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On Chaplygin's investigations of two-dimensional vortex structures in an inviscid fluid

Published online by Cambridge University Press:  26 April 2006

V.V. Meleshko  and
G.J.F. van Heijst
V.V. Meleshko
Affiliation:
Institute of Hydromechanics of the Ukrainian Academy of Sciences, 252057Kiev, Ukraine
G.J.F. van Heijst
Affiliation:
J. M. Burgers Centre for Fluid Mechanics, Fluid Dynamics Laboratory, Department of Technical Physics, Eindhoven University of Technology, PO Box 513, 5600MBEindhoven, The Netherlands
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Abstract

This paper describes exact solutions of two-dimensional vortex structures that were published by Chaplygin (1899, 1903) at the turn of the last century, which seem to have escaped the attention of later investigators in this field. Chaplygin's solutions include that of an elliptical patch of uniform vorticity in an exterior field of pure shear and that of a (symmetric or non-symmetric) dipolar vortex with a continuous distribution of vorticity translating steadily along a straight path. In addition, a solution is presented for a non-symmetric vortex dipole moving along a circular trajectory. A concise account of Chaplygin's solutions is given, complemented by a more detailed analysis of some of their relevant properties.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 272 , 10 August 1994 , pp. 157 - 182
Copyright
Copyright © Cambridge University Press 1994

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