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The Turbulent Circulation of a Snowball Earth Ocean

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  • 1 Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois
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Abstract

Theoretical arguments are developed to derive general properties of the ocean circulation in a “snowball” world, and the predictions are confirmed in a series of idealized numerical simulations. As suggested previously, a turbulent flow is driven by geothermal heating at the seafloor, which is balanced by a similar heat loss through the ice sheet above. It is argued that the expected horizontal inhomogeneities in these heat fluxes are sufficient to generate baroclinic instability, which drives geostrophic turbulence. Turbulent eddies then transport heat upward and poleward 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 bottom boundary layer. The resulting characteristic flow speed is estimated to be on the order of 1 cm s−1, which is in agreement with previous numerical simulations. Eddy diffusivities are estimated to be on the order of 100 m2 s−1, which is smaller than in the present-day ocean but probably within one order of magnitude. Because of the weak forcing, the resulting gradients of temperature and salinity would be much smaller than in the present-day ocean, with global-scale potential temperature variations on the order of 0.1 K, again in agreement with previous numerical simulations. The presented theoretical arguments may also be relevant to other planetary bodies with an ice-covered ocean.

Corresponding author address: Malte F. Jansen, Department of the Geophysical Sciences, University of Chicago, 5734 South Ellis Avenue, Chicago, IL 60637. E-mail: mfj@uchicago.edu

Abstract

Theoretical arguments are developed to derive general properties of the ocean circulation in a “snowball” world, and the predictions are confirmed in a series of idealized numerical simulations. As suggested previously, a turbulent flow is driven by geothermal heating at the seafloor, which is balanced by a similar heat loss through the ice sheet above. It is argued that the expected horizontal inhomogeneities in these heat fluxes are sufficient to generate baroclinic instability, which drives geostrophic turbulence. Turbulent eddies then transport heat upward and poleward 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 bottom boundary layer. The resulting characteristic flow speed is estimated to be on the order of 1 cm s−1, which is in agreement with previous numerical simulations. Eddy diffusivities are estimated to be on the order of 100 m2 s−1, which is smaller than in the present-day ocean but probably within one order of magnitude. Because of the weak forcing, the resulting gradients of temperature and salinity would be much smaller than in the present-day ocean, with global-scale potential temperature variations on the order of 0.1 K, again in agreement with previous numerical simulations. The presented theoretical arguments may also be relevant to other planetary bodies with an ice-covered ocean.

Corresponding author address: Malte F. Jansen, Department of the Geophysical Sciences, University of Chicago, 5734 South Ellis Avenue, Chicago, IL 60637. E-mail: mfj@uchicago.edu
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