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Periodic steady vortices in a stagnation-point flow

Published online by Cambridge University Press:  26 April 2006

Oliver S. Kerr  and
J. W. Dold
Oliver S. Kerr
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 4TW, UK Current address: Department of Mathematics, City University. Northampton Square, London EC1V 0HB. UK.
J. W. Dold
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 4TW, UK
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Abstract

A stagnation point flow of the form U = (0, Ay, — Az) is unstable to three-dimensional disturbances. It has been shown that the vorticity components of such a disurbance that are perpendicular to the direction of the diverging flow will decay, and that the parallel component of vorticity can grow. We augment these findings by showing that fully nonlinear steady-state deviations from this flow exist that consist of a periodic distribution of counter-rotating vortices whose axes lie parallel to the direction of the diverging flow. These solutions have two independent parameters: the dimensionless strength of the converging flow, and the intensity of the vortices. We examine the structure of these vortices in the asymptotic limits of large strain rate of the converging flow, and of large amplitude of the vortices.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 276 , 10 October 1994 , pp. 307 - 325
Copyright
© 1994 Cambridge University Press

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