Momentum🔗
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
\[\mu_t = \mu\left(\frac{y^+}{u^+} - 1\right)\]