Mixing time of heterogeneities in a buoyancy-dominated magma ocean

Abstract

SUMMARY During the accretion stage, large impacts provided sufficient energy to melt the entire mantle into a terrestrial magma ocean. Processes occurring in the magma ocean may have led to the formation of heterogeneities still found in modern ocean island basalts. So far, no definitive mechanism exists to explain the survival of early heterogeneities for approximately 4.5 Ga. Addressing this question requires understanding the efficiency of convective mixing during both the early molten and the solid-state stages experienced by the Earth’s mantle. While mixing in the solid mantle and in an essentially crystallized magma ocean has been relatively well documented, the efficiency of convective mixing in a liquid magma ocean has received less attention. In this paper we characterized the mixing efficiency of a convecting fluid in a rotating spherical shell, accounting for inertial effects, by computing finite-time Lyapunov exponents (i.e. the Lagrangian strain rate). We conducted a series of numerical experiments for a regime where the influence of the buoyancy force dominates that of rotation and we derived scaling laws to predict the mixing efficiency. We found that for a terrestrial magma ocean, in its fully liquid state, mixing time is of the order of a few minutes or less, even for initially large (∼1000 km) heterogeneities. Therefore, passive early mantle heterogeneities cannot survive a fully molten magma ocean stage. This suggests that short-lived heterogeneities (e.g. 182Hf−182W) were either created at the end of the accretional stage, or were stored in deeper regions of the Earth.