University of Melbourne using the nano-scale thermal anemometry probe (NSTAP) to conduct velocity measurements in the high Re number boundary layer up to $Re_\tau  = 20000$. The NSTAT has a sensing length almost one order of magnitude smaller than conventional hot-wire, hence allows for a fully resolved NSTAT measurement of velocity fluctuations, [@Sa18], [@Ba19]. The size of the University of Melbourne wind tunnel and the accuracy of the NSTAT permit the measurement over a very large range of scales. We use the averaged velocity time-series at Reynolds numbers $Re_\tau=6000, 10000,14500, 20000$ and the averaged variance at the same Reynolds numbers. Fig. \[fig:mean velocity\] shows the mean velocity profiles as a function of normalized distance from the wall, whereas Fig. \[fig:mean variation\] shows the averaged fluctuation squared (variation) as a function of the normalized distance to the wall. Both are semi-log plots.

First, let us consider the curve describing the MVP in Fig. \[fig:mean velocity\] (panel b). It starts with the Eq. (\[eq:u\_o\]) for the viscous profile because the $I$-function is zero. But then we reach the value $y_v$ where the first attached eddies appear ($y=4.17$) and then the viscous profile changes, instead of reaching its maximum $u=Re \sqrt{f}/2$ at $y=Re 