Abstract

The stability of continuously stratified vortices with large displacement of isopycnal surfaces on the f-plane is examined both analytically and numerically. Using an appropriate asymptotic set of equations, we demonstrated that sufficiently large vortices (i.e. those with small values of the Rossby number) are unstable. Remarkably, the growth rate of the unstable disturbance is a function of the spatial coordinates. At the same time, the corresponding boundary-value problem for normal modes has no smooth square-integrable solutions, which would normally be regarded as stability.

We conclude that (potentially) stable vortices can be found only among ageostrophic vortices. Since this assumption cannot be verified analytically due to complexity of the primitive equations, we verify it numerically for the particular case of two-layer stratification.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 355 , 25 January 1998 , pp. 139 - 162
Copyright
© 1998 Cambridge University Press

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