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Wall modelling

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# 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

$\mu_t = \mu\left(\frac{y^+}{u^+} - 1\right)$

# High Reynolds number

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