The Turbulent Circulation of a Globally Ice-Covered Ocean

Theoretical arguments are developed to derive general properties of the circulation in a globally ice covered ocean, which is driven by geothermal heating and heat loss through the ice sheet. Theoretical predictions are confirmed in a series of idealized numerical simulations. Results are discussed primarily for the parameter regime expected for Snowball Earth, but the theoretical arguments are also relevant to other planetary bodies with an ice-covered ocean.

It is argued that even small mismatches in the spatial patterns of geothermal heat flux and heat loss through the ice sheet are sufficient to drive baroclinic instability and geostrophic turbulence. Turbulent eddies then transport heat upward and horizontally along isolines of constant density, thereby maintaining a statically stable stratification, contrary to previous findings from numerical models that do not adequately resolve the geostrophic turbulence. The kinetic energy of the turbulent flow is expected to be controlled by a balance between the potential energy input by the diabatic forcing, and frictional dissipation in the boundary layers. For Snowball Earth, the resulting characteristic flow speed is estimated to be on the order of 1 cm/s, which is in agreement with previous numerical simulations. Eddy diffusivities are estimated to be on the order of 100 m²/s, which is only moderately smaller than in Earth’s present-day ocean. Because of the weak forcing, the resulting gradients of temperature and salinity would be very small (O(0.1K)), again in agreement with previous numerical simulations.