Mixing in a 3D spherical model of present-day mantle convection

Abstract

We present the first study of present-day mixing efficiency of the Earth that is based on a 3D spherical model of convection in the Earth's mantle. The stationary model we employ is derived from the present-day slab buoyancy forces using an approximate plate rheology, a weak upper mantle above the transition zone and an increase of viscosity into the lower mantle. The model is quite successful in predicting surface plate velocities and the geoid. We consider this model an appropriate approximation of the present-day internal velocity structure in the Earth's mantle. The mixing efficiency is studied by studying particle traces, evaluating Poincaré sections, and quantifying stretching efficiency. This allows for determining regions in the present-day mantle that are characterized by laminar or chaotic mixing and indicate the connection between different mantle regions. The modeling indicates that a variety of mixing scales exist in the present mantle velocity field. Only certain regions exhibit laminar single cell mixing. Convection in most other regions is characterized by corkscrew-like particle tracks that allow for transport of particles far from their source and possibly for chaotic mixing. The key components governing the efficiency of mixing of the present-day mantle are the driving forces of the slabs, in particular those along the Pacific rim, and the vorticity (or toroidal motion) induced by the rotation and resulting strike-slip motion of surface plates. Our approach is a conservative one, as the intrinsic time-dependence of plate tectonics and more vigorous convection in a younger and hotter Earth would cause stronger mixing. Based on this simple model approach, we conclude that the mixing in the present-day Earth is relatively efficient, and that it is not possible for large portions of the Earth mantle to remain isolated over the life time of the Earth.