Mixing Time of Geochemical Heterogeneities in a Vigorously Convecting and Rapidly Rotating Terrestrial Magma Ocean.

The recent discovery that several hotspots (Hawaii, Samoa, Iceland and Galápagos) exhibit a negative µ182W value [1] poses first-order questions about mantle processes. This is because 182Hf, the parent element, has such a short half-life that it became extinct ~50Myr after the formation of the solar system. The negative µ182W values observed in present-day volcanic rocks therefore require that material formed at the beginning of Earth history is present in their source. Two main processes have been proposed: (a) Reactions between the lowermost mantle and the metallic core, a reservoir with a strongly negative µ182W[1]; (b) Preservation of heterogeneities formed while 182Hf was extant. Understanding whether, and how, heterogeneities can survive for ~4.5Gyr in the convecting mantle, requires quantifying mixing efficiency both in the solid mantle and at the magma ocean stage. We therefore studied the efficiency of mixing in a turbulently convecting magma ocean, and we assessed the time-scales required to further homogenize heterogeneities by chemical diffusion.

To model thermal convection in a low viscosity magma ocean we modified the PARODY-JA code commonly used for MHD simulations[2][3] in a spherical shell, to compute Finite-time Lyapunov exponents (i.e., the Lagrangian strain rate). We explored a parameter space reaching the regime of hard-turbulence with rotational effects (i.e. Prandtl number of 1, Rayleigh number up to 109, Ekman number as low as 10-6). We then derived scaling laws for the buoyancy-dominated and for the rotation-dominated regimes, and extrapolated our results to terrestrial magma oceans.

We find that in a buoyancy-dominated regime, heterogeneities of 1000 km size are stretched very rapidly down to length-scales where chemical diffusion operates. This suggests that in a buoyancy-dominated regime, heterogeneities cannot survive in a global terrestrial magma ocean.

[1]Mundl-Petermeier, A., Walker, R. J., Fischer, R. A., Lekic, V., Jackson, M. G., Kurz, M. D., (2020)., Geochim. Cosmochim. Acta 271, 194-211.

[2]Aubert J., (2019)., Geophys. J. Int., 219, 137-151. https://doi.org/10.1093/gji/ggz232

[3]Schaeffer N., (2013)., Geophys. Geochem. Geosyst., 14(3), 751-758. 10.1002/ggge.20071