The effect of viscosity on the stability of planar vortices with fine structure

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.