Thermal versus isothermal rotating shallow water equations: comparison of dynamical processes by simulations with a novel well-balanced central-upwind scheme

We introduce a new high-resolution well-balanced central-upwind scheme for two-dimensional rotating shallow water equations with horizontal temperature/density gradients–thermal rotating shallow water equations. The scheme maintains the equilibrium states in the presence of topography and temperature/density variations, and allows for high-resolution tracking of the active scalar field together with velocity and pressure fields. We use the new scheme to highlight both the similarities and differences in the predictions of the thermal and isothermal shallow water models for the fundamental dynamical processes: evolution of isolated vortices in the midlatitude β-plane in the presence of topography and relaxation of localised pressure and temperature perturbations in the equatorial β-plane.