Velocity profile
$$
U(z)=\frac{u^*}{k}log(\frac{z+z0}{z0})
$$
Where $u^$ is friction velocity,
Reynolds number $$ \mathrm{Re}{\mathrm{x}}=\frac{\rho U{\infty} L}{\mu} $$
Turbulence Intensity $$ I \equiv \frac{u^{\prime}}{u_{a v g}}=0.16\left(R e_{D_{H}}\right)^{-1 / 8} $$
Turbulence Length Scale $$ \ell=\frac{0.07 L}{C_{\mu}^{3 / 4}} $$
Turbulent Kinetic Energy
$$
k=\frac{3}{2}\left(u_{a v g} I\right)^{2}
$$
Turbulent Dissipation Rate
$$
\varepsilon=\frac{k^{3 / 2}}{l}
$$