Macroturbulent equilibration in a thermally forced primitive equation system

A major question for climate studies is to quantify the role of turbulent eddy fluxes in maintaining the observed ocean-atmosphere state. Starting with Stone (1978), it has been argued that eddy fluxes keep the mid-latitude atmosphere in a state that is marginally critical to baroclinic instability, which provides a powerful constraint on the response of the atmosphere to changes in external forcing. Marginal criticality arguments do not appear to hold for the ocean. This is particularly surprising for the Southern Ocean, a region whose dynamics are very similar to the mid-latitude atmosphere, but observations and numerical models suggest that the currents are supercritical.

A combination of theoretical results and eddy-resolving numerical simulations will be presented to resolve this apparent contradiction. It will be shown that both marginally critical and supercritical mean states can be obtained in an idealized diabatically forced (and thus atmosphere-like) Boussinesq system, if the thermal expansion coefficient is varied from atmosphere-like values to ocean-like values. The difference in the thermal expansion coefficient dominantly controls the difference in the deformation scale between the two fluids and ultimately renders eddies ineffective in maintaining a marginally critical state in the limit of small thermal expansion coefficients. This suggests that marginal criticality arguments hold only in a limited parameter range, which includes the present day atmosphere but not the present day ocean.