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


Benilov, ES and Broutman, D and Kuznetsova, EP, On the stability of large-amplitude vortices in a continuously stratified fluid on the f-plane, Journal of Fluid Mechanics, 355 pp. 139-162. ISSN 0022-1120 (1998) [Refereed Article]

DOI: doi:10.1017/S0022112097007581


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.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Pure mathematics
Research Field:Algebra and number theory
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Benilov, ES (Dr Eugene Benilov)
UTAS Author:Kuznetsova, EP (Mr Kuznetsova)
ID Code:14316
Year Published:1998
Web of Science® Times Cited:18
Deposited By:Mathematics
Deposited On:1998-08-01
Last Modified:2011-08-09

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