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The Quarterly Journal of Mechanics and Applied Mathematics 2003 56(4):649-657; doi:10.1093/qjmam/56.4.649
© 2003 by Oxford University Press
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The Effect of Viscosity on the Stability of Planar Vortices with Fine Structure

Ian M. Hall1, Andrew P. Bassom1 and Andrew D. Gilbert1

( 1 Department of Mathematical Sciences, University of Exeter, North Park Road, Exeter EX4 4QE )

We examine the viscous response of sharp-edged vortices surrounded by fine structure. Such compact vortices admit normal mode solutions, and when weak vorticity is superimposed around the edge of the vortex a quasi-mode appears. A critical layer is formed at the location at which the angular velocity of the fluid matches the frequency of the normal mode. Fine-scale vorticity within this layer, combined with the presence of viscosity, can affect the stability of the quasi-mode in a number of ways. Here we discuss briefly one situation for which viscosity can have a destabilizing effect.

Received 20 March 2003. Revised 27 May 2003.


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