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A popular model for a generic fat-cored vortex ring or eddy is Hill'sspherical vortex (Phil. Trans. Roy. Soc. A vol. 185, 1894, p. 213). Here wefind an exact solution for such a spherical vortex steadily propagating alongthe axis of a rotating ideal fluid. The spherical vortex swirls in such a wayas to exactly cancel out the background rotation of the system. The flowexternal to the spherical vortex exhibits fully nonlinear inertial wave motion.We show that above a critical rotation rate, closed streamlines form in thisouter fluid region and hence fluid is carried along with the spherical vortex.As the rotation rate is further increased, further concentric "sibling" vortexrings are formed, counter rotating with respect to the original sphericalvortex.

Hill's Spherical Vortex in a Rotating Fluid