Mesoscale eddy statistics and implications for parameterization refinements from a diagnosis of a high resolution model of the North Pacific

Mesoscale eddy statistics in mid-latitude wind-driven gyre interior are obtained using results of an eddy-active z-coordinate model of the North Pacific, whose horizontal resolution is about 6 km, to draw implications for possible refinements to the present eddy parameterization methods. Mainly two materials are presented. First, eddy fluxes of Ertel potential vorticity (PV), salinity, and thickness are evaluated in time-average after projection onto isopycnal coordinates. A largely rotational part, which is constrained to be small-scale (less than 3 ° × 3 ° ) and is nearly divergenceless when compared to the full flux, is removed from these fluxes. The remaining fluxes are regressed onto the along-gradient direction of the mean fields (diagonal part of a mixing tensor or Fickian diffusion) and the direction perpendicular to them (off-diagonal part or skew streamfunction). While the PV and salinity fluxes show agreement in Fickian diffusion coefficients and skew streamfunction magnitude as well as largely down-gradient features, the thickness fluxes are less well-behaved. Instead, thickness fluxes are correlated well with PV fluxes, indicating that they could be parameterized using a diffusive parameterization for PV. Overall, the present diagnosis supports the use of spatially-varying Fickian diffusion and skew streamfunction. Second, a mixing length approach using the eddy size as lengthscale is tested for explaining spatial distributions of Fickian diffusion coefficients for conservative scalars. The Fickian diffusivities are shown to be scaled with a factor of one-fifth to one-third by the ones based on the present mixing length approach. Mixing lengths are connected to instability lengthscales and Eady instability intensity. Overall, the present mixing length approach turns out to be a plausible, but incomplete, predictor of the eddy flux magnitudes.