Wall-wake laws for the mean velocity and the turbulence

A new wall-wake law is proposed for the streamwise turbulence in the outer region of a turbulent boundary layer. The formulation pairs the logarithmic part of the profile (with a slope A₁ and additive constant B₁ ) to an outer linear part, and it accurately describes over 95 % of the boundary layer profile at high Reynolds numbers. Once the slope A₁ is fixed, B₁ is the only free parameter determining the fit. Most importantly, B₁ is shown to follow the same trend with Reynolds number as the wake factor in the wall-wake law for the mean velocity, which is tied to changes in scaling of the mean flow and the turbulence that occur at low Reynolds number.