Orientation of Eddy-Flux of Potential Vorticity in Geostrophic Turbulence

Given its importance in parameterizing eddies, we consider the orientation of eddy flux of potential vorticity in geostrophic turbulence. We take two different points of view,a classical ensemble or time-average point of view and a second scale-decomposition point of view. A net alignment of the eddy flux of pv with the appropriate mean gradient or the large-scale gradient of pv is required. However,we find this alignment to be very weak.We find, instead, that the orientation of the eddy flux of pv is better correlated with a nonlinear combination of resolved gradients.
Implications of this alignment to eddy parameterizations will be considered.