Reynolds Number Required to Accurately Discriminate Between Proposed Trends of Peak Normal Stress in Wall Turbulence

In Nagib, Chauhan and Monkewitz (Phil Trans R. Soc. A, 2007) we concluded that nearly all available C_f relations are in remarkable agreement over the entire range Re_τ < O(10⁸), provided one coefficient is adjusted in each relation by anchoring it with accurate measurements. Regarding the peak of the streamwise turbulence intensity <uu>⁺_P, we conclude here that accurate measurements in flows with Re_τ > O(10⁶) are required to discriminate between recently proposed trends of <uu>⁺_P. We also find remarkable agreement between the three analyses of Monkewitz (JFM 2022), Chen and Sreenivasan (JFM 2021) and Monkewitz and Nagib (JFM 2015), with some coefficients slightly modified, by underpinning them with the same accurate measurements of <uu>⁺_P from reliable channel and boundary layer data. All the three analyses conclude that the inner peak of <uu>⁺ remains finite in the limit of infinite Reynolds number, which is at variance with the unlimited growth of <uu>⁺_P as ln(Re_τ) predicted by the attached eddy model (Marusic & Monty, Annu. Rev. Fluid Mech., 2019). Accurate measurements of high-order moments and the guidance of consistent asymptotic expansions may help clarify the issue at lower Re_τ values.