The Effect of Viscosity on the Stability of Planar Vortices with Fine Structure

Authors: Hall I.M.; Bassom A.P.; Gilbert A.D.

Source: Quarterly Journal of Mechanics and Applied Mathematics, Volume 56, Number 4, November 2003 , pp. 649-657(9)

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Abstract:

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.

Document Type: Research article

Publication date: 2003-11-01

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The Quarterly Journal of Mechanics and Applied Mathematics publishes original research articles on the application of mathematics to the field of mechanics interpreted in its widest sense. In addition to traditional areas, such as fluid and solid mechanics, the editors welcome submissions relating to any modern and emerging areas of applied mathematics.