The effect of mesoscales on the tracer equation in z-coordinates OGCMs

In z-coordinates ocean codes, mesoscale fluxes entering the T,S equations are represented by three terms: an eddy-induced velocity, a diapycnal flux Σ and a diffusion (Redi-like) term. Several eddy resolving codes have shown that the diapycnal flux Σ is quite large. However, all ocean codes have been run with zero diapycnal flux, Σ = 0.We model Σ and show that its contribution is of the same order of magnitude as the other two mesoscale terms usually accounted for.We also assess the validity of the two arguments most frequently cited to neglect Σ: (1) in an adiabatic regime, fluxes across isopycnal surfaces must vanish and so must the diapycnal flux Σ (we show that since Σ is not the total buoyancy flux but only part of it, there is no justification in demanding that Σ should satisfy the same conditions as the total flux) and (2) the results of a z-coordinate ocean code without Σ can be re-interpreted as those derived from the TRM (temporal residual mean) in which there is no Σ almost by definition since TRM is quite close to an isopycnal model.