Convection in planetary mantles interacting with magma oceans – MaCoMaOc

It is generally thought that in its earliest times the Earth was largely molten, owing to the enormous energy associated with its formation. On the basis of lunar observations, it has been proposed that the upper few hundreds of km of the mantle were initially liquid, forming what is commonly called a magma ocean. More recently, we proposed that a dense magma ocean could have existed at the bottom of the mantle (the basal magma ocean) and that the remnants of its slow crystallization could be observed at the present time in the form of the seismically detected ultra low velocity zones. The solid mantle is then formed from the crystallization of the magma oceans, upwards and downwards. Convection in the solid mantle is then the engine responsible for plate tectonics, while the mechanisms that allowed the transition from the dynamics in the magma ocean to that in the solid mantle are still largely unknown.
This project aims at studying the effect of being bounded above and/or below by magma oceans on the dynamics of the solid mantle. The possibility of a solid/liquid phase change at the horizontal boundaries of the mantle changes the boundary conditions felt by the flow in the solid: whereas in classical convection problems a non-penetrating condition is generally applied (zero vertical velocity on the horizontal boundaries), which is based on the assumption that the vertical motion associated with mountain building is negligible compared to the horizontal motion of plates, the possibility of a vertical flow towards the surface melting as it gets to the molten region can effectively suppress the “braking” effect of the horizontal boundary. This effect has been studied in the context of the dynamics of the Earth’s inner core and we now plan to apply the same boundary conditions to the case of the mantle interacting with magma oceans. Preliminary studies that we have performed show that several effects are to be expected: the horizontal wavelength is widened, velocities and heat transfer are larger, and the onset of convection is facilitated. We will study these effects in a systematic manner as function of the main parameters: the Rayleigh number (measuring the vigor of convection), internal heating rate, rheology, geometry (spherical versus cartesian, aspect ratio), variations of density of chemical origin, and the parameters controlling the type of boundary conditions. Using several dynamical models taking into accounts these effects, we will specifically study the first overturn of the crystallizing mantle during its crystallization, the onset of solid state thermal convection, and the developed regimes and their heat transfer characteristics. These results will allow us to address important questions on the dynamics of the early Earth and the different possible mantle convection regimes across geologic ages.
The development of scaling laws for the thermal structure and heat transfer as function of the control parameters will allow us to construct a parameterized model for the coupled evolution of the core, the basal magma ocean and the mantle. This model will have the potential to solve the decades old problem of the thermal evolution of the Earth with a moderate evolution of the mantle and a large core cooling. Finally, we will build a model coupling the full dynamics of the solid mantle with moving boundaries to the core and the basal magma ocean in order to study the long term evolution of mantle dynamics, the formation of dense thermo-chemical piles at the base of the solid mantle by fractional crystallization of the basal magma ocean.