The Influence of Curvature on Convection in a Temperature‐Dependent Viscosity Fluid: Implications for the 2‐D and 3‐D Modeling of Moons

Abstract

AbstractConvection in terrestrial bodies occurs within spherical shells described by the ratio, f, of their bounding radii. Previous studies that have modeled convection with a temperature‐dependent viscosity noted the strong effect of f on transition to the stagnant‐lid regime. Here we analyze stagnant‐lid convection in 2‐D and 3‐D systems with curvatures including relatively small‐core shells (f as small as 0.2) as well as in thin shell and plane‐layer cases. Several peculiarities of convection in a strongly temperature‐dependent viscosity fluid are identified for both high and low curvature systems. We demonstrate that effective Rayleigh numbers may differ by orders of magnitude in systems with different curvatures, when all other parameters are maintained at fixed values. Furthermore, as f is decreased, the nature of stagnant‐lid convection in small‐core bodies shows a divergence in the temperature and velocity fields found for 2‐D annulus and 3‐D spherical shell systems. In addition, substantial differences in the behavior of thin shell (f = 0.9) and plane‐layer (Cartesian geometry) models occur in both 2‐D and 3‐D, indicating that the latter (emulating a toroidal topology rather than spherical) may be inappropriate approximations for modeling variable viscosity convection in thin spherical shells. Our findings are especially relevant to understanding and accurately modeling the thermal structure that may exist in bodies characterized by thin shells (e.g., f = 0.9) or relatively small cores, such as shells comprising the Galilean satellites and other moons.