NUMERICAL-SIMULATION OF FINITE-AMPLITUDE THERMAL-CONVECTION WITH LARGE VISCOSITY VARIATION IN AXISYMMETRIC SPHERICAL GEOMETRY - EFFECT OF MECHANICAL BOUNDARY-CONDITIONS

Finite-difference numerical simulations of finite amplitude thermal convection with large viscosity variations in an axisymmetric sphere and spherical shells have been carried out. The mathematical formulation and numerical schemes are described in detail. Effects of the mechanical boundary conditions on the steady state solutions have been investigated. Results show that flows are strongly dependent on the mechanical boundary condition at the outer surface and relatively insensitive to the core boundary condition in the case of spherical shells. A shear stress free condition results in the upward concentration of convection flow, while a no-slip condition tends to push the flow towards the deeper interior. Numerical results obtained in this study imply that mantle convection within the Moon, Mercury and Mars is probably confined at depth because of the lack of horizontal surface tectonic activity on these three planets. However, mantle convection within the Earth probably concentrates near the surface because plate tectonics are active. © 1978.