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The amount and spatial pattern of heat extracted from cores of terrestrialplanets is ultimately controlled by the thermal structure of the lower rockymantle. Using the most common model to tackle this problem, a rapidly rotatingand differentially cooled spherical shell containing an incompressible andviscous liquid is numerically investigated. To gain the physical basics, weconsider a simple, equatorial symmetric perturbation of the CMB heat fluxshaped as a spherical harmonic $Y_{11}$. The thermodynamic properties of theinduced flows mainly depend on the degree of nonlinearity parametrised by ahorizontal Rayleigh number $Ra_h=q^\ast Ra$, where $q^\ast$ is the relative CMBheat flux anomaly amplitude and $Ra$ is the Rayleigh number which controlsradial buoyancy-driven convection. Depending on $Ra_h$ we characterise threeflow regimes through their spatial patterns, heat transport and flow speedscalings: in the linear conductive regime the radial inward flow is found to bephase shifted $90^\circ$ eastwards from the maximal heat flux as predicted by alinear quasi-geostrophic model for rapidly rotating spherical systems. Theadvective regime is characterised by an increased $Ra_h$ where nonlinearitiesbecome significant, but is still subcritical to radial convection. There theupwelling is dispersed and the downwelling is compressed by the thermaladvection into a spiralling jet-like structure. As $Ra_h$ becomes large enoughfor the radial convection to set in, the jet remains identifiable ontime-average and significantly alters the global heat budget in the convectiveregime. Our results suggest, that the boundary forcing not only introduces anet horizontal heat transport but also suppresses the convection locally tosuch an extent, that the net Nusselt number is reduced by up to 50\%, eventhough the mean CMB heat flux is conserved.

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