On the logarithmic region in wall turbulence

Abstract

Considerable discussion over the past few years has been devoted to the question of whether the logarithmic region in wall turbulence is indeed universal. Here, we analyse recent experimental data in the Reynolds number range of nominally $2\times 1{0}^{4} \lt {\mathit{Re}}_{\tau } \lt 6\times 1{0}^{5} $ for boundary layers, pipe flow and the atmospheric surface layer, and show that, within experimental uncertainty, the data support the existence of a universal logarithmic region. The results support the theory of Townsend (The Structure of Turbulent Shear Flow, Vol. 2, 1976) where, in the interior part of the inertial region, both the mean velocities and streamwise turbulence intensities follow logarithmic functions of distance from the wall.

Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers

“…The fitting procedures were carried out with κ = 0.38 for all surfaces. This value is close to the value of κ suggested by Marusic et al (2013), for high Reynolds number smooth-wall boundary layers, where κ = 0.39±0.02. A different choice of κ alters the numerical values of y 0 and d but not the trends shown in the following sections.…”

Statistical evidence of anasymptotic geometric structure to the momentum transporting motions in turbulent boundary layers

“…In the context of the mean momentum equation, this is the origin of distance-from-thewall scaling that underlies a logarithmic mean velocity profile, and recent empirical studies at high Reynolds number support the onset of logarithmic dependence on the inertial domain as specified by the present theory (e.g. [5,16]). …”

“…[3,4]), has met with considerable success in the recent past (e.g. [5]). Along a slightly different line of enquiry, tools from flow instability have been used to understand the recurring motions in turbulent flows, the most notable being the physical mechanism of the self-sustaining near-wall cycle (e.g.…”

A Cautionary Note on the Use of Monin–Obukhov Similarity Theory in Very High-Resolution Large-Eddy Simulations

“…Recently, Marusic et al (2013) analyzed surface-layer data from both laboratory experiments and field measurements from the SLTEST site over Utah's western desert. They proposed a conservative limit of z * as a function of the friction Reynolds number (Re τ ),…”

“…For the SLTEST data, Marusic et al (2013) reported: u * = 0.188 m s −1 , ν = 1.8 ×10 −5 m 2 s −1 , and Re τ = 6.3×10 5 . Using Eq.…”