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The structure of organized vortices in a free shear layer

Published online by Cambridge University Press:  20 April 2006

R. T. Pierrehumbert  and
S. E. Widnall
R. T. Pierrehumbert
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Present address: Department of Meteorology, Massachusetts Institute of Technology.
S. E. Widnall
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
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Abstract

A new family of solutions to the steady Euler equations corresponding to spatially periodic states of a free shear layer is reported. This family bifurcates from a parallel shear layer of finite thickness and uniform vorticity, and extends continuously to a shear layer consisting of a row of concentrated pointlike vortices. The energetic properties of the family are considered, and it is concluded that a vortex in a row of uniform vortices produced by periodic roll-up of a vortex sheet must have a major axis of length approximately 50% or more of the distance between vortex centres; it is also concluded that vortex amalgamation events tend to reduce vortex size relative to spacing. The geometric and energetic properties of the solutions confirm the mathematical basis of the tearing mechanism of shear-layer growth first proposed in an approximate theory of Moore & Saffman (1975).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 102 , January 1981 , pp. 301 - 313
Copyright
© 1981 Cambridge University Press

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