Is the coefficient of eddy potential vorticity diffusion positive? part 1: Barotropic zonal flow

The question of whether the coefficient of diffusivity of potential vorticity 
 by mesoscale eddies is positive is studied for a zonal barotropic channel using 
 the quasi-geostrophic approach.  The topography is limited to the first mode 
 in the meridional direction but is unlimited in the in zonal direction.
 We derive an analytic solution for the stationary (time-independent) case.
 New terms appear both in the equations for the mean zonal momentum balance, 
 and the kinetic energy balance associated with parameterized eddy fluxes of 
 potential vorticity.  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.