Invariant p.d.f. property of velocity fluctuation in high-Reynolds-number turbulent boundary layer

Streamwise velocity fluctuations are measured in a zero-pressure gradient turbulent boundary layer at high Reynolds numbers. When normalised by the mean and standard deviation, u Subscript r u r uᵣ , the probability density function (p.d.f.) of the fluctuations exhibits invariance within distinct wall-normal regions. Two such regions were identified: one situated near the plateau of the turbulence intensity profile and the other associated with the logarithmic region ( left parenthesis u Subscript r Superscript plus Baseline right parenthesis squared equals upper A 1 ln left parenthesis y divided by delta right parenthesis plus upper B 1 ( u r + ) 2 = A 1 ln ⁡ ( y / δ ) + B 1 (uᵣ⁺)²=A₁ ln (y/δ )+B₁ ) consistent with Townsend’s attached-eddy hypothesis. The p.d.f. shapes in both regions are independent of Reynolds number, demonstrating their universality. The slope, upper A 1 A 1 A₁ , and additive constant, upper B 1 B 1 B₁ , were evaluated to be upper A 1 asymptotically equals 1.42 A 1 ≃ 1.42 A₁ 1.42 and upper B 1 asymptotically equals 1.75 B 1 ≃ 1.75 B₁ 1.75 , respectively, for upper O left parenthesis 10 Superscript 4 Baseline right parenthesis less than italic Re Subscript tau O