Multiple critical Froude numbers for the centrifugal effects on heat transport in rotating Rayleigh-Bénard convection

Abstract

The influence of centrifugal effects in rotating Rayleigh-Benard convection is investigated using direct numerical simulations. We find that the Nusselt number decreases beyond a critical Froude number, Fr_c*. This critical value depends on both the Rayleigh number Ra and the aspect ratio Gamma, following power-law scalings with each parameter. We interpret Fr_c* as the onset of centrifugal effects within the thermal boundary layers. This interpretation is supported by the thickening of the boundary layers and a reduction in the planar heat flux. We compare Fr_c* with two previously proposed critical Froude numbers. The first, Fr_Hu, marks the onset of centrifugal effects in the bulk, as evidenced by changes in local heat flux and radial vortex motion. For Fr_Hu < Fr < Fr_c*, centrifugal effects primarily redistribute heat within the bulk and have little influence on the global heat transfer. The second, Fr_Horn, is based on a global force-balance argument. The similar dependence of Fr_c* and Fr_Horn on the aspect ratio suggests a close connection between the global force balance and the onset of centrifugal effects in the thermal boundary layers. These results demonstrate that centrifugal forcing influences the bulk flow and the thermal boundary layers differently in rotating Rayleigh-Benard convection. While relatively weak centrifugal forcing modifies the bulk dynamics, substantially stronger forcing is required to alter boundary-layer properties and global heat transport.