Non-linear and finite-amplitude thermal convection in a heterogeneous terrestrial planet

Abstract

Summary. Equations governing non-linear and finite-amplitude convection in a heterogeneous planetary interior are developed. Using spherical harmonic expressions of variables, together with Green's function of Laplacian operator in a spherical coordinate, the equations are reduced to one-dimensional integro-differential equations and their numerical solu6ons are obtained by a finite-difference scheme. The theory is then applied to several lunar models and the following conclusions are obtained. (1) The mean temperatures and velocities of convecting zones of variable viscosity models are higher than those of constant viscosity ones. This is due to the development of lithospheres with 400-500 km thicknesses in the former models, which reduce heat loss considerably. (2) Molten regions are continuous shells in variable viscosity models whereas they become discontinuous and localized in a constant viscosity model. The continuous molten shells decrease lateral variations of tempera- ture significantly and tend to stabilize convection. (3) Lateral variations of viscosity have negligible effects on the thermal evolution of the models considered.