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. el Σ and show that its contribution is of the same order of magnitude as the other two mesoscale terms usually accounted for. o 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.