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Horizontal eddy viscosity

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Horizontal eddy viscosity is a term in the momentum equations to cover the well-known turbulence closure problem. For background on the problem, see, e.g. the AMS glossary definition, the Wikipedia entry on turbulence modeling, or a fluid mechanics textbook such as Kundu's[1]. Readers unfamiliar with these concepts should note that, contrary to the name, eddy viscosity is unrelated to true viscosity, even though the units (length squared over time) are the same. Typically, one should expect eddy viscosity to be many orders of magnitude larger than the viscosity of actual water (around 1x10-6 meters2/second for seawater). In ADCIRC, horizontal eddy viscosity can be treated via either a manually specified eddy viscosity or a Smagorinsky-type eddy viscosity. In all cases, the parameter is useful both for dealing with the true turbulence closure problem and for aiding with numerical stability.

Manually Specified Eddy Viscosity

A spatially constant eddy viscosity can be supplied via the `ESLM` parameter in the fort.15 file. Alternatively, the `average_horizontal_eddy_viscosity_in_sea_water_wrt_depth` nodal attribute permits a spatially variable eddy viscosity.

Usage Notes

Commonly used values range from 1 to 50 meters2/second, with 10 being a good starting point for many coastal ocean modeling scenarios. By the nature of turbulence closure, one might expect the value to be smaller as mesh resolution increases. However, this may not always be the case since areas with high resolution may also be more turbulent. In particular, some modelers use a larger value in overland areas, which can also improve stability. However, specifying a value that is too large can induce instabilities, as well.

Smagorinsky Eddy Viscosity

ADCIRC also allows a Smagorinsky-type turbulence closure model[2]. There are currently two slightly different ways of enabling this in the model. One is by specifying a negative value for `ESLM` in the fort.15 file. If this is done, the Smagorinsky turbulence closure is enabled and the absolute value of `ESLM` is used as the coefficient. Alternatively, the `Smag_Control` namelist can be used, e.g.
`&Smag_Control SMAG_LOWER_LIM=1.0d-8, SMAG_UPPER_LIM=100 /`
When this is done, the value of `ESLM` is taken as the coefficient. This also allows the user to optionally specify lower and upper bounds on the actual eddy viscosity determined via the Smagorinsky formulation. The values given in the above example of 1E-8 m2/s and 100 m2/s are the default values. There is no way to supply upper and lower bounds with the other method.

Usage Notes The two methods currently result in different flags being set in the code, which have inconsistent behavior. Most notably, the "negative `ESLM` method" results in a check being run at model initialization to verify that the Kolar-Gray formulation of the lateral stresses in the GWCE is not in use, and the code errors out if it is. This choice is specified by the first digit in a six-digit IM code being set to 1.

digit 1 of IM==1 isn't allowed

References

1. Pijush K. Kundu, Ira M. Cohen, David R. Dowling (2012). Fluid Mechanics.
2. Smagorinsky, J. “General Circulation Experiments with the Primitive Equations.” Monthly Weather Review 91, no. 3 (March 1, 1963): 99–164. https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2.