Rotating shallow water and potential vorticity dynamics on the sphere

Rotating shallow water (rSW) theory provides a simple dynamical framework for understanding atmospheric fluid flow. The additional simplification of quasigeostrophy (QG) reduces the dynamics to the advection of potential vorticity, which represents the slow, balanced winds governing large-scale extratropical weather. Midlatitude QG does not apply at the equator where Coriolis effects vanish. Recent modifications have extended QG theory to the entire sphere and now allow interhemispheric fluid motion. The simplest idealization of the earth's density stratification generalizes rSW to two fluid layers. The ability to include vertical shear in a mean eastward flow is sufficient to capture the baroclinic instability -- the mechanism responsible for the meandering jetstream and midlatitude low pressure storms. We investigate various properties of the unstable modes including their growth rate, phase speed and structure. Results are consistent with atmospheric observations, including the trapping of modes outside the equatorial region and a westward vertical phase tilt.