On the evolution of nearly circular vortex patches

P. Constantin, E. S. Titi

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

Recently, the classical problem of the evolution of patches of constant vorticity was reformulated as an evolution equation for the boundary of the patch. We study this equation in the neighborhood of the circular vortex patch and introduce a hierarchy of area-preserving nonlinear approximate equations. The first of these equations is shown to have a rich rigid structure: it possesses an exhaustive increasing sequence of linear invariant manifolds of arbitrarily large finite dimensions. On each of these manifolds the equation can be written as an explicit finite system of ordinary differential equations. Solutions of these ODEs, starting from arbitrarily small neighborhoods of the circular vortex patch, are shown to blow up.

Original languageEnglish (US)
Pages (from-to)177-198
Number of pages22
JournalCommunications In Mathematical Physics
Volume119
Issue number2
DOIs
StatePublished - Jun 1 1988
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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