Convective Instability in Ice I: Application to Callisto and Ganymede

Laboratory experiments measuring ice rheology suggest that it deforms under the influence of several nonNewtonian creep mechanisms, where the viscosity depends on both strain rate and temperature [Goldsby & Kohlstedt, 2001]. Whether or not a fluid with a purely temperature-dependent viscosity convects can be determined by comparing the Rayleigh number of the system to the critical Rayleigh number (Racr), which depends on rheological, thermal, and physical parameters of the fluid layer. However, in a nonNewtonian fluid where viscosity depends on the strain rate (i.e. velocity), convection can only occur if a temperature or velocity perturbation is issued to the system to lower the viscosity and permit fluid motions. Therefore, whether convection occurs in an ice I layer depends on initial conditions, in addition to rheological, thermal, and physical properties of the layer. We show new results for a scaling between the critical Rayleigh number and perturbation amplitude for grain boundary sliding rheology. This scaling can be used to determine the conditions required to initiate convection in the ice I shell of a generic icy satellite. We use this scaling to judge the convective instability of Ganymede and Callisto's ice shells in the absence of tidal dissipation.