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

TL;DR

This paper extends the understanding of turbulence intensity scaling in pipe flow to very high Reynolds numbers, showing inverse logarithmic scaling and confirming the relationship between turbulence intensity squared and the friction factor.

Contribution

It extrapolates turbulence intensity scaling laws to Reynolds numbers much greater than 10^5, assuming no further transitions occur, and confirms key theoretical predictions.

Findings

TI scales inversely with log(Re_tau)

Different TI measures have distinct multipliers

TI squared is proportional to the friction factor at high Re_tau

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 $Re_{\tau} \gg 10^5$.