Regular vs. chaotic mantle mixing

Most quantitative models of mantle mixing have been based on simulations of tracer advection by 2-D flows. The present work shows that the mixing properties of 3-D time-independent flows cannot be understood or extrapolated from previous 2-D models. Steady convective flows appropriate to simulate a uniform fluid with large viscosity are restricted to poloidal components. They seem to have regular streamlines. However, the existence of plates on the Earthʹs surface imposes the existence of a strong toroidal field. Flows where both poloidal and toroidal components are present can yield chaotic pathlines which are very efficient in mixing the mantle. Within areas of turbulent mixing where the stretching increases exponentially with time, regular islands of laminar stretching persist in which unmixed material can survive. Our findings indicate that the intrinsic three-dimensionality of convection coupled with plates as much as its time dependence must be included in numerical models to understand the mixing properties of the mantle. As the viscosity is significantly larger in the lower mantle than in the upper mantle, the toroidal component of the flow is confined to the upper mantle, where a more thorough mixing should take place.