Eddy Induced Velocity (traadv_eiv.F90, ldfeiv.F90)

When Gent and McWilliams [1990] diffusion is used (key_ traldf_eiv defined), an eddy induced tracer advection term is added, the formulation of which depends on the slopes of iso-neutral surfaces. Contrary to the case of iso-neutral mixing, the slopes used here are referenced to the geopotential surfaces, $i.e.$ (9.10) is used in $z$-coordinates, and the sum (9.10) + (9.11) in $s$-coordinates. The eddy induced velocity is given by:

$$\begin{split}u^* & = \frac{1}{e_{2u}e_{3u}}\; \delta_k \left[... ... \; \overline{r_{2w}}^{ j+1/2} \right] \right\} \end{split}$$ (9.15)

where $A^{eiv}$ is the eddy induced velocity coefficient whose value is set through rn_aeiv, a nam_traldf namelist parameter. The three components of the eddy induced velocity are computed and add to the eulerian velocity in traadv_eiv.F90. This has been preferred to a separate computation of the advective trends associated with the eiv velocity, since it allows us to take advantage of all the advection schemes offered for the tracers (see §5.1) and not just the $2^{nd}$ order advection scheme as in previous releases of OPA [Madec et al., 1998]. This is particularly useful for passive tracers where positivity of the advection scheme is of paramount importance.

At the surface, lateral and bottom boundaries, the eddy induced velocity, and thus the advective eddy fluxes of heat and salt, are set to zero.