### Abstract

Original language | English |
---|---|

Pages (from-to) | 515-528 |

Number of pages | 14 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 134 |

DOIs | |

Publication status | Published - 2003 |

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**Vortex-rings of prescribed impulse.** / Burton, G R.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Vortex-rings of prescribed impulse

AU - Burton, G R

N1 - ID number: ISI:000183479400011

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

U2 - 10.1017/s0305004102006631

DO - 10.1017/s0305004102006631

M3 - Article

VL - 134

SP - 515

EP - 528

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

ER -