35.1.3 Summary of the options and namelist parameters

Option isoneutralmix is referred to as a hybrid mixing scheme since it only mixes tracers, not momentum. One basic horizontal mixing scheme (e.g. option consthmix) and one basic vertical mixing scheme (e.g. option constvmix) must also be enabled for use with option isoneutralmix. Optionsredi_diffusion, gent_mcwilliams, and biharmonic_rm are the three main sub-options to option isoneutralmix. Enabling either of these three sub-options will automatically enable isoneutralmix. There is one other sub-option, diff_nonconstant, which is described in Section 34.2.

For conceptual orientation, the combined mixing tensor which defines the default tracer fluxes arising from redi_diffusion, gent_mcwilliams, and biharmonic_rm takes the form

 

$$J^{mn} = \left( \begin{array}{ccc} A_{I} & 0 & (A_{I}-\kappa + B ... ...a -B \, \nabla_{h}^{2}) \, S_{y} & (A_{I} \, S^{2} + A_{D}) \end{array}\right),$$ (35.1)

where A_I is the along isoneutral diffusivity, $\kappa$ is the GM90 diffusivity, B is the RM98 biharmonic diffusivity, S_x and S_y are the isoneutral slopes in the x and y directions, respectively, S² = S_x² + S_y², A_D is the dianeutral diffusivity, approximated here as vertical diffusion, and $\nabla_{h}^{2}$ is the horizontal Laplacian operator. This tensor represents the sum of the symmetric small angle isoneutral diffusion tensor, the anti-symmetric GM90 tensor, and the anti-symmetric RM98 tensor. The central goals of the numerical algorithms are to discretize the tracer fluxes arsing from this tensor in a numerically stable and physically consistent fashion. It is believed that the current algorithms in MOM provide a workable approximation to these two goals.

1.

Option redi_diffusion enables the Redi isoneutral diffusion process. There are two sub-options for  redi_diffusion.

• Option small_tensor (Section 34.1.5) is the default version of redi_diffusion. It employs the small angle approximated tensor first written down by Gent and McWilliams (1990). This approximation is discussed further in Griff ies et al. (1998).
• Option full_tensor employs the full, unapproximated isoneutral diffusion tensor of Redi (1982). This scheme requires roughly 5-10 times more computational time than small_tensor; it is not compatible with the default option gm_skew; it is not compatible with option diff_nonconstant, and it has questionable physical relevance in mixed layer regions (see Section 34.1.9). Therefore, option full_tensor is not recommended. The code for the full tensor remains frozen and so will not be made compatible with future options, unless trivially done. It remains in MOM, nevertheless, since the full tensor code is cleanly isolated, and it is of potential interest to those comparing the results from different ways to handle the steep sloped regions.

For the small tensor, and for most parameter ranges of the full tensor, some form of tapering is required in order to scale to zero the along isoneutral diffusivity as the slope increases. There are two options for implementing this tapering.

• Option dm_taper (section 34.1.9.1) uses the scheme of Danabasoglu and McWilliams (1996).
• Option gkw_taper (Section 34.1.9.2) uses the scheme of Gerdes et al. (1991). This is the default option.

If one uses a mixed layer scheme such as option kppvmix (Section 32.2.3), it might be useful to compute horizontal tracer fluxes within the boundary layer using the same horizontal diffusivity as used to compute vertical tracer fluxes. Option isotropic_mixed (Section 34.1.9.3) enables this choice to be made in MOM.

The namelist parameters (refer to Section 14.4 for information on namelist variables) for  redi_diffusion are the following:

• ahisop is the along isoneutral diffusion coefficient. The default value is 10⁷ cm²/sec. ahisop is identical to A_I in the mixing tensor shown in equation (34.1).
• slmx is the maximum isoneutral slope. The default value is 0.01. For slopes with magnitudes larger than slmx, one of the tapering schemes dm_taper or gkw_taper is used.
• ahsteep is the horizontal diffusion coefficient which kicks in whenever the isoneutral slopes are larger than slmx. The default value is ahsteep = ahthk. When one of the nonconstant diffusivity schemes described in Section 34.2 is used, ahsteep defaults to the value of the non-constant skew-diffusivity. This default for the horizontal diffusion in steep regions is based on the ideas in Treguier et al. (1997).
• del_dm is the transition for scaling isoneutral diffusivities with option dm_taper. The default value is 0.004.
• s_dm is the half width scaling for diffusivity with option dm_taper. The default is 0.001.

In order to obtain the standard small slope tensor using the Gerdes et al. (1991) form for tapering, the option redi_diffusion is all that is needed. Default options small_tensor and gkw_taper are automatically enabled. Setting the alternatives will override these defaults.

2.

Option gent_mcwilliams enables the GM90 adiabatic stirring process. There are two sub-options for gent_mcwilliams.

• Option gm_skew (Section 34.1.6.1) implements GM90 in terms of the skew-flux approach described in Griff ies (1998). This is the default option.
• Option gm_advect (Section 34.1.6.2) implements GM90 in terms of the advective-flux approach discussed in Danabasoglu and McWilliams (1996).

The namelist parameter for  gent_mcwilliams is the following:

• athkdf is the GM90 diffusion coefficient. The default value is 10⁷ cm²/sec. athkdf is identical to $\kappa$ in the mixing tensor shown in equation (34.1).

Just as for the isoneutral diffusion scheme, it is necessary to scale the GM90 diffusivity to zero as the isoneutral slope increases. The same options, with the same maximum slope slmx, are used here as for isoneutral diffusion.

In order to obtain the standard gent_mcwilliams scheme, employing skew-fluxes and the Gerdes et al. (1991) form for tapering, the option gent_mcwilliams is all that is needed. Default options gm_skew and gkw_taper are automatically enabled. Setting the alternatives will override these defaults.

3.

Option biharmonic_rm (Section 34.1.8) enables the RM98 adiabatic biharmonic operator in terms of skew-fluxes. There are no sub-options for biharmonic_rm. The namelist parameter is

• abihrm is the RM98 diffusion coefficient. The default value is 10¹⁹ cm⁴/sec. abihrm is identical to B in the mixing tensor shown in equation (34.1).

Just as for the isoneutral diffusion scheme, it is necessary to scale the RM98 diffusivity to zero as the isoneutral slope increases. The same options, with the same maximum slope slmx, are used here as for isoneutral diffusion.

4.

Option diff_nonconstant enables one of the mesoscale eddy closures for use in producing an eddy diffusivity which is a function of space and time. This option is described in Section 34.2.