SOLITARY WAVES OF VORTICES WITHIN A ROTATING, FLUID SHELL

We consider a spherical, solid planet surrounded by a thin layer of an incompressible, inviscid fluid. The planet rotates with constant angu lar velocity about a fixed axis. The motion imparted by this planetary rotation upon the fluid particles of the ocean has been assumed to be governed by a linear version of the Navier-Stokes equation. We study the vortex motion within this rotating ocean and establish that the pr opagation of vortices depends on a third-order partial differential eq uation for the stream function. We prove that, in the most general cas e, this vorticity equation cannot generate any solitary waves; however , should the vertical component of vorticity satisfy a certain functio nal relationship, then we have obtained a family of solitary waves of permanent form.