[1] The large temperature difference between the core and mantle of Mars at the end of planetary accretion creates a hot, internally convecting thermal boundary layer at the base of the mantle, whose viscosity is several orders of magnitude lower than the viscosity of the mantle above it. Theoretical analysis and numerical simulations of the instability of this thermal boundary layer show that it is likely that only one large plume forms. This superplume may play a role in the formation of crustal dichotomy and generation of the magnetic field in the early history of Mars.

[1] Several arguments point out that at the end of planetary accretion, the core of Mars was likely to be much hotter than its mantle, resulting in the formation of a completely or partially molten thermal boundary layer at the base of the mantle. Here we address the following questions: How did the superheated core cool and what role did it play in the early mantle dynamics of Mars? We divide the coupled core-mantle evolution of early Mars into two stages. During the first stage, vigorous convection within the molten boundary layer removes the heat from the core so that the boundary layer expands up. As the boundary layer gets thicker, the temperature of the layer decreases. Eventually, the temperature of the molten boundary layer drops down to the temperature for the rheological transition (melt fraction $40%) within 100 years. This stage is described by a parameterized convection approach. The second stage is modeled in spherical shell geometry using the fully three-dimensional finite element code CitcomS. A single plume (''superplume'') forms by the instability of the thermal boundary layer. The superplume stage lasts much longer, on the scale of millions to hundreds of millions of years, depending on the mantle viscosity. During both stages of evolution the heat flux can easily satisfy the requirements for the dynamo.

Plume formation in a strongly temperature-dependent viscosity fluid placed on a very hot surface involves an intermediate step-small-scale convection in the thermal boundary layer. We perform numerical simulations and suggest a simple analysis of this process using the stagnant lid convection theory and Canright and Morris' theory of Rayleigh-Taylor instability of two layers with different viscosities. We show that plume formation can approximately be predicted from the requirement that the growth of the large-scale instability becomes faster than the growth of the convecting thermal boundary layer.

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