Force balance in rapidly rotating turbulent Rayleigh-Bénard convection

We study the force balance of turbulent rotating Rayleigh–Bénard convection, a simple model for large-scale natural flows. Direct numerical simulations are carried out on a laterally periodic domain, vertically bounded by no-slip walls. We provide a comprehensive overview of the interplay between the governing forces. Flow transitions are identified as distinct changes in the dominant or subdominant force balance, leading to a natural identification of each flow regime. In the rapidly rotating geostrophic regime, where the principal balance is between Coriolis and pressure gradient forces, we observe various flow states: cells, convective Taylor columns, plumes, and large-scale vortices. These geostrophic flow features can be distinguished by the subdominant force balance, where inertia, buoyancy and viscous forces can contribute. Closer to the plates the contribution of inertia is larger, though still a dominant geostrophic balance is observed. Kinetic boundary layers are of Ekman type, as expected for rapidly rotating flows. By contrast, in rotation-affected convection inertial and pressure-gradient forces form the dominant balance, with a change in boundary layer structure.