Unstably stratified geophysical fluid dynamics

The linear dynamics of the unstably stratified geophysical flows is investigated with a two-layer formulation. A ‘convective’ deformation radius classifies the dynamics into three regimes:

• 1. 

  1. the scales smaller than the deformation radius: the dynamics characterized by unstable inertial-gravity modes;

• 2. 

  2. the scales larger than the deformation radius: a quasi-geostrophic regime;

• 3. 

  3. the scales close to the deformation radius, where the dynamics transits from the inertial-gravity regime to the quasi-geostrophic regime.

The Rossby wave can propagate eastward in the unstably stratified quasi-geostrophic regime. The baroclinic instabilities are basically realized as a larger-scale extent of the inertial-gravity instabilities, but the former can be isolated from the latter in a limit of small β-effect, with a very deep lower layer. The results suggest that the convectively unstable Jovian atmospheric dynamics can be well described as a quasi-geostrophic system.