Mantle dynamics - A case study

Solid state convection in the rocky mantles is a key to understanding the thermochemical evolution and tectonics of terrestrial planets and moons. It is driven by internal heat and can be described by a system of coupled partial differential equations. There are no analytic solutions for realistic configurations and numerical models are an indispensable tool for researching mantle convection. After a brief general introduction, we introduce the basic equations that govern mantle convection and discuss some common approximations. The following case study is a contribution towards a self-consistent thermochemical evolution model of the Earth. A crude approximation for crustal differentiation is coupled to numerical models of global mantle convection, focussing on geometrical effects and the influence of rheology on stirring. We review Earth-specific geochemical and geophysical constraints, proposals for their reconciliation, and discuss the implications of our models for scenarios of the Earth’s evolution. Specific aspects of this study include the use of passive Lagrangian tracers, highly variable viscosity in 3-d spherical geometry, phase boundaries in the mantle and a parameterised model of the core as boundary condition at the bottom of the mantle.