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Vortex-rings of prescribed impulse


Reference:

Burton, G. R., 2003. Vortex-rings of prescribed impulse. Mathematical Proceedings of the Cambridge Philosophical Society, 134, pp. 515-528.

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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.

Details

Item Type Articles
CreatorsBurton, G. R.
DOI10.1017/s0305004102006631
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code7346
Additional InformationID number: ISI:000183479400011

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