Momentum wall functions are imposed by setting the turbulence viscosity at the wall. By combining the dimensionless velocity
\[ u^+ = \frac{u}{u_t} \]
dimensionless wall distance
\[ y^+ = \frac{\rho y u_t}{\mu} \]
and friction velocity
\[ u_t = \sqrt {\frac{\tau_{wall}}{\rho}} \]
the wall shear stress can be described according to:
\[ \tau_{wall} = \mu \frac{y^+}{u^+} \frac{u}{y} = (\mu + \mu_t) \frac{u}{y} \]
where
\[ \mu_t = \mu\left(\frac{y^+}{u^+} - 1\right) \]
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