Streamwise inclination angle of wall-attached eddies in turbulent channel flows

TL;DR

This study introduces a new method to measure the streamwise inclination angles of wall-attached eddies in turbulent channel flows, revealing their Reynolds-number dependence and saturation at 45 degrees, thus refining the attached-eddy model.

Contribution

A novel methodology combining spectral stochastic estimation and the attached-eddy hypothesis to accurately assess eddy inclination angles across Reynolds numbers.

Findings

SIAs are Reynolds-number dependent at low and medium Re

SIAs tend to saturate at 45 degrees at high Re

Previous mean SIA values are due to multi-scale eddy effects

Abstract

We develop a new methodology to assess the streamwise inclination angles (SIAs) of the wall-attached eddies populating the logarithmic region with a given wall-normal height. To remove the influences originating from other scales on the SIA estimated via two-point correlation, the footprints of the targeted eddies in the vicinity of the wall and the corresponding streamwise velocity fluctuations carried by them are isolated simultaneously, by coupling the spectral stochastic estimation with the attached-eddy hypothesis. Datasets produced with direct numerical simulations spanning $Re_{\tau} \sim O(10^2)-O(10^3)$ are dissected to study the Reynolds-number effect. The present results show, for the first time, that the SIAs of attached eddies are Reynolds-number dependent in low and medium Reynolds numbers and tend to saturate at $45^{\circ}$ as the Reynolds number increases. The mean SIA reported by vast previous experimental studies are demonstrated to be the outcomes of the additive effect contributed by multi-scale attached eddies. These findings clarify the long-term debate and perfect the picture of the attached-eddy model.