Evolution of convective rolls to zonal flows in horizontally rotating Rayleigh–Bénard convection

Zonal winds on Jovian planets play an important role in governing the cloud dynamics, transport of momentum, scalars and weather patterns. Therefore, it is crucial to understand the evolution of zonal flows and their sustainability. Based on studies in two-dimensional $\beta$ -plane set-ups, zonal flow is believed to be forced at the intermediate scale via baroclinic instabilities, and the inverse cascade leads to the transfer of energy to large scales. However, whether such a process exists in