Quasigeostrophic movements in barotropic and baroclinic fluid

The dynamics of large-scale motions in a thin fluid layer on a rotating sphere in a gravity field is reviewed, and a classification of these motions is derived in a quasi-geostrophic approximation in response to the observation of certain soliton-type effects in quasi-geostrophic motions not subject to the standard vortex equation. For a barotropic model with quasi-two-dimensional motions, a nonlinear equation is obtained which describes the motion on such surfaces for which the radius of curvature is much larger than the Obukhov radius, permitting a quasi-soliton-type solution. An analogous equation is obtained for a baroclinic atmosphere whose radius of curvature is much larger than the interior Rossby radius of deformation. The barotropic case of planetary waves on an arbitrary surface of rotation is considered.