Unstably stratified geophysical fluid dynamics

The linear dynamics of unstably stratified geophysical flows is investigated using a two-layer formulation to classify dynamics into three regimes based on a 'convective' deformation radius. These regimes include: 1) scales smaller than the deformation radius characterized by unstable inertial-gravity modes; 2) scales larger than the deformation radius which exhibit a quasi-geostrophic regime; and 3) scales close to the deformation radius where dynamics transition from the inertial-gravity regime to the quasi-geostrophic regime. The study finds that Rossby waves propagate eastward in the unstably stratified quasi-geostrophic regime, and that baroclinic instabilities can be differentiated from inertial-gravity instabilities under specific limits, suggesting that convectively unstable dynamics may explain the behaviors of Jovian atmospheric systems. The research aims to expand the understanding of geophysical fluid dynamics beyond the traditionally stable stratification to include various types of planetary atmospheres, particularly where internal heat sources disrupt standard conditions.