Geostrophic Vortices on a Circle of Latitude in a Cap on a Rotating Sphere - Peters, A S (1974)
This report contains an analysis of the linear stability of the motion of n+l geostrophic vortices confined in a polar cap on a rotating sphere. It is supposed that initially one vortex is at the north pole while the others are symmetrically arranged on a circle of latitude; and that the motion is subject to a certain condition along the latitude circle which bounds the cap. The development stems from the demonstration that a concentrated geostrophic vortex in a rotating spherical layer is characterized by a singular spherical harmonic of degree nu and order zero. This function has a role analogous to that of the Bessel function which characterizes a rectilinear geostrophic vortex in a rotating planar layer.