Nonlinear stability of steady vortex pairs

Geoffrey Burton, Helena Nussenzveig Lopes, Milton C. Lopes Filho

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this article, we prove nonlinear orbital stability for steadily translating vortex pairs, a family of nonlinear waves that are exact solutions of the incompressible, two-dimensional Euler equations. We use an adaptation of Kelvin's variational principle, maximizing kinetic energy penalised by a multiple of momentum among mirror-symmetric isovortical rearrangements. This formulation has the advantage that the functional to be maximized and the constraint set are both invariant under the flow of the time-dependent Euler equations, and this observation is used strongly in the analysis. Previous work on existence yields a wide class of examples to which our result applies.
Original languageEnglish
Pages (from-to)445-463
Number of pages19
JournalCommunications in Mathematical Physics
Volume324
Issue number2
DOIs
Publication statusPublished - Dec 2013

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