Penetrative convection in the planetary mantle

Publisher Website
Google Scholar
Abstract
The hydrodynamic equations for thermal convection in a plane layer of viscous, heat conducting fluid are scaled using the normalization of Ostrach (1965) in which the magnitude of the non-dimensional group τ = gαd/cp determines the importance of compression work and viscous dissipation in the energy balance of the flow. A linear asymptotic theory valid in the limit τ → ∞ is constructed for the Bénard problem and this is shown to be analogous to Couette flow between contra-rotating cylinders. For sufficiently large τ the flow becomes penetrative. This fact is illustrated for homogeneous fluids by the numerical integration of a set of coupled 1st order differential equations, both for the Bénard and internally heated configurations. The effect of viscosity and thermal conductivity in-homogeneity on the depth of penetration of the main cell in the circulation pattern are assessed and it is concluded that such interactions may be sufficient to effectively limit the depth extent of mantle convection. Finally a discussion of the effect of phase transitions is given following the technique of Busse and Schubert (1971).

This publication has 26 references indexed in Scilit: