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.