On rotating doubly connected vortices

Taoufik Hmidi (1) , Joan Mateu (2) , Joan Verdera (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 UAB - Departament de Matemàtiques [Barcelona]

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.

Mots clés: 2D incompressible Euler equations; Rotating patches; Inverse problems; Potential theory

Domaines: Equations aux dérivées partielles [math.AP]

Taoufik Hmidi, Joan Mateu, Joan Verdera. On rotating doubly connected vortices. Journal of Differential Equations, 2015, 258 (4), pp.1395-1429. ⟨10.1016/j.jde.2014.10.021⟩. ⟨hal-00870294⟩