43.0.3 Neutral directions

Within the functional framework, provision is made for a discretization of the diffusion fluxes which are aligned according to a self-consistent approximation to the neutral directions. Self-consistency means that there is a zero along isoneutral flux of locally referenced potential density. A zero isoneutral flux of locally referenced potential density implies a balance between the neutral direction flux of the two active tracers: $\alpha \vec{F}(\theta) = \beta \vec{F}(s)$, where $\alpha = -\rho_{\theta}/\rho$ and $\beta = \rho_{s}/\rho$ are the thermal expansion and saline contracion coefficients. In order to ensure this balance in a z-coordinate ocean model, it is sufficient to compute the density gradients in terms of the active tracer gradients and the thermal and saline coefficients (see Griffies et al. 1998 for more details). Special care must be taken when choosing the reference points for evaluating these gradients, and the details are given in Section . Without a self-consistent discretization which guarantees a zero flux of locally referenced potential density, the isoneutral diffusion operator will produce grid noise, even if it ensures variance does not increase.