Using a two-layer quasigeostrophic model with weak interfacial and bottom friction we propose a mechanism for potential vorticity homogenization in a non-eddying, wind-driven gyre closed through a viscous western boundary layer, to which the previous theory based on the Prandtl–Batchelor theorem cannot be applied. It is shown that there exist steady states in which the lower-layer potential vorticity in a large pool of closed geostrophic contours becomes substantially uniform. The homogenization process is dominated by advection and thus completed within a single passage through the gyre. This is because an O (1) anomaly of potential vorticity that is comparable to the value at the pool boundary can be produced in the boundary layer by westward intensification of gyre-scale vorticity inputs via friction, however weak it may be, and is then transported to the interior by the characteristic flow to fill the pool. Both asymptotic and numerical analyses verify that the homogenized state is in higher-order Sverdrup-like balance between the advection and the frictional source. This style of homogenization occurs if the ratio of the friction coefficients, which determines the strength of the initial anomaly and deviations from downgradient diffusion, falls into specific ranges. This similarity feature implies the existence of an unventilated pool with uniform potential vorticity in an appropriate inviscid limit.
Sakamoto, Toshihiro. 2007. "The role of westward intensification in potential vorticity homogenization." Journal of Marine Research 65, (1). https://elischolar.library.yale.edu/journal_of_marine_research/158