Vortex rings in R-3 and rearrangements

T V Badiani, G R Burton

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We study the existence of steady axisymmetric vortex rings in an ideal fluid. A functional, comprising a linear combination of kinetic energy and impulse, is to be maximized subject to the constraint that a quantity related to vorticity belongs to a set of rearrangements of a given function. Generalized solutions of a quite specific type are shown to exist, arising as extreme points of a convex extended constraint set. In the case when the given function is the indicator of a set of finite measure, the existence of proper maximizers and local maximizers is demonstrated.
Original languageEnglish
Pages (from-to)1115-1135
Number of pages21
JournalProceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences
Volume457
Issue number2009
Publication statusPublished - 2001

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Vortex Ring
vortex rings
Rearrangement
Vortex flow
ideal fluids
Vorticity
Kinetic energy
vorticity
impulses
Ideal Fluid
kinetic energy
Generalized Solution
Extreme Points
Impulse
Fluids
Linear Combination

Cite this

Vortex rings in R-3 and rearrangements. / Badiani, T V; Burton, G R.

In: Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences, Vol. 457, No. 2009, 2001, p. 1115-1135.

Research output: Contribution to journalArticle

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