On the validity of downgradient eddy closures in ocean models

Results are presented from an eddy-resolving primitive equation ocean model to test the hypothesis that geostrophic eddies can be parameterized throug h a variety of downgradient closures. Time-mean eddy fluxes of temperature, isopycnic thickness, and quasi-geostrophic potential vorticity are diagnos ed on level surfaces from 5 years of model data and are spatially correlate d with the corresponding time-mean gradients. We find no discernible correl ation between the absolute eddy fluxes and mean gradients. However, after d ecomposing the eddy fluxes into "rotational" and "divergent" components we find a positive correlation between the divergent eddy fluxes and the mean gradients, although the overall correlation coefficients remain small, typi cally O(0.2). The correlation between the eddy temperature fluxes and mean temperature gradients is positive only over the upper 2 km and is negative at depth, suggesting that the abyssal temperature fluxes are upgradient. In contrast, the correlations between eddy fluxes and mean gradients of isopy cnic thickness and potential vorticity are positive over the most of the fl uid column. The overall correlations are similar for both thickness and pot ential vorticity closures. We further decompose the divergent component of the eddy fluxes into components directed perpendicular and parallel to mean contours. We find that both the perpendicular and the parallel components are similar in magnitude.