Vortex Motion on a Sphere

Abstract

The theory of the vortex motion of two-dimensional incompressible inviscid flow on a sphere is presented. Vorticity and stream function, which are related by the Laplace-Beltrami operator, are initially outlined. Green’s function of the equation is obtained in which the stream function is expressed as an integral form. The equations of motion for two vortex models on a sphere are derived. In particular, the equation for vortex patches with constant vorticity is given in terms of the contour integral appropriate for the contour dynamics.