Numerical studies on the dynamics of two-layer Rayleigh-Bénard convection with an infinite Prandtl number and large viscosity contrasts

Abstract

The fundamental physics and dynamics relating to two-layer convection with an infinite Prandtl number and large viscosity contrasts have not yet been quantitatively resolved by previous numerical analyses or simulations and laboratory experiments. Here, a series of high-resolution numerical simulations of Rayleigh-Bénard convection with a highly viscous outer layer (HVL) and a low-viscosity inner layer (LVL) in 2-D spherical-shell geometry were performed to investigate the dynamics of convection between the two layers with large viscosity contrasts of up to 103. To achieve a two-layer thermal convection system considering a thermally and mechanically continuous interface between the two layers without any specified boundary conditions, an “effective thermal expansion coefficient” was introduced to the buoyancy term of the momentum equation, discretized in a finite-volume-based regular grid system. In this study, the heat transport efficiency of two-layer convection was evaluated, and the coupling modes between the two layers were directly analyzed using the temperature anomaly and deviatoric stress fields near the interface. Results show that the mechanical coupling mode is dominant in two-layer convection when the absolute viscosity contrast between the two layers is sufficiently small, and it weakens, becoming closer to the thermal coupling mode, as the LVL viscosity decreases. This transition from the mechanical coupling to the thermal coupling modes is quantitatively detected even when the viscosity contrast between the two layers is 10−3, and results in the stabilizing of the convection speed and the heat transport efficiency of the HVL. Applying the mantle–outer core coupling of the present Earth with an extremely large absolute viscosity contrast, our numerical results imply that thermal convection in the mantle may control the heat transport efficiency of a layered whole solid-earth system and the convective style in the outer core.