Quasi-geostrophic dynamics in an eddy-resolving zonal re-entrant channel in the Southern Hemisphere have been studied for east- and westward wind forcing scenarios. The main difference is seen in the zonally averaged velocity profiles. In the case of eastward forcing, transient eddies strongly intensify the flow in the channel center into a jet, a feature totally absent in the westward forcing cases. The free jet is associated with a five times higher available potential energy compared to the westward flow. We have used these two distinctly different flow regimes to investigate possible parameterizations of the eddy fluxes in both situations. Parameterizations using a diffusion concept for the quasi-geostrophic potential vorticity (QPV) fluxes, based on earlier work by Green and Welander, have raised a number of questions concerning the transfer (or diffusion) coefficients. These coefficients must satisfy three basic integral constraints, the balances of momentum, energy and enstrophy. It is shown that the constraints related to momentum and energy conservation are associated with Pedlosky's instability conditions. An analytical solution developed in this paper shows that the transfer coefficients have a theoretical upper limit in the eastward-forcing scenarios, resulting in a greater Reynolds number than a theoretically derived critical Reynolds number. A general parameterization scheme, based on the quasi-geostrophic eddy enstrophy balance, is presented, which accounts for both scenarios, a weakly baroclinic westward flow and a strongly baroclinic eastward flow. This new parameterization reproduces the main difference in the east- and westward flows; i.e., a strong jet in the eastward-forcing case and a broad smooth flow in the westward-forcing case, in agreement with the numerical results of the eddy-resolving experiments.