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The current view about the mixing of heat and salt in the ocean is that itshould be parameterised by means of a rotated diffusion tensor based on mixingdirections parallel and perpendicular to the local neutral vector. However, theimpossibility to construct a density variable in the ocean that is exactlyneutral because of the coupling between thermobaricity and density-compensatedtemperature/salinity anomalies implies that the effective diapycnal diffusivityexperienced by any possible density variable is partly controlled by isoneutraldiffusion when using neutral rotated diffusion. Here, this effect is quantifiedby evaluating the effective diapycnal diffusion coefficient for five widelyused density variables: Jackett and McDougall (1997) $\gamma^n$, Lorenzreference state density $\rho_{ref}$ of Winters et al. (1996), Saenz et al.(2015), and three potential density variables $\sigma_0$, $\sigma_2$ and$\sigma_4$.Computations use the World Ocean Circulation Experiment climatology,assuming either a uniform value for isoneutral mixing or spatially varyingvalues inferred from an inverse calculation. Isopycnal mixing contributions tothe effective diapycnal mixing yields values systematically larger than$10^{-3}$ $\text{m}^2/\text{s}$ in the deep ocean for all density variables,with $\gamma^n$ suffering the least from the isoneutral control of effectivediapycnal mixing, and $\sigma_0$ the most. These high values are due tospatially localised large values of non-neutrality, mostly in the deep SouthernOcean. Removing only 5\% of these high values on each density surface reducesthe effective diapycnal diffusivities to less than $10^{-4}$$\text{m}^2/\text{s}$. This work highlights the potential pitfalls ofestimating diapycnal diffusivities by means of Walin-like water masses analysisor in using Lorenz reference state for diagnosing spurious numerical diapycnalmixing.

Isoneutral control of effective diapycnal mixing in numerical ocean models with neutral rotated diffusion tensors