Scaling of global properties of fluctuating and mean streamwise velocities in pipe flow: Characterisation of a high Reynolds number transition region

TL;DR

This paper investigates how the turbulence intensity in pipe flow scales at high Reynolds numbers, proposing models based on the logarithmic region assumption and identifying a transition point around Re_tau of 11000.

Contribution

It introduces a new high Reynolds number scaling framework for streamwise turbulence intensity based on the assumption of an extended logarithmic region in wall turbulence.

Findings

Transition to asymptotic scaling at Re_tau ~ 11000

Derived scaling expressions for log-law and power-law functions

Matched theoretical models with Princeton Superpipe measurements

Abstract

We study the global, i.e. radially averaged, high Reynolds number (asymptotic) scaling of streamwise turbulence intensity squared defined as ${I^2=\overline{u^2}/U^2}$, where $u$ and $U$ are the fluctuating and mean velocities, respectively (overbar is time averaging). The investigation is based on the mathematical abstraction that the logarithmic region in wall turbulence extends across the entire inner and outer layers. Results are matched to spatially integrated Princeton Superpipe measurements [Hultmark M, Vallikivi M, Bailey SCC and Smits AJ. Logarithmic scaling of turbulence in smooth- and rough-wall pipe flow. J. Fluid Mech. Vol. 728, 376-395 (2013)]. Scaling expressions are derived both for log-law and power-law functions of radius. A transition to asymptotic scaling is found at a friction Reynolds number $Re_{\tau} \sim 11000$.