Open Collections

Vortex motion in thin films

University of British Columbia

The classical theory of rectilinear vortex motion has been generalized to include vortices in thin fluids of varying depth on curved surfaces. The equations of motion are examined to lowest order in a perturbation expansion in which the depth of fluid is considered small in comparison with the principal radii of curvature of the surface. Existence of a generalized vortex streamfunction is proved and used to generate conservation laws. A number of simple vortex systems are described. In particular, criteria for the stability of rings of vortices on surfaces of revolution are found. In contradistinction to the result of von Karman, double rings (vortex streets) in both staggered and symmetric configurations may be stable. The effects of finite core size are examined. Departures from radial symmetry in core vorticity distributions are shown to introduce small wobbles in the vortex motion. The case of an elliptical core is treated in detail. Applications of the theory to atmospheric cyclones and superfluid vortices are discussed.

Text

2010-03-23

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http://hdl.handle.net/2429/22397

Physics

University of British Columbia

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