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.
Original languageEnglish
Pages (from-to)S68-S80
JournalJournal of Mathematical Fluid Mechanics
Volume7
DOIs
Publication statusPublished - 2005

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Isoperimetric
Vortex
Vortex flow
vortices
Kinetic energy
kinetic energy
Functional Integral
Conserved Quantity
Stream Function
Vorticity
Impulse
vorticity
impulses
Duality
formulations
Formulation

Cite this

Isoperimetric properties of Lamb's circular vortex-pair. / Burton, G R.

In: Journal of Mathematical Fluid Mechanics, Vol. 7, 2005, p. S68-S80.

Research output: Contribution to journalArticle

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