Eddy mixing of potential vorticity versus thickness in an isopycnic ocean model

Parameterizations of the eddy-induced velocity that advects tracers in addi tion to the Eulerian mean flow are traditionally expressed as a downgradien t Fickian diffusion of either isopycnal layer thickness or large-scale pote ntial vorticity (PV). There is an ongoing debate on which of the two closur es is better and how the spatial dependence of the eddy diffusivity should look like. To increase the physical reasoning on which these closures are b ased, the authors present a systematic assessment of eddy fluxes of thickne ss and PV and their relation to mean-flow gradients in an isopycnic eddy-re solving model of an idealized double-gyre circulation in a flat bottom, clo sed basin. The simulated flow features strong nonlinearities, such as tight inertial recirculations, a meandering midlatitude jet, pools of homogenize d PV, and regions of weak flow where beta /h dominates the PV gradient. It is found that the zonally averaged eddy flux of thickness scales better wit h the zonally averaged meridional thickness gradient than the eddy flux of PV with the PV gradient. The reason for this is that the two-scale approxim ation, which is often invoked to derive a balance between the downgradient eddy flux of PV and enstrophy dissipation, does not hold. It is obscured by advection of perturbation enstrophy, which is multisigned and weakly relat ed to mean-flow gradients. On the other hand, forcing by vertical motions, which enters the balance between the downgradient eddy flux of thickness an d dissipation in most cases, acts to dissipate thickness variance. It is do minated by the conversion from potential to kinetic energy and the subseque nt downgradient transport of thickness. Also, advection of perturbation thi ckness variance tends to be more single-signed than advection of perturbati on enstrophy, forcing the eddy flux of thickness to be more often down the mean gradient. As a result, in the present configuration a downgradient dif fusive closure for thickness seems more appropriate to simulate the diverge nt eddy fluxes than a downgradient diffusive closure for PV, especially in dynamically active regions where the eddy fluxes are large and in regions o f nearly uniform PV.