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Stability of large-amplitude geostrophic flows localized in a thin layer

Published online by Cambridge University Press:  26 April 2006

E. S. Benilov
E. S. Benilov
Affiliation:
Department of Applied Computing and Mathematics, University of Tasmania, PO Box 1214, Launceston, 7250, Australia
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Abstract

In this paper the dynamics of geostrophic flows localized in a thin layer of continuously stratified fluid, which overrides a thick homogeneous layer are studied. The displacement of isopycnal surfaces is assumed large; the β-effect is strong, i.e. \[(R_0/R_e)\cot\theta\gtrsim\epsilon, \] where ε is the Rossby number, θ is the latitude; Re is the Earth's radius, and R0 is the deformation radius based on the total depth of the ocean. An asymptotic system of equations is derived and used to study the stability of zonal currents. Three sufficient conditions of stability are obtained, which restrict the slope of the interface between the stratified and non-stratified layers. The results obtained are applied to the subtropical and subarctic frontal currents in the Northern Pacific: the former was found to be stable, the latter was found to be unstable. However, the growth rate of the instability is very small (the effective time of growth is about 2 years).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 288 , 10 April 1995 , pp. 157 - 174
Copyright
© 1995 Cambridge University Press

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