Geodynamo models with a stable layer and heterogeneous heat flow at the top of the core

The mean heat flow at the core-mantle boundary (CMB) could be less than the heat that can be transported by conduction along a core adiabat. If the difference is significant, it may render the top few hundred kilometres of the core to be stably stratified. The geodynamo then operates in deeper parts of the core, driven from the inner-core boundary by thermochemical convection. The CMB heat flow is probably strongly heterogeneous. Locally the thermal gradient below the CMB could be unstable while on average it is stable. The way in which lateral heat flux differences are accommodated and the consequences for the dynamics of a stable layer are not clear a priori. This is studied in numerical dynamo simulations with a strongly stabilizing average density gradient near the outer boundary and large lateral differences in the heat flux. The results suggest that a circulation in a thin layer immediately below the CMB balances the differences in heat flow by lateral advection. Deeper parts of the stable layer and the convecting region remain unaffected by the thermal heterogeneity at the CMB. A simple scaling theory for the shallow circulation layer is developed and is found to be in rough agreement with the numerical results. Applied to the Earth's core, it predicts that the thickness of the layer is a few hundred metres, the horizontal velocity reaches values around 1 mm s(-1), and lateral temperature differences at the CMB are slightly less than 1 K. The morphology of the magnetic field is found to be only marginally compatible with characteristic properties of the geomagnetic field when the stable layer thickness is around 400 km and is incompatible for a thicker layer. Therefore, the total CMB heat flow should exceed 10 TW unless unaccounted compositional buoyancy effects close to the CMB play a major role. If a sufficiently stable layer exists at the top of the core, thermal heterogeneity at the CMB would not influence the flow pattern in deeper parts of the core or affect heterogeneous growth of the inner core. Likewise, proposed mechanisms for the dipole offset from the centre of Mercury based on heterogenous CMB heat flow are unlikely to work if the upper part of Mercury's core is thermally stable.