The persistence of viscous effects in the overlap region, and the mean velocity in turbulent pipe and channel flows

TL;DR

This paper investigates the wall-normal region near the peak of Reynolds shear stress in turbulent pipe and channel flows, revealing viscous effects' significance and challenging classical assumptions about flow structure and velocity profiles.

Contribution

It identifies the importance of viscous effects at a specific wall-normal position and questions the classical matching principle, offering new insights into flow dynamics near the peak shear stress region.

Findings

Viscous effects dominate near the peak of Reynolds shear stress at y_p^+ = O(R^{1/2})

Classical semi-logarithmic velocity profiles remain useful approximations

Power-law profiles may approximate data over extended regions but are unlikely exact

Abstract

We argue that important elements of the dynamics of wall-bounded flows reside at the wall-normal position $y_p^+$ corresponding to the peak of the Reynolds shear stress. Specializing to pipe and channel flows, we show that the mean momentum balance in the neighborhood of $y_p^+$ is distinct in character from those in the classical inner and outer layers. We revisit empirical data to confirm that $y_p^+ = O(R^{1/2})$ and show that, in a neighborhood of order $R^{1/2}$ around $y_p^+$, only the viscous effects balance pressure-gradient terms. Here, R is the Reynolds number based on friction velocity and pipe radius (or channel half-width). This observation provides a mechanism by which viscous effects play an important role in regions traditionally thought to be inviscid or inertial; in particular, it throws doubt on the validity of the classical matching principle. Even so, it is shown that the classical semi-logarithmic behavior for the mean velocity distribution can be a useful approximation. It is argued that the recently advanced power-law profiles possess a rich underlying structure, and could be good approximations to the data over an extended region (but they too are unlikely to be exact).