Why Are Eddy Fluxes of Potential Vorticity Difficult to Parameterize?

Abstract

Eddy fluxes systematically affect the larger-scale, time-mean state, but their local behavior is difficult to parameterize. To understand how eddy fluxes of potential vorticity (PV) are controlled, the enstrophy budget is diagnosed for a five-layer, 1/16°, eddy-resolving, isopycnic model of a wind-driven, flat-bottom basin. The direction of the eddy flux across the mean PV contours is controlled by the Lagrangian evolution of enstrophy, including contributions from the temporal change and mean and eddy advection, as well as dissipation of enstrophy. During the spinup, an overall increase in enstrophy is consistent with eddy fluxes being directed downgradient on average and homogenization of PV within intermediate layers. Enstrophy becomes largest along the flanks of the gyre, where PV gradients are large, and becomes smallest in the interior. At a statistically steady state, there is a reversing pattern of up- and downgradient eddy PV fluxes, which are locally controlled by the advection of enstrophy. A downgradient eddy PV flux occurs only on the larger scale over the gyre flanks and part of the western boundary. These larger-scale patterns are controlled by the eddy advection of enstrophy, which becomes significant in regions of high eddy enstrophy. As a consequence, at a statistically steady state, the eddy PV fluxes are not simply related to the mean fields, and their local, finescale pattern is difficult to parameterize.