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

Fingerprint

Nonlinear Stability
Euler Equations
Vortex
vortices
Orbital Stability
translating
Kelvin
Nonlinear Waves
variational principles
Rearrangement
Kinetic energy
Variational Principle
Mirror
Momentum
Exact Solution
kinetic energy
mirrors
momentum
formulations
orbitals

Cite this

Nonlinear stability of steady vortex pairs. / Burton, Geoffrey; Nussenzveig Lopes, Helena; Lopes Filho, Milton C.

In: Communications in Mathematical Physics, Vol. 324, No. 2, 12.2013, p. 445-463.

Research output: Contribution to journalArticle

Burton, Geoffrey ; Nussenzveig Lopes, Helena ; Lopes Filho, Milton C. / Nonlinear stability of steady vortex pairs. In: Communications in Mathematical Physics. 2013 ; Vol. 324, No. 2. pp. 445-463.
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