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Baroclinic instability of large-amplitude geostrophic flows

Published online by Cambridge University Press:  26 April 2006

E. S. Benilov
E. S. Benilov
Affiliation:
School of Mathematics, University of New South Wales, PO Box 1, Kensington, NSW 2033, Australia
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Abstract

This paper examines the large-scale dynamics of a layer of stratified fluid on the β-plane. A three-dimensional asymptotic system is derived which governs geostrophic flows with large displacement of isopycnal surfaces. This is then reduced to a two-dimensional set of equations which describe the interaction of a baroclinic ‘quasi-mode’ with arbitrary vertical profile and barotrophic motion. The baroclinic instability of large-amplitude zonal flows with vertical shear is studied within the framework of these equations. In the case where the displacement of isopycnal surfaces is small, the results obtained should overlap with the ‘traditional’ baroclinic instability of quasi-geostrophic (small-amplitude) flows. In order to compare the two types of instability, the quasi-geostrophic boundary-value problem is solved asymptotically for the case of long-wave disturbances and weak β-effect (the latter limit of quasi-geostrophic theory has not been considered previously). The instability that is found is linked to the Hamiltonian structure of the governing equations. The equations derived are generalized for the case of more than one baroclinic quasi-mode.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 251 , June 1993 , pp. 501 - 514
Copyright
© 1993 Cambridge University Press

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