Latitudinal point vortex rings on the spheroid

Point vortex motion on the surface of a spheroid is studied. Exact dynamical equations from the corresponding Hamiltonian are constructed by computing the conformal metric which induces a modified stereographic projection. As a concrete example, the motion of point vortices at the same latitude (called the point vortex ring) is investigated as an extension of the sphere case. The role of eccentricity to the stability of the rotating motion is analysed. The influence of a pole vortex is also discussed.