Numerical Simulations of Non-newtonian Convection in Ice: Application to Europa

Introduction: Numerical simulations of solidstate convection in Europa’s ice shell have so far been limited to consideration of Newtonian flow laws, where the viscsoity of ice is strongly dependent upon temperature, predicting that a stagnant lid should form at the top (10-40%) of a convecting ice shell [1, 2]. Such large thicknesses seem to contradict estimates of the effective elastic thickness of Europa’s ice shell during its geologically active period [3, 4]. Recent laboratory experiments characterize the rheology of ice as the sum of contributions from several temperature and strain rate-dependent creep mechanisms [5]. We present the results of numerical simulations of convection within Europa’s ice shell using the finite-element model Citcom [6], applying the non-Newtonian rheology of grain boundry sliding. Our calculations suggest a shallower brittle/ductile transition and larger interior convective velocities compared to Newtonian rheology. The flow field is time-dependent, with small, localized upwellings and downwellings at the thermal boundary layers that have minimal topographic expression at the surface. Geological Setting: The surface of Europa is geologically young, with an inferred crater age of ~50 Myr [7, 8]. Despite its young age, Europa displays a rich variety of surface features that are inferred to form from the effects of tidal forcing on the shell and/or from convective upwellings [3, 9]. Convection has been suggested to drive the formation of three classes of features observed on Europa for which formation by upwelling of warm ice seems to best explain their mophologies: bands; large-scale chaos regions; smallscale pits, spots, and domes (collectively, “lenticulae”). The apparent lack of obvious compressional features on Europa’s surface also constrains the surface expression of convective downwellings. A nominal value of the elastic thickness of Europa’s lithosphere at the time of active surface deformation is ~2 km [9]. The elastic plate thickness has a somewhat imprecise definition but we adopt the T=180 K isotherm as the base of the elastic lithosphere, and seek to compare our calculated thermal structures with those inferred for Europa. Rheology: Based on laboratory experiments [5], the rheology of ice has been characterized as a sum of contributions from four different creep mechanisms: diffusional flow, basal slip accomodated grain boundary sliding, grain boundary sliding, and dislocation creep. Each of the flow laws has a different stress and temperature dependence. Different creep mechanisms control the flow of ice in different portions of the ice shell, and no single creep mechanism can adequately describe motion of ice within the entire shell. The purpose of our study is to determine whether the convective style operational within Europa’s shell differs from the style predicted by Newtonian rheologies. In this preliminary work, we provide a first glimpse of the differences in convective style between Newtonian and non-Newtonian convection within Europa’s shell by adopting only the grain boundary sliding (GBS) term. Grain boundary sliding has the smallest n of non-linear terms in the combined flow law; therefore, this rheology provides a conservative view of how a non-linear rheology might affect the convection within Europa’s shell. A summary of parameters used in the Newtonian and non-Newtonian convection simulations is shown in Table 1. To simplify our numerical model, we construct an approximated GBS flow law: