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Equation of motion of a diffusing vortex sheet

Published online by Cambridge University Press:  26 April 2006

M. R. Dhanak
M. R. Dhanak
Affiliation:
Department of Ocean Engineering, Florida Atlantic University, Boca Raton, FL 33431, USA
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Abstract

Moore's (1978) equation for following the evolution of a thin layer of uniform vorticity in two dimensions is extended to the case of a non-uniform, instantaneously known, vorticity distribution, using the method of matched asymptotic expansions. In general, the vorticity distribution satisfies a boundary-layer equation. This has a similarity solution in the case of a vortex layer of small thickness in a viscous fluid. Using this solution, an equation of motion of a diffusing vortex sheet is obtained. The equation retains the simplicity of Birkhoff's integro-differential equation for a vortex sheet, while incorporating the effect of viscous diffusion approximately. The equation is used to study the growth of long waves on a Rayleigh layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 269 , 25 June 1994 , pp. 265 - 281
Copyright
© 1994 Cambridge University Press

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