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The velocity profile is defined as law of the wall is defined as $u^+ = f(y^+)$, where $u^+ = \frac{\bar{u}}{v^*}$; $y^+ = \frac{yv^*}{v}$ and $v^*=\sqrt{\frac{\tau_w}{\rho}}$.

How would one then non dimensionalize the eddy viscosity $v_t$ and turbulent sheer stress $\tau_{turb} / \rho = -\overline{u^{'}v^{'}}$ ?

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