Centerline Kármán "constant" revisited and contrasted to log-layer Kármán constant at CICLoPE

In early pipe flow experiments, the emphasis has been on the scaling of the centerline velocity and the friction factor with Reynolds number. As measurement techniques have evolved, attention has shifted towards the "law of the wall" U+ = (1=kwall) ln(y+)+B and its Kármán constant kwall. In the last years the value of kwall in pipes has closely approached the "most popular" value of 0.384 for the zero-pressure-gradient boundary layer (Furuichi et al. (2015), Örlü et al. (2016)) which seemingly supports the claim of Marusic et al. (2013) that k = 0.39 is universal for pipe flow and zero-pressure-gradient boundary layers. However, the asymptotic matching to the "wake", already discussed by Coles (1956), has not received enough attention. It requires that kwall be the same as kCL in the expression for the centerline velocity UCL+ = (1/kCL) ln(Reτ)+C, but kCL has consistently remained larger than 0.42. Only very recently Monkewitz (2017)) has proposed a resolution of this conundrum by introducing a universal internal wall log-law with kint = 0.384 for the range 102 ≤ y+ ≤ 103, followed by an external log-law with kext = kCL for y+ ≤ 0.05Reτ and the wake. The analysis of Monkewitz (2017) for pipe flow was based on the Superpipe data where kext = 0.42. So the question arises whether the difference between kint and kext is statistically significant. The purpose of this contribution is to show that this is indeed the case, as kCL in CICLoPE is found to be 0.446 ± 0.008. Interestingly, this value is very close to the original kCL = 0.436 of Zagarola & Smits (1998) for the Superpipe and the value of 0.437 found in the first CICLoPE experiments by Fiorini (2017).