Numerical Simulations of Melting-Crystallisation Processes at the Boundaries Between Magma Oceans and Solid Mantle

The idea that the Earth had a global magma ocean, mostly created by impacts, core formation, radiogenic and tidal heating, is well accepted nowadays. When this ocean starts to crystallise, if the melt is denser than the solid, a basal magma ocean is created below the solid part. These two magma oceans influence the dynamics and evolution of solid mantle. Near the boundaries, the vertical flow in the solid part creates a topography. If this topography is destroyed by melting/crystallisation processes in a time scale much shorter than the time needed to adjust the topography by viscous relaxation, then matter can cross the boundary. In this case, the boundary is said to be permeable. On the other hand, if this time is longer, matter cannot cross and the boundary is said impermeable. This permeability is defined by a non-dimensional phase change number, φ, introduced by Deguen, 2013. This φ is the ratio of the two timescales mentioned, and defines a permeable boundary when φ « 1, and an impermeable one when φ » 1. To understand the impact of magma oceans on the dynamics of the solid mantle, we use the convection code StagYY, with a 2D spherical annulus geometry, to compute the convection of the solid part. Our results show different convection behaviours depending on the type of boundary chosen. For the permeable case, we investigate the thermo-compositional evolution of the solid domain, explicitly taking into account the compositional evolution of the magma oceans. Reference: Deguen, R. Thermal convection in a spherical shell with melting/freezing at either or both of its boundaries. Journal of Earth Science, Vol. 24, No. 5, p. 669-682, 2013. doi: 10.1007/s12583-013-0364-8