Thermal Coupling between the Earth's Mantle, Basal Magma Ocean and Core

It has been proposed that after formation of the core, a basal magma ocean (BMO) was formed at the base of the Earth's mantle and slowly solidified since (Labrosse et al., 2007). Remnants may nowadays be seismically observed in ULVZs as partial molten regions at the core-mantle boundary. The BMO, which thickness could have been initially 1000 km, slowly cooled down while vigorously convecting because of its high temperature and low viscosity. We study the coupled convection/diffusion problem in the melt layer underlying the solid boundary layer by means of numerical modeling. Our numerical set up allows us to systematically investigate the dynamics of the coupled convecting layer with crystallization model. We focus on determining the dimensionless heat flux for which we propose a scaling law. Only weak dependence of the heat transfer on the depth of the convecting liquid is observed. Parametrized relations are then used to estimate the super-isentropic temperature difference maintained across the BMO, which happens to be minute (< 0.1 K), implying that the Earth's core must cool at the same pace as the BMO. Convection in the BMO can change the way the lateral variation of heat flow at the bottom of the solid mantle are transmitted to the core. To mimic the effect of convection in the overlying solid mantle, we impose laterally varying temperature at the top surface. We are, in this case, interested in the spectrum of the lateral variations of the heat flux at the bottom boundary. We can therefore estimate the buffering effect of the BMO on the lateral variations imposed by the solid mantle as seen by the core.