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Prandtl's mixing length hypothesis

In 1925 Prandtl visualized a simplified model for turbulence motion and expressed idea of mixing length, to be distance which is travelled by the turbulent whirl before is destroyed by mixing. Prandtl’s mixing length hypothesis leads to formula for dynamic eddy viscosity:
$\displaystyle \mu_T = \rho l_{mix}^2 \Bigg\vert \frac{\partial u}{\partial y} \Bigg\vert$ (27.14)
where $ l_{mix}$ is mixing length. Prandtl postulated further for flows near solid boundaries the mixing length is proportional to distance from the surface:
$\displaystyle \frac{l_{mix}}{\delta} = \digamma \Bigg( \frac{d_w}{\delta} \Bigg)$ (27.15)
where $ d_w$ is the distance to nearest wall and $ \delta$ is boundary layer thickness, which is distance for which holds:
$\displaystyle \frac{{\mathsf {v}}}{{\mathsf {v}}_\infty} = 0.99$ (27.16)
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