Equation of motion of a diffusing vortex sheet-Reference-Cited by-同舟云学术

Equation of motion of a diffusing vortex sheet

Published:1994-06-25 Issue: Volume:269 Page:265-281
ISSN:0022-1120
Container-title:Journal of Fluid Mechanics
language:en
Short-container-title:J. Fluid Mech.

Author:

Dhanak M. R.

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.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference11 articles.

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