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 angular 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 propagation of vortices depends on a third-order partial differential equation for the stream function. We prove that, in the most general case, this vorticity equation cannot generate any solitary waves; however, should the vertical component of vorticity satisfy a certain functional relationship, then we have obtained a family of solitary waves of permanent form.Retired, U.S. Naval Research Laboratory, Washington, D.C., U.S.A.