Remarks on potential vorticity mixing over topography and momentum conservation

Recent works have shown that parameterizing eddy fluxes as a downgradient diffusion of potential vorticity (PV) generates circulation over topography. This result is examined in the context of a simple barotropic quasi-geostrophic model. It is shown that, unless a constraint on the eddy diffusivity is maintained, the PV mixing parameterization creates a fictitious torque which generates angular momentum. These considerations indicate that momentum conservation is not maintained in recent models that purport to show generation of net alongslope flow associated with PV mixing over topography.