Phase transitions of the energy-relative enstrophy theory for a coupled barotropic fluid-rotating sphere system

We find that at extremely high energy levels or small negative temperatures, the preferred state is a super-rotational equilibrium state aligned with the planetary spin. This phenomenon has been observed in the Venusian middle atmosphere for many decades but remains difficult to explain [〈http://www-atm.physics.ox.ac.uk/project/virtis/venus-super.html〉]. For large values of the planetary spin compared with the relative enstrophy there appears to be two phase transitions when the temperature varies from a numerically large negative value to a large positive value. The latter arises as constrained energy minimizers.