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Figure 1 
DNS results for a turbulent channel flow. Velocity fluctuation intensities in wall units. -, u’; - -, v’; -.-, w’. The symbols represent three different Reynolds numbers (547: triangle down, 934: triangle up and 2,003: circle). Source: Hoyas (2006) [2]
Despite its admitted deficiencies, the eddy viscosity assumption provides reasonable results in many cases. The number of additional unknowns in the RANS equations decreased from six to one, the eddy viscosity μt. The big challenge of turbulence modeling lies in the description of this eddy viscosity.

References

[1] J. Boussinesq. Theorie de l’ecoulement tourbillonnant et tumultueux des liquides dans les lits rectilignes a grande section. Comptes-rendus des seances de l’academie des sciences, 23:46, 1877.

[2] S. Hoyas and J. Jiménez. Scaling of the velocity fluctuations in turbulent channels up to Re= 2003. Physics of fluids, 18:011702, 2006.

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