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On rotating doubly connected vortices. (English) Zbl 1446.76086

Summary: 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.

MSC:

76B47 Vortex flows for incompressible inviscid fluids
76U05 General theory of rotating fluids
35Q31 Euler equations
76M21 Inverse problems in fluid mechanics
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