Convection in ice I shells and mantles with self‐consistent grain size

Abstract

[1] The viscosity of ice I is grain size dependent for temperature and stress conditions appropriate for ice I shells and mantles of large and midsized icy satellites. Satellite thermal evolution, heat flux, critical shell thickness for convection, brittle/ductile transition temperature, and potential for surface deformation are therefore grain size dependent. Using measured grain sizes from terrestrial ice sheets experiencing temperature and strain rate conditions similar to convecting ice shells in icy satellites, we develop two end-member models of grain size and its evolution. In the absence of non-water ice impurities, grain size in a convecting ice shell of a large icy satellite will evolve over time to an equilibrium value, which we determine to be between 30 and 80 mm, because of dynamic recrystallization. Such large grains imply viscous ice, so convection in an ice shell thinner than 35 km in a large icy satellite such as Ganymede and Callisto would be sluggish at best and may cease after a few convective overturns (if it starts). Soluble ions and silicate microparticles may keep grains small, however, of order 1-5 mm, and permit convection in shells as thin as 30 km in large icy satellites. The dynamic recrystallization model provides a plausible upper limit on grain size in a geodynamically evolved ice shell, whereas grain sizes from dust-contaminated terrestrial ice cores provide a plausible lower limit on grain size in an icy satellite. On the basis of these constraints, grain sizes in evolved ice shells of large water ice satellites, in the absence of tidal forcing, should be of order 1 mm to 10 cm.

Effects of insoluble particles on grain growth in polycrystalline ice: Implications for rheology of ice shells of icy satellites

“…These observations have revealed that the grain size within terrestrial ice sheets is controlled not only by the temperature depen dent normal grain growth process but also by the concen tration of non water ice impurities (e.g., Durand et al, 2006) and the recrystallization due to strain accumulation (e.g., De La Chapelle et al, 1998). In a recent study, these results were used to set constraints for the grain size de pendent convection model for ice shells and mantles (Barr and McKinnon, 2007b).…”

Elastic thickness and heat flux estimates for the uranian satellite Ariel

“…All three creep regimes are implemented to calculate a range 220 in T b. Only the grain boundary sliding (GBS) regime is dependent on grain size, in which a range 221 from 1mm to 10cm (appropriate for a convecting ice mantle in which grain size has reached 222 equilibrium) was used (Barr and McKinnon 2007). 223 T b also depends on the strain rate ε , the gas constant R, grain size d, and the shear 224 modulus µ, which is calculated from v and E used in equation (1).…”

Heat flow and thickness of a convective ice shell on Europa for grain size-dependent rheologies

“…This effect is poorly known, but preliminary works suggest that grain sizes in equilibrium with convection in icy satellites could vary largely, both vertically and laterally, and to be relatively large, between one millimeter and several centimeters (Barr and McKinnon, 2006;Tobie et al, 2006). These works do not account for the effect of tidal stresses: if tidal stresses in the ice shell of Europa, typically of ∼0.1 MPa (Greenberg et al, 1998), are considered, the grain size in dynamic equilibrium would be ∼4 mm (Barr and McKinnon, 2006). These grain sizes are mostly beyond the preferred range obtained by the present study for grain boundary sliding, and implies freezing of the entire water crust for diffusion creep.…”

“…(1)- (3) are appropriate for homogeneous heat dissipation rates. The grain size could similarly be heterogeneous in the ice shell, due to variations in ice contaminants or to differential temperature-enhanced crystal growth or dynamical re-crystallization (Tobie et al, 2006;Barr and McKinnon, 2006). Although these effects can be incorporated to numerical models, parameterized formalisms have the advantage of more easily to explore of the influence of varying the rheology on the convective heat transfer.…”

“…For tidal stresses and grain sizes greater than 10 mm the dominant flow mechanism should be dislocation creep (see Durham and Stern, 2001), not considered in this work. Finally, grain size values must be taken as averages, since this parameter could be very heterogeneous both vertically and horizontally (Tobie et al, 2006;Barr and McKinnon, 2006). Fig.…”