On convection in the earth's core driven by lateral temperature variations in the lower mantle

Abstract

Lateral variations in heat flux or temperature in the lowermost mantle, associated with mantle convection, will drive fluid flow in the liquid core. The effect is modelled by a rotating spherical shell with uniform lower boundary temperature and a laterally varying upper surface temperature and the solutions found by numerical calculation, some for a density-stratified fluid. The problem depends upon two dimensionless numbers, a horizontal Rayleigh number and a stratification parameter. The calculations are restricted to surface temperatures which are symmetric about the equator and steady solutions are found. Induced toroidal flows near the surface are closely linked with the applied temperature profile through the thermal wind equation and Coriolis forces make the convection penetrate into the shell. Stratification acts mainly to suppress radial flow but the surface toroidal flow is relatively unaffected. The results illustrate the powerful influence exerted by the surface temperature but are difficult to apply directly to the earth's core because molecular values of the thermal diffusivity entail a very long time-scale. Assuming a turbulent thermal diffusivity equal to the magnetic diffusivity gives a more realistic time-scale and it is possible to recover, for specific simple imposed temperature profiles, flows similar to those found in the earth's core from inversion of geomagnetic secular change.