Does Grain Growth Stop Convection in the Icy Galilean Satellites?

Mathematics – Logic

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The composite Newtonian/non-Newtonian rheology of ice I implies that the conditions required to trigger convection in an initially conductive ice I shell depend on the ice grain size (d) [Barr and Pappalardo, JGR in press, 2005]. For the icy Galilean satellites, volume diffusion accommodates initial plume growth if d<0.5 mm. Non-Newtonian GBS dominates for d>0.5 mm for sufficient thermal perturbations. The critical ice shell thickness for convection exceeds the depth to the ice I - III phase transition if d>2 cm. Vigorous convection can only occur if the grain size is small and deformation is accommodated by volume diffusion [McKinnon, Icarus in press, 2005]. If the ice grain size is sufficient for convection by GBS, convection is sluggish at best. If the grains in the shells grow to values greater than 2 cm, convection will cease.
What is the likelihood that the grain size in the ice shells remains small enough to permit convection over geological time scales? We estimate ice grain sizes in a convecting shell using the empirical observation from polar ice sheets that d ˜ A σ -1, where A is a thermal activation term, and σ is shear stress [De La Chappelle et al., JGR 103, 1998], due to a balance between dynamic recrystallization and dislocation generation during flow by GBS. We use a composite volume diffusion/GBS rheology for ice I in the convection model Citcom [Barr et al., JGR, 109, 2004] to determine convective strain rates and grain sizes expected in the shells. When GBS accommodates convective strain, we find good agreement between input and predicted steady state grain sizes. Therefore, a balance between grain growth and recrystallization during flow by GBS may allow sluggish convection to persist in ice I shells with a relatively large grain size.

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