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.