The dependence of convection in planetary mantles upon the magnitude of the Rayleigh number

Abstract

The conservation equations of mass, energy and momentum when applied to the problem of convection produced by isothermal compression as well as by thermal expansion in a self-gravitating sphere of uniform density, consisting of a core extending to a fractionŋ of the radius of the sphere and with a viscous mantle overlying the core, lead to a relationship between two characteristic numbers. In the present paper these characteristic numbers are evaluated, for the case when both boundaries of the mantle are free, for spherical harmonic disturbances of orders 1 → 6. It is found that the ease with which different patterns of convection can be excited changes as the characteristic numbers are varied.