Exploring Ocean Circulation on Icy Moons Heated From Below

Abstract

We numerically explore convection and general circulation of an ocean, encased in a spherical shell of uniform thickness, heated from below by a spatially uniform heat flux, and whose temperature at the upper surface is relaxed to the freezing point of water. The role of salt is not considered. We describe the phenomenology and equilibrium solutions across a broad range of two key non‐dimensional numbers: the natural Rossby number, a measure of the influence of rotation, and the ratio of inner to outer radius of the moon's ocean, a measure of the geometry of the moon's tangent cylinder. Two distinct regimes of circulation are identified, both dominated by Taylor columns aligned with the rotation axis—“plumes” and “rolls” which predominate inside and outside the tangent cylinder, respectively. Inside the tangent cylinder, convective plumes align with Taylor columns that extend from the bottom to the ice shell. The plumes energize geostrophic turbulence which in turn generates a general circulation consisting counter‐rotating zonal jets. Moreover, the plumes are efficient at transferring heat from the bottom to the surface, resulting in loss of heat from the ocean to the polar ice. If the plumes are suppressed rolls outside the tangent cylinder become the dominant mode of heat transfer resulting in equatorial cooling. We conclude that if moons such as Enceladus and Europa were to be predominantly heated from below, they will likely have a “Jovian‐like” circulation: an unstratified, turbulent, geostrophically controlled ocean with strong “Taylor column” behavior and a circulation dominated by counter‐rotating zonal jets.

Different Ice-shell Geometries on Europa and Enceladus due to Their Different Sizes: Impacts of Ocean Heat Transport

“…3-f,g. Due to the strong rotation effect, the eddy motions tend to be aligned with the direction of rotation axis, forming convective "rolls" along the equatorial plane and wave-like structures in higher latitudes, consistent with recent icy moon studies Ashkenazy & Tziperman (2021); Soderlund et al (2014); Bire et al (2022); . These eddies facilitate stronger equatorward heat transport than the overturning circulation in 2D configuration, as shown by Fig.…”

“…With heat produced in the silicate core, the oceanʼs stratification will change: A fresh ocean on a small moon with negative α will become more stratified, whereas a salty ocean on a large moon with positive α will become less stratified and even globally convective. In the appearance of convection (salty/ high pressure), the heating delivered to the ice shell by convective Taylor plumes is not going to be evenly distributed if the heating released from the seafloor is (Soderlund et al 2014;Soderlund 2019;Bire et al 2022). This may induce 5 Notice that a smaller η m means more freezing/melting is needed to counterbalance the ice flow and thereby more latent heating and stronger salinity-driven circulation.…”

“…Finally, the prominent eddy size is computed by averaging different wavelengths by the corresponding power spectrum of the U field between 40N/S and 60N/S, and the results are compared against Equation (17) and Equation (24) because the eddies' energy-containing scale follows the Rhines scale (Held & Larichev 1996). All these diagnostics are carried out in high latitudes inside the tangent cylinder-a cylinder whose sides are parallel to the moonʼs axis of rotation and are tangential (hence the name) to the oceanʼs floor at the equator because the dynamics outside the tangent cylinder are very different Bire et al 2022). As shown in Figure A7, the theory also captures the eddy and jet characteristics reasonably well, indicating that the agreement between the predicted and simulated ocn  may not be a coincidence.…”

“…( 24), because the eddies' energy-containing scale follows the Rhines scale (Held & Larichev 1996). All these diagnostics are carried out in high-latitudes inside the tangent cylinder -a cylinder whose sides are parallel to the moon's axis of rotation and are tangential (hence the name) to the ocean's floor at the equator, because the dynamics outside the tangent cylinder are very different Bire et al 2022). As shown in Fig.…”

How does salinity shape ocean circulation and ice geometry on Enceladus and other icy satellites?

“…Second, thickness variations will drive ice to flow from thick-ice regions to thin-ice regions on million-year time scales (38)(39)(40)(41). To compensate the smoothing effect of the ice flow, ice must form in low latitudes and melt in high latitudes.…”