Recent progress in the relative equilibria of point vortices — In memoriam Hassan Aref

Peter Beelen, Morten Brøns, Vikas S. Krishnamurthy, Mark A. Stremler

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Hassan Aref, who sadly passed away in 2011, was one of the world's leading researchers in the dynamics and equilibria of point vortices. We review two problems on the subject of point vortex relative equilibria in which he was engaged at the time of his death: bilinear relative equilibria and the geometry of the three-vortex problem as it relates to equilibria. A set of point vortices is in relative equilibrium if it is at most rotating rigidly around the center of vorticity, and the configuration is bilinear if the vortices are placed on two orthogonal lines in the co-rotating frame. A very complete characterisation of the bilinear case can be obtained when one of the lines contains only two vortices. The classic three-vortex problem can be viewed anew by considering the dy- namics of the circle circumscribing the vortex triangle and the interior angles of that triangle. This approach leads naturally to the observation that the equilateral triangle is the only equilibrium configuration for three point vortices, regardless of their strength values.
Original languageEnglish
JournalI U T A M. Procedia
Pages (from-to)3-12
Publication statusPublished - 2013
EventTopological Fluid Dynamics II (IUTAM Symposium) - Cambridge, United Kingdom
Duration: 23 Jul 201227 Jul 2012


ConferenceTopological Fluid Dynamics II (IUTAM Symposium)
Country/TerritoryUnited Kingdom
Internet address


  • Point vortices
  • Relative equilibria
  • Vortex crystals


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