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Vortex-rings of prescribed impulse

Published online by Cambridge University Press:  02 May 2003

G. R. BURTON
Affiliation:
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY

Abstract

We consider a variational problem for steady axisymmetric vortex-rings, in which kinetic energy is maximised subject to prescribed impulse, with the ratio of vorticity to axial distance belonging to the class of rearrangements of a prescribed function, as proposed by Benjamin. We prove existence of maximisers in an extended constraint set, allowing some loss of vorticity. We then study a particular family of vortex-rings including Hill's spherical vortex, determining the precise range of impulse values for which the maximiser loses vorticity, and show that the maximisers are spherical when this happens.

Type
Research Article
Copyright
2003 Cambridge Philosophical Society

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