# Dimensionless properties of turbulence with law of the wall

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 $$\tau_{turb} / \rho = -\overline{u^{'}v^{'}}$$ ?