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