Is the coefficient of eddy potential vorticity diffusion positive? Part1: barotropic zonal channel.

The question of whether the coefficient of diffusivity of potential vorticity by mesoscale eddies is positive is studied for a zonally reentrant barotropic channel using the quasi-geostrophic approach. The topography is limited to the first mode in the meridional direction but is unlimited in the zonal direction. We derive an analytic solution for the stationary (time-independent) solution. New terms associated with parameterized eddy fluxes of po-tential vorticity appear both in the equations for the mean zonal momentum balance, and the kinetic energy balance. These terms are linked with the topographic form stress exerted by parameterized eddies. It is demonstrated that in regimes with zonal flow (analogous to the Antarctic Circumpolar Current), the coefficient of eddy potential vorticity diffusivity must be positive.