How far below the critical Rayleigh number can convection occur in temperature-dependent viscosity fluids?

Abstract

We use 2D numerical simulations to study the onset of convection below the critical Rayleigh number in a basally-heated fluid with temperature-dependent viscosity. The existence of convection below the critical Rayleigh number has previously been demonstrated in variable-viscosity fluids. Under these, subcritical conditions, convection can be initiated by finite-amplitude perturbations and can assume a number of different steady-state planforms. We find the absolute minimum critical Rayleigh number and aspect ratio for the onset of subcritical convection in a broad range of viscosity contrasts. For various planetary bodies, the threshold for the onset of convection by finite-amplitude perturbations is about 40% below the critical Rayleigh number. The lowest viscosity contrast at which subcritical convection can occur is 1.3 × 102. The existence of subcritical regime extends the range of conditions under which convection can occur in planetary interiors and expands the assortment of possible convective planforms that can explain various surface features on planetary bodies.