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On the equilibrium and stability of a row of point vortices

Published online by Cambridge University Press:  26 April 2006

Hassan Aref
Hassan Aref
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
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Abstract

The equilibrium and stability of a single row of equidistantly spaced identical point vortices is a classical problem in vortex dynamics, which has been addressed by several investigators in different ways for at least a century. Aspects of the history and the essence of these treatments are traced, stating some in more accessible form, and pointing out interesting and apparently new connections between them. For example, it is shown that the stability problem for vortices in an infinite row and the stability problem for vortices arranged in a regular polygon are solved by the same eigenvalue problem for a certain symmetric matrix. This result also provides a more systematic enumeration of the basic instability modes. The less familiar theory of equilibria of a finite number of vortices situated on a line is also recalled.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 290 , 10 May 1995 , pp. 167 - 181
Copyright
© 1995 Cambridge University Press

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