Tracer Vertical Diffusion (trazdf.F90)

!-----------------------------------------------------------------------
&namzdf        !   vertical physics
!-----------------------------------------------------------------------
   rn_avm0     =   1.2e-4  !  vertical eddy viscosity   [m2/s]          (background Kz if not "key_zdfcst")
   rn_avt0     =   1.2e-5  !  vertical eddy diffusivity [m2/s]          (background Kz if not "key_zdfcst")
   nn_avb      =    0      !  profile for background avt & avm (=1) or not (=0)
   nn_havtb    =    0      !  horizontal shape for avtb (=1) or not (=0)
   ln_zdfevd   = .true.    !  enhanced vertical diffusion (evd) (T) or not (F)
   nn_evdm     =    0      !  evd apply on tracer (=0) or on tracer and momentum (=1)
   rn_avevd    =  100.     !  evd mixing coefficient [m2/s]
   ln_zdfnpc   = .false.   !  Non-Penetrative Convective algorithm (T) or not (F)
   nn_npc      =    1            !  frequency of application of npc
   nn_npcp     =  365            !  npc control print frequency
   ln_zdfexp   = .false.   !  time-stepping: split-explicit (T) or implicit (F) time stepping
   nn_zdfexp   =    3            !  number of sub-timestep for ln_zdfexp=T
/

Options are defined through the namzdf namelist variables. The formulation of the vertical subgrid scale tracer physics is the same for all the vertical coordinates, and is based on a laplacian operator. The vertical diffusion operator given by (2.34) takes the following semi-discrete space form:

$$\begin{split}D^{vT}_T &= \frac{1}{e_{3t}} \; \delta_k \left[ ... ...\frac{A^{vS}_w}{e_{3w}} \delta_{k+1/2}[S] \;\right] \end{split}$$ (5.10)

where $A_w^{vT}$ and $A_w^{vS}$ are the vertical eddy diffusivity coefficients on temperature and salinity, respectively. Generally, $A_w^{vT}=A_w^{vS}$ except when double diffusive mixing is parameterised ($i.e.$ key_ zdfddm is defined). The way these coefficients are evaluated is given in §10 (ZDF). Furthermore, when iso-neutral mixing is used, both mixing coefficients are increased by $\frac{e_{1w} e_{2w} }{e_{3w} } \left( {r_{1w} ^2+r_{2w} ^2} \right)$ to account for the vertical second derivative of (5.9).

At the surface and bottom boundaries, the turbulent fluxes of heat and salt must be specified. At the surface they are prescribed from the surface forcing and added in a dedicated routine (see §5.4.1), whilst at the bottom they are set to zero for heat and salt unless a geothermal flux forcing is prescribed as a bottom boundary condition (see §5.4.3).

The large eddy coefficient found in the mixed layer together with high vertical resolution implies that in the case of explicit time stepping (ln_zdfexp=true) there would be too restrictive a constraint on the time step. Therefore, the default implicit time stepping is preferred for the vertical diffusion since it overcomes the stability constraint. A forward time differencing scheme (ln_zdfexp=true) using a time splitting technique (nn_zdfexp $> 1$) is provided as an alternative. Namelist variables ln_zdfexp and nn_zdfexp apply to both tracers and dynamics.