GEOSTROPHIC TURBULENCE

The geostrophic-balance equation is a singular perturbation with respect to neglected accelerations and frictional forces. The curl of the full momentum equation is unaffected by the dominant part of the pressure force and gives a fully predictive potential vorticity equation. The derivation of the vorticity equations appropriate to a spherical planet is a length process; here the author takes them as given. The dominant small parameters are Ro, the fluid depth/planetary radius, the aspect ratio of the motion, H/L, and the ratio of Coriolis to buoyancy forces.