Hydrothermal convection in moderately thin spherical shells.
ABSTRACT Hydrothermal convection of pore water with a temperature-dependent viscosity within a permeable, internally heated, moderately thin spherical shell is investigated by both a perturbation analysis and a direct numerical simulation. The analysis and simulation are mainly focused on a thin spherical shell in that convective instabilities are characterized by the spherical harmonic degree l=6 with a 13-fold mathematical degeneracy. Four different three-dimensional analytical solutions of convection are derived by removing the degeneracy through the nonlinear effect. A direct numerical simulation of the nonlinear problem is also carried out, showing satisfactory agreement between the analytical solutions and the numerical simulations.