Parameterization of the effects of eddies on the background "mean" flow requires both a theory for the eddies and an appropriate mathematical framework within which to determine how they impact the mean state. The most obvious mathematical formulation of the problem for the mean state, in the presence of eddies, may represent the eddy terms in a way such that the physical signifance of those terms is obscure, and which are therefore difficult to parameterize. Examples commonly encountered in large-scale atmospheric and oceanic contexts are: (1) transport of quasi-conserved tracers in more than one dimension, and (2) momentum transport. (1) can be dealt with through exploiting the ambiguities inherent in the definition of "mean" to re-formulate the mean flow problem. (2) can be treated in the same way for balanced flows (in which velocities can be determined from an inversion of the quasi-conserved potential vorticity) but there remain some uncertainties about to how best to express the momentum budget.
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