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Nonlinear stability of steady vortex pairs


Reference:

Burton, G., Nussenzveig Lopes, H. and Lopes Jr, M., 2013. Nonlinear stability of steady vortex pairs. Communications in Mathematical Physics, 324 (2), pp. 445-463.

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http://dx.doi.org/10.1007/s00220-013-1806-y

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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.

Details

Item Type Articles
CreatorsBurton, G., Nussenzveig Lopes, H. and Lopes Jr, M.
DOI10.1007/s00220-013-1806-y
Related URLs
URLURL Type
http://arxiv.org/abs/1206.5329Free Full-text
DepartmentsFaculty of Science > Mathematical Sciences
Publisher Statementburtonlopes2.pdf: The original publication is available at www.springerlink.com
RefereedYes
StatusPublished
ID Code32407

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