Core flows and heat transfer induced by inhomogeneous cooling with sub- and supercritical convection

The amount and spatial pattern of heat extracted from cores of terrestrial planets is ultimately controlled by the thermal structure of the lower rocky mantle. Using the most common model to tackle this problem, a rapidly rotating and differentially cooled spherical shell containing an incompressible and viscous liquid is numerically investigated. To gain the physical basics, we consider a simple, equatorial symmetric perturbation of the CMB heat flux shaped as a spherical harmonic Y11. The thermodynamic properties of the induced flows mainly depend on the degree of nonlinearity parametrised by a horizontal Rayleigh number Rah=q∗Ra, where q∗ is the relative CMB heat flux anomaly amplitude and Ra is the Rayleigh number which controls radial buoyancy-driven convection. Depending on Rah we identify and characterise three distinctive flow regimes through their spatial patterns, heat transport and flow speed scalings: in the linear conductive regime the radial inward flow is found to be phase shifted 90° eastwards from the maximal heat flux as predicted by a linear quasi-geostrophic model for rapidly rotating spherical systems. The advective regime is characterised by an increased Rah where nonlinearities become significant, but is still subcritical to radial convection. There the upwelling is dispersed and the downwelling is compressed by the thermal advection into a spiralling jet-like structure. As Rah becomes large enough for the radial convection to set in, the jet remains identifiable on time-average and significantly alters the global heat budget in the convective regime. Our results suggest, that the boundary forcing not only introduces a net horizontal heat transport but also suppresses the convection locally to such an extent, that the net Nusselt number is reduced by up to 50%, even though the mean CMB heat flux is conserved. This also implies that a planetary core will remain hotter under a non-homogeneous CMB heat flux and is less well mixed. A broad numerical parameter investigation regarding Rayleigh number and the relative heat flux anomaly further fosters these results.