Mapping the Subcritical Regimes of Temperature-Dependent Viscosity Convection

Abstract:

Convection in planetary interiors is widely modeled at supercritical conditions, i.e., when the Rayleigh number is above the critical Rayleigh number for the onset of convection. However, in fluids with strongly temperature-dependent viscosity, such as planetary interiors, non-decaying convective motions can exist even under subcritical conditions. This is in sharp contrast to constant-viscosity fluids, where all convective motions decay below the critical Rayleigh number. Furthermore, power-law viscosity convection is subcritical at all Rayleigh numbers. Subcritical convection is initiated by finite-amplitude rather than infinitesimal perturbations. It can have multiple stable solutions, one of which is localized convection wherein only a single cell pair exists in the entire layer and is surrounded by nearly immobile fluid (Solomatov, 2012). Such a dynamic regime is impossible at supercritical conditions.

Subcritical convection may play an important role in the interior dynamics of planetary bodies including icy satellites. In this study, we perform the first systematic investigation of subcritical convection in fluids with strongly temperature-dependent viscosity using the finite element code CITCOM. Most of our numerical calculations are conducted in 2D on a high-performance computer cluster. We determine the extent of the subcritical region in a wide range of viscosity contrasts and estimate the boundaries of the stability of localized convection. Our simulations reveal different patterns of localized convection, ranging from a localized cell pair to more complex structures characterized by several cells whose amplitude decays with the distance from the localization center. We summarize our findings as a regime diagram of the subcritical region and discuss the implications of our results for icy satellites.