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Isoperimetric Properties of Lamb’s Circular Vortex-Pair

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Abstract.

Lamb’s circular vortex-pair was shown by the author [4] to be the unique maximiser, up to axial translations, of a certain integral functional of the stream function subject to a kinetic energy constraint. The present paper proves that the axial translations of Lamb’s circular vortex-pair are the unique maximisers of kinetic energy subject to constraints on the vorticity and impulse. This formulation is more natural, in that it involves only conserved quantities. The result is deduced from [4] by non-convex duality. The analogous theory for Hill’s spherical vortex is also discussed briefly.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, U.K

    G. R. Burton

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  1. G. R. Burton
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Correspondence to G. R. Burton.

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Burton, G.R. Isoperimetric Properties of Lamb’s Circular Vortex-Pair. J. math. fluid mech. 7 (Suppl 1), S68–S80 (2005). https://doi.org/10.1007/s00021-004-0126-6

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  • DOI: https://doi.org/10.1007/s00021-004-0126-6

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