STABILITY OF PLANETARY INTERIORS

Summary Many accept thermal convection within the mantle of the Earth as the driving mechanism for continental drift. It is also of considerable interest to determine whether thermal convection is occurring within Venus, Mars, and the Moon. In this paper a systematic treatment of the stability of planetary interiors is given. The thermal stability problem for a layer of fluid heated from below is solved when the viscosity of the fluid increases exponentially with depth. For a semi‐infinite fluid with exponentially increasing viscosity the critical Rayleigh number based on the surface viscosity and the scale length of the viscosity increase is found to be 30 for a fixed surface boundary condition and 23 for a free surface boundary condition. This stability analysis is also extended to include volume heat release. The thermal stability of the interiors of the Earth, Venus, Mars and the Moon is examined. Using temperature‐depth profiles in the literature and a theoretical expression for the viscosity of a crystalline solid based on diffusion creep, viscosity depth profiles for planetary interiors are obtained. Because of the strong pressure effect the viscosity within the Earth and Venus increases greatly from a near surface minimum. For Mars the increase is less pronounced and within the interior of the Moon the viscosity is nearly constant. For all the cases considered the planetary interiors are found to be thermally unstable. Because of the dependence of viscosity on depth the interiors of the Moon and Mars are found to be considerably less stable than Venus and the Earth. It is concluded that thermal convection is occurring within the planetary bodies considered. Copyright © 1969, Wiley Blackwell. All rights reserved