The following literature may be useful for your research

The purpose of this short note is to list a multitude of stability critera for Bryan-Semtner-Cox [Bryan(1969), Semtner (1974), Cox (1984)] type ocean general circulation models. None of the results listedhere are new, rather this note brings together results (but not their derivation) into what is hopefully auseful form

In this studies, viscosity ceofficient is expressed in time function, The timestep limitation due to the horizontal diffusive terms is well known and can be found in almost

any text on numerical analysis, for example O’Brien (1986)

Ref:Computational Stability of Bryan-Semtner-Cox type models (Draft)

David P. Stevens, School of Mathematics, University of East Anglia, Norwich, NR4 7J, England.

www.uea.ac.uk/~dps/publications/stab.pdf

Another reference

The ‘‘basic configuration’’ is a rectangular basin of dimensions 1200 x 100

(x,y) km. The grid resolution is 1.5 km in the horizontal. In the vertical 40 levels

are equally spaced to cover the total depth of the ocean (H = 2000 meters). In the

basic configuration, the model does not employ explicit horizontal dissipation. In

the vertical there is a viscosity and diffusivity, both equal to 10-5 m2

s-1; there is no explicit mixed layer scheme. At the bottom a free-slip condition is used with nobottom drag in order to isolate the energy conversion from barotropic to baroclinictide. The conversion estimates are computed over a ‘‘polynomial” ridge

Numerical and analytical estimates of M2 tidal conversion at

steep oceanic ridges;

Emanuele Di Lorenzo et al

School of Earth and Atmospheric Sciences

Georgia Institute of Technology

eros.eas.gatech.edu/web_db_papers/edl.../DiLorenzo_tides_jpo2005.pdf

Nobody knows the answer to this question. Some progress can be made in particular situations by trying various values and seeing which ones produce predictions that seem to best match observations. However, there is no fundamental (i.e. dynamically-founded) reason to believe that those values will carry over to other situations. There is a vast literature on this sort of thing, and your reading will be easier if you realize that diffusivities, convenient though they may be, are essentially a kludge.

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Totally agree with Dan's response and, in my judgment, I think the only right way to go out of this impasse is you find some physical indicator in the region under study for determinares the coefficients of your model.

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Attention, a mesh results for the measurement is not necessary, but if you have, for example, data floats, sediment and erosion deposit areas, concentration measurements or something like that then you can try to simulate the model with approximate coefficients and optimize them.

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To do the simulation you must be using some boundary condition and the same way you found this boundary condition you should seek conditions inside the mesh.

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The easy part. The ratio between viscosity and diffusivity (or viceversa) is the Prandlt number (Pr). There are manuscripts about Pr number estimation in the ocean and even if a numerical model is not exactly the ocean my personal idea is that we should stay close to the observed value.

About the values. A basic check can be done using a scale analysis. Your diffusive (visc.) terms should not provide accelerations larger than other terms and the basic ocean balances should be always respected (geostrophy quasi-geostrophy). On the other hand, you should know about the ocean area you want to model enough to perform this basic check.

An idea to obtain reasonable values could be to combine non Primitive equation models (like the on used in LES) and primitive equation calibration exercise. With the first you explicitly resolve the turbulent diffusion (viscosity) and you can use this value in your P.E. model. If you get funded for this study let me know :)

I hope this help.