On rotating doubly connected vortices

Taoufik Hmidi, Joan Mateu, Joan Verdera

Research output: Contribution to journalArticlepeer-review


In this paper we consider rotating doubly connected vortex patches for the Euler equations in the plane. When the inner interface is an ellipse we show that the exterior interface must be a confocal ellipse. We then discuss some relations, first found by Flierl and Polvani, between the parameters of the ellipses, the velocity of rotation and the magnitude of the vorticity in the domain enclosed by the inner ellipse.

Original languageEnglish (US)
Pages (from-to)1395-1429
Number of pages35
JournalJournal of Differential Equations
Issue number4
StatePublished - Feb 15 2015


  • 2D incompressible Euler equations
  • Inverse problems
  • Potential theory
  • Rotating patches

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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