Extending a potential vorticity transport eddy closure to include a spatially-varying coefficient

The use of spatially varying eddy diffusivities is explored with the extended Gent–McWilliams (eGM) closure for both passive tracers and potential vorticity (PV). Numerical experiments are conducted with a wind-forced isopycnal channel model. It is shown that, the eGM closure with eddy diffusivities derived from a high-resolution reference solution produces the best results compared to the reference solution in terms of the thickness, PV profiles and volume fluxes. The use of spatially varying eddy diffusivities also removes the unphysical reverse jets near the channel walls shown by the eGM with constant eddy diffusivities.