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.