Quasi-geostrophic wave-CISK in an unbounded baroclinic shear

The free-shear problem, a minimal version of baroclinic, quasi-geostrophic wave-CISK is analyzed. The basic state consists of a zonal flow, unbounded above and below, with constant vertical shear and Brunt-Vaisala frequency and zero meridional gradient of the potential vorticity. Convective heating is parameterized in terms of the convergence below an arbitrary level. Consideration of the potential vorticity dynamics of the unstable modes illustrates how heating may act as a dynamical surrogate for potential vorticity gradients. Although highly idealized, the free-shear problem also explains much of the behavior of more general wave-CISK models.