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The roll-up of vorticity strips on the surface of a sphere

Published online by Cambridge University Press:  26 April 2006

David G. Dritschel  and
Lorenzo M. Polvani
David G. Dritschel
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
Lorenzo M. Polvani
Affiliation:
Department of Applied Physics, Columbia University, New York, NY 10027, USA
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Abstract

We derive the conditions for the stability of strips or filaments of vorticity on the surface of a sphere. We find that the spherical results are surprisingly different from the planar ones, owing to the nature of the spherical geometr. Strips of vorticity on the surface of a sphere show a greater tendency to roll-up into vortices than do strips on a planar surface.

The results are obtained by performing a linear stability analysis of the simplest, piecewise-constant vorticity configuration, namely a zonal band of uniform vorticity located in equilibrium between two latitudes. The presence of polar vortices is also considered, this having the effect of introducing adverse shear, a known stabilizing mechanism for planar flows. In several representative examples, the fully developed stages of the instabilities are illustrated by direct numerical simulation.

The implication for planetary atmospheres is that barotropic flows on the sphere have a more pronounced tendency to produce small, long-lived vortices, especially in equatorial and mid-latitude regions, than was previously anticipated from the theoretical results for planar flows. Essentially, the curvature of the sphere's surface weakens the interaction between different parts of the flow, enabling these parts to behave in relative isolation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 234 , January 1992 , pp. 47 - 69
Copyright
© 1992 Cambridge University Press

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