  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.
