The resolution of present ocean numerical models is generally at several km. The viscosity coefficient is used as a compromise between suppressing the grid-scale noise and maintaining shear instability. As there is a certain range to choose the magnitude of the coefficient, is there any other criterion for selecting the best one? The relationship between diffusivity and viscosity coefficients is also unclear in the model.
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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