Determination of the Coefficient of Diffusivity of Potential Vorticity in a Zonal Channel

Understanding mesoscale eddies and their interaction with the basin scale mean flow remains an important problem in physical oceanography. Several different approaches to parameterization of the effects of mesoscale eddies have been examined in the literature. In quasi-geostrophic potential vorticity (PV) transfer theory, mesoscale eddies are assumed on average to transfer PV downgradient and the main free parameter is the PV diffusivity coefficient, which is assumed to depend on the mean flow. Here, we adopt a new, complementary approach, which aims to develop strong constraints on the possible magnitude of the PV diffusivity due to parameters independent of the flow such as the wind stress and bottom topography. Combining results from an eddy resolving quasi-geostrophic model and a corresponding analytic model with parameterized eddies in a barotropic channel configuration, it is demonstrated that the PV diffusivity strongly varies for different types of bottom topography and for different wind stress with important consequences for the strength of the mean circulation. For monoscale (sinusoidal) topography, an algebraic equation is developed linking the PV diffusivity coefficient with the transport, wind stress, bottom topography, and geophysical and geometrical parameters. We present the result of statistical analysis of solutions of this equation with prescribed zonal transport obtained from a number of the eddy resolving model simulations and propose a new equation linking the PV diffusivity coefficient with wind stress and a parameter related to topographic roughness. We anticipate that similar relationships will hold for more realistic flow configurations and other types of mesoscale eddy closures.