Vortex-wave interaction on the surface of a sphere.

The time-dependent interaction of a point vortex with a vorticity jump separating regions of opposite signed and constant vorticities on the surface of a non-rotating sphere is examined. First, small amplitude interfacial waves are considered where linear theory is applicable. A point vortex in a region of same-signed vorticity will initially move away from the interface and a point vortex in a region of opposite-signed vorticity will move towards it. Weak vortices sufficiently far from the interface then undergo meridional oscillation while precessing about the sphere. The sense of azimuthal precession is determined by the sign of the vorticity jump at the interface. It is demonstrated by both linear and nonlinear theories that a vortex at a pole in a region of same-signed vorticity is a stable equilibrium whereas a vortex at a pole in a region of opposite-signed vorticity is an unstable equilibrium. Numerical computations using contour dynamics confirm these results and the dynamics of more nonlinear cases are examined. [ABSTRACT FROM AUTHOR]