Polar heat transport enhancement in sub-glacial oceans on icy moons

The icy moons of the solar system show several phenomena in their polar regions like active geysers or a thinner crust than at the equator, all of which might be related to a non-uniform heat transport in the underlying ocean of liquid water. We investigate the potential for local heat transport enhancement in these sub-glacial oceans by conducting direct numerical simulations of rotating Rayleigh-Bénard convection (RRBC) in spherical geometry at a water-like Prandtl number Pr=4.38, Rayleigh number Ra=10⁶, and Rossby number ∞≥Ro≥0.03 (or in terms of the Ekman number ∞≥Ek≥6.28·10^-5). We probe two ratios of inner to outer radius η=r_i/r_o=0.6 and η=0.8, which is closer to the presumed conditions on most icy moons, for different gravitational laws g(r)∝r^γ. The simulations cover the full range from zero to rapid rotation close to where convection ceases, and therefore cross the rotation-affected regime of intermediate rotation rates with a potentially enhanced dimensionless heat transport Nu>Nu_non–rot as known from planar RRBC.

Although the global heat transport does not increase (Nu_global≤Nu_non–rot), we find an enhancement up to 28% at high latitudes around the poles (Nu_hl>Nu_non–rot), which is compensated by a reduced heat transport at low latitudes around the equator (Nu_ll<Nu_non–rot). In the tangent cylinder around the poles, Ekman vortices connect the inner and the outer shell, which allows for a more effective transport of heat through the bulk by Ekman pumping, whereas these vortices impede radial heat transport towards the equator. Interestingly, the polar enhancement decreases for the thinner shell (η=0.8 compared to η=0.6) with a larger tangent cylinder, but still remains significantly larger than the non-rotating reference value (≈10%).

We also analyze the thicknesses of the thermal and kinetic boundary layers λ_Θ and λ_u to identify whether a ratio λ_Θ/λ_u≈1 is beneficial for the maximal polar heat transport, as hypnotized from planar RRBC. Overall, our study reveals that the same mechanisms, which govern the heat transport enhancement in planar RRBC, also enhance the heat transport in the polar regions in spherical RRBC. On the bigger picture, our results may help to improve the understanding of latitudinal variations in the crustal thickness on icy moons.