Convection in earth's mantle: Impacts of solid-solid phase transformations and crystalline rheology

I first present a detailed analysis of the linear stability of an internal thermal boundary layer. In the absence of effects due to convective motion, this boundary layer is shown to be extremely unstable. When effects due to the background flow are parameterized through a Péclet number and an endothermic phase transition is present, it is shown that the boundary layer is stabilized to the extent seen in numerical simulations of mantle convection.; A series of detailed numerical calculations are presented in which I perform a broad survey of the effects of internal heating, depth-dependent viscosity, and differing Clapeyron slopes of the endothermic phase transition. The size distribution of mass flux events that cross the 660-km depth horizon is examined. It is determined that as the degree of layering increases, the number of small mass flux events increases while the number of large events decreases. I also determine that when the core-mantle boundary temperature is set such as to be in accord with high pressure experiments, the calculated surface heat flow is significantly greater than that of the real Earth. Earth-like surface heat flows were calculated only when convection was very strongly layered or when the mean viscosity was significantly greater than the viscosity inferred on the basis of post-glacial rebound.; I also derive a simple parameterized model of convection and demonstrate that its predictions are very close to those of the full dynamical model. This parameterized model is further used to calculate possible Earth thermal histories. It is determined that for models which have a constant degree of layering, the Earth's initial core temperature must be improbably high in order to match the constraint of the observed surface heat flow today. If the degree of layering is allowed to vary with the system Rayleigh number, a novel mechanism occurs which buffers the upper mantle temperature allowing for long periods of time with constant, Earth-like, surface heat flow with reasonable initial core temperatures. All acceptable models also require high viscosities which argues that the viscosity of the mantle that controls convection may be greater than that for post-glacial rebound.