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The instability of an axisymmetric vortex with monotonic potential vorticity in rotating shallow water

Published online by Cambridge University Press:  26 April 2006

Rupert Ford
Rupert Ford
Affiliation:
Centre for Atmospheric Science, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, UK Current address: Scripps Institution of Oceanography, 9500 Gilman Drive, La Jolla, CA 92093-0225, USA.
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Abstract

The stability of an axisymmetric vortex with a single radial discontinuity in potential vorticity is investigated in rotating shallow water. It is shown analytically that the vortex is always unstable, using the WKBJ method for instabilities with large azimuthal mode number. The analysis reveals that the instability is of mixed type, involving the interaction of a Rossby wave on the boundary of the vortex and a gravity wave beyond the sonic radius. Numerically, it is demonstrated that the growth rate of the instability is generally small, except when the potential vorticity in the vortex is the opposite sign to the background value, in which case it is shown that inertial instability is likely to be stronger than the present instability.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 280 , 10 December 1994 , pp. 303 - 334
Copyright
© 1994 Cambridge University Press

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