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Baroclinic instability of Kirchhoff's elliptic vortex

Published online by Cambridge University Press:  26 April 2006

Takeshi Miyazaki  and
Hideshi Hanazaki
Takeshi Miyazaki
Affiliation:
Department of Mechanical and Control Engineering, University of Electro-Communications, Chofu, Tokyo 182, Japan
Hideshi Hanazaki
Affiliation:
Division of Atmospheric Environment, National Institute for Environmental Studies, Tsukuba, Ibaraki 305, Japan
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Abstract

The linear instability of Kirchhoff's elliptic vortex in a vertically stratified rotating fluid is investigated using the quasi-geostrophic, f-plane approximation. Any elliptic vortex is shown to be unstable to baroclinic disturbances of azimuthal wavenumber m = 1 (bending mode) and m = 2 (elliptical deformation). The axial wavenumber of the unstable bending mode approaches Λc = 1.7046 in the limit of small ellipticity, indicating that it is a short-wave baroclinic instability. The instability occurs when the bending wave rotates around the vortex axis with angular velocity identical to the rotation rate of the undisturbed elliptic vortex. On the other hand, the wavenumber of the elliptical deformation mode approaches zero in the same limit, showing that it is a long-wave sideband instability.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 261 , 25 February 1994 , pp. 253 - 271
Copyright
© 1994 Cambridge University Press

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