Mixing times in the mantle of the early Earth derived from 2-D and 3-D numerical simulations of convection

[1] The Earth's mantle is chemically heterogeneous at all scales, as shown by elemental and isotopic analysis of oceanic basalts. This heterogeneity is continuously destroyed by convective stirring and slow diffusion. It has been argued that 3-D time-dependent convection is less efficient than 2-D convection, except in the presence of a toroidal component. In this study we question this conclusion with numerical simulations and show that mixing in 3-D time-dependent convection is as efficient as in 2-D, and only depends on convective vigor. We compute mixing times of thermal and chemical heterogeneities in the early Earth of 10 and 100 Myrs respectively.