Results are presented from an eddy-resolving primitive equation ocean model to test the hypothesis that geostrophic eddies can be parameterized through a variety of downgradient closures. Time-mean eddy fluxes of temperature, isopycnic thickness, and quasi-geostrophic potential vorticity are diagnosed on level surfaces from 5 years of model data and are spatially correlated with the corresponding time-mean gradients. We find no discernible correlation between the absolute eddy fluxes and mean gradients. However, after decomposing 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, typically 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 isopycnic thickness and potential vorticity are positive over the most of the fluid column. The overall correlations are similar for both thickness and potential 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. ¿ 2000 American Geophysical Union