Tidal theory of the thermal wind

Abstract

The baroclinic instability problem is considered in the framework of Laplacian tidal theory. The Hilbert space of the quasigeostrophic vorticity budget is spanned by spheroidal functions. The fluid is linearly stable against quasigeostrophic disturbances. As the essential source of irregular ocean-atmosphere motions, baroclinic instability is ruled out by tidal theory. The midlatitude beta-plane budget of vorticity fluxes is inconsistent with basic laws of motion on the rotating spherical surface. Realistic numerical simulations of global wave dynamics and dynamical circulation instabilities require a covariant account of fluid motion on the spherical planet.