Contour dynamics/surgery on the sphere
This note derives remarkably simple equations governing the motion of an inviscid fluid of constant but negligible depth on the surface of a sphere and outlines an associated numerical algorithm. The algorithm offers an alternative approach for investigating idealised geophysical flows. Inviscid, incompressible flow on a spherical surface and on an infinite plane share the property that the vorticity normal to the surface is conserved on fluid particles. Material conservation of vorticity implies that one may consider the simple piecewise-constant subclass of vorticity distributions for which the boundaries of vorticity discontinuity or contours alone determine the dynamics of the flow.
scientific article; zbMATH DE number 4070493