Non-Newtonian effects in simple models of mantle convection

One of the difficulties with self consistent plate-mantle models capturing multiple physical features, such as elasticity, non-Newtonian flow properties, and temperature dependence, is that the individual behaviours cannot be considered in isolation. For instance, if a viscous mantle convection model is generalized idealistically to include hypo-elasticity, then problems based on Earth-like Rayleigh numbers exhibit almost insurmountable numerical stability issues due to spurious softening associated with the co-rotational stress terms. These difficulties can be avoided if a stress limiter is introduced in the form of a power law rheology or yield criterion. A general Eulerian model is discussed and it is shown that the basic convection modes of a cooling planet are reproduced.