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The instability and breakdown of tall columnar vortices in a quasi-geostrophic fluid

Published online by Cambridge University Press:  26 April 2006

David G. Dritschel  and
Manuel De La Torre JuáRez
David G. Dritschel
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
Manuel De La Torre JuáRez
Affiliation:
Departamento de Física Aplicada a la Ingeniería Aeronáutica, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, 28040 Madrid, Spain
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Abstract

We examine the linear stability of elliptical columns of uniform potential vorticity subject to two-dimensional (horizontal) straining within a rapidly rotating, stratified (quasi-geostrophic) fluid. We find that horizontal straining can promote the exponential growth of three-dimensional disturbances when the vortex height-to-width aspect ratio exceeds, qualitatively, three times the ratio of the Coriolis parameter to the buoyancy frequency. This instability is not related to the usual baroclinic instability which operates on shallow vortex columns whose potential vorticity changes sign with height. The nonlinear development of these instabilities is investigated numerically using a high-resolution contour surgery algorithm. Simulations are conducted for both a Boussinesq (ocean-like) fluid and a compressible (atmospheric-like) fluid having exponentially decreasing density with height. The simulations reveal a generic nonlinear development that results in a semi-ellipsoidal baroclinic vortex dome at the lower surface and, in the case of a Boussinesq fluid, another such dome at the upper surface.

The related problem of two interacting vortex columns is also examined. A generic three-dimensional instability and nonlinear development occurs no matter how great the distance between the vortex columns, provided that they are sufficiently tall.

Our results may bear upon the observed structure of many atmospheric and oceanic vortices, whose height-to-width aspect ratios are consistent with our findings. Remarkably, even strongly ageostrophic vortices, such as tropical cyclones, fit the pattern. Our results furthermore re-open questions about the long-time nature of freely decaying quasi-geostrophic turbulence, for which recent simulations indicate a progressive two-dimensionalization by vortex alignment, while earlier simulations have indicated long-lived baroclinic vortices, not unlike what we find here.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 328 , 10 December 1996 , pp. 129 - 160
Copyright
© 1996 Cambridge University Press

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