An isolated logarithmic layer

TL;DR

This study introduces a numerical experiment that isolates the logarithmic layer in turbulent flows, demonstrating its autonomous dynamics and challenging the necessity of large-scale motions for its behavior.

Contribution

The paper presents a novel method to isolate the logarithmic layer, showing it maintains its dynamics independently of buffer and outer zones in wall-bounded turbulence.

Findings

Logarithmic layer dynamics are largely autonomous.

Large-scale motions are not essential for the logarithmic layer.

The mean velocity gradient is determined by the tallest eddies.

Abstract

To isolate the multiscale dynamics of the logarithmic layer of wall-bounded turbulent flows, a novel numerical experiment is conducted in which the mean tangential Reynolds stress is eliminated except in a subregion corresponding to the typical location of the logarithmic layer in channels. Various statistical comparisons against channel flow databases show that, despite some differences, this modified flow system reproduces the kinematics and dynamics of natural logarithmic layers well, even in the absence of a buffer and an outer zone. This supports the previous idea that the logarithmic layer has its own autonomous dynamics. In particular, the results suggest that the mean velocity gradient and the wall-parallel scale of the largest eddies are determined by the height of the tallest momentum-transferring motions, implying that the very large-scale motions of wall-bounded flows are not an intrinsic part of logarithmic-layer dynamics. Using a similar set-up, an isolated layer with a constant total stress, representing the logarithmic layer without a driving force, is simulated and examined.