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Rough wall function vs. atmospheric rough wall function

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Old   September 23, 2015, 07:30
Default Rough wall function vs. atmospheric rough wall function
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I have been looking into homogeneity of atmospheric boundary layer profiles through an empty fetch. I noticed that nutkAtmRoughWallFunction performed slightly worse than nutkRoughWallFunction.

When looking at the code to work out what the atmospheric version was doing, I came across a definition I can't work out:

As expected, both define effective viscosity as:

For nutkRoughWallFunction, E' is defined as expected, based on roughness regime. For fully rough (most practical ABL applications), it's:

However, for the nutkAtmRoughWallFunction, it is defined as:

I've not seen this definition in the literature, and can't work out why it's used. It means that the sand grain roughness is never defined in the equation, which seems odd.

Can anyone shed any light on this?
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Old   February 27, 2016, 09:12
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I am working on the same. I can't see the expressions you provided. I have some improves regarding the papers I have reviewed until now.
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Old   February 6, 2020, 10:32
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The last equation corresponds to Eq. 5 from

Hargreaves, D. M., & Wright, N. G. (2007).
On the use of the kε model in commercial CFD software to model
the neutral atmospheric boundary layer.
Journal of wind engineering and industrial aerodynamics, 95(5), 355-369.
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boundary layer, k-epsilon, wall functions

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