Does the theory of parameterized conveciton apply to layered mantle convection?

Abstract

There are numerous models for convection of the Earth's mantle, the end cases of which are whole-mantle convection and layered convection. Heat flow is an important consideration in the evalution of these models. Simple thermal evolution models based on boundary layer theory have in the past been used to look at these models. However, insufficient attention has been paid to how well the theory applies. This was particularly uncertain for the case of layered convection with a radiogenically enriched lower mantle. I modified the finite-element code ConMan to include exponentially decaying internal heating so that the radiogenic isotopes in the lower layer would be accurately represented, and compared the experimental results of a one-layer case and a two-layer case to the theoretical solutions for those cases from boundary layer theory. It turns out that boundary layer theory does indeed seem to be accurate for the case of a two-layered convecting system with a radiogenic lower layer that produces exponentially decaying internal heating.