Extrapolation of Turbulence Intensity Scaling to $Re_{\tau} \gg 10^5$

Abstract

We have characterized a transition of turbulence intensity (TI) scaling for friction Reynolds numbers $Re_{\tau} \sim 10^4$ in the companion papers [Basse, N.T. Scaling of global properties of fluctuating and mean streamwise velocities in pipe flow: Characterization of a high Reynolds number transition region, Physics of Fluids, Volume 33, 065127 (2021)] and [Basse, N.T. Scaling of global properties of fluctuating streamwise velocities in pipe flow: Impact of the viscous term, Physics of Fluids, Volume 33, 125109 (2021)]. Here, we build on those results to extrapolate TI scaling for $Re_{\tau} \gg 10^5$, under the assumption that no further transitions exist. Scaling of the core, area-averaged and global peak TI demonstrates that they all scale inversely with the logarithm of $Re_{\tau}$, but with different multipliers. Finally, we confirm the prediction that the TI squared is proportional to the friction factor for $Re_{\tau} \gg 10^5$.