Scaling of heat transfer in stagnant lid convection for the outer shell of icy moons: Influence of rheology

Abstract

The persistence of subsurface oceans in icy moons primarily depends on the efficiency of heat transfer through the outer ice shell. Scaling laws for heat transfer have already been determined by previous studies. These consider however a simplified rheology assuming a single creep mechanism, often using a linearized version of the temperature-dependent viscosity law (called Frank-Kamenetskii approximation). In the present study, we test the influence of ice rheology on the efficiency of heat transfer by considering a more realistic composite viscosity law, including diffusion creep, grain boundary sliding, basal slip and dislocation creep. We performed a large number of numerical simulations of thermal convection in the stagnant lid regime using a 2-D spherical annulus geometry with different rheology assumptions. Our results show that the dynamics of the ice shell is mainly controlled by the dominant creep mechanism in the rheological sublayer (the unstable lower portion of the cold boundary layer beneath the stagnant lid), which is mostly determined by grain size. For grain sizes lower than 3 mm, diffusion creep is the dominant creep mechanism in the rheological sublayer, while a combination of grain boundary sliding and basal sliding prevails for coarser grains. We derive new simple scaling relationships for the heat transfer suitable for the specific case of thin ice shells that account for the activation energy of the dominant creep mechanisms, thus allowing for a more accurate quantification of the temperature profile in the ice shell and cooling rate of the internal oceans.