Thermal instability in rotating shallow water with horizontal temperature/density gradients

A specific instability of vortices is found in rotating shallow water equations with horizontal density/temperature gradients, which is used for modelling atmospheric and oceanic mixed layers. The model is re-interpreted as dynamics of rotating non-isentropic two-dimensional gas. The instability, which was not reported previously, develops in a way suggesting its convective character. It appears when anomaly of buoyancy at the center of the vortex and the vorticity have opposite signs (for positive Coriolis parameters), and coexists with the standard barotropic instability, having higher growth rates in a wide range of parameters and leading to efficient mixing at a nonlinear stage.