A scaling improved inner-outer decomposition of near-wall turbulent motions

TL;DR

This paper improves the inner-outer decomposition of near-wall turbulent motions in channel flows, demonstrating Reynolds-number invariance of small scales at high Reynolds numbers and proposing a mechanism for anomalous scaling behavior.

Contribution

The study introduces a scaled inner-outer model that effectively separates small and large-scale motions and reveals Reynolds-number invariance of small scales at high Reynolds numbers.

Findings

Small-scale motions are Reynolds-number invariant between Re_τ=1000 and 5200.

At lower Re, small scales cannot be scaled by viscous units and structures strengthen with Re.

A small part of the large-scale footprint can be scaled by viscous units.

Abstract

Near-wall turbulent velocities in turbulent channel flows are decomposed into small-scale and large-scale components at $y^+<100$ by improving the predictive inner-outer model of Baars et al. [Phys. Rev. Fluids 1, 054406 (2016)], where $y^+$ is the viscous-normalized wall-normal height. The small-scale one is obtained by reducing the outer reference height (a parameter in the model) from the center of the logarithmic layer to $y^+=100$, which can fully remove outer influences. On the other hand, the large-scale one represents the near-wall footprints of outer energy-containing motions. We present plenty of evidences that demonstrate that the small-scale motions are Reynolds-number invariant with the viscous scaling, at friction Reynolds numbers between 1000 and 5200. At lower Reynolds numbers from 180 to 600, the small scales can not be scaled by the viscous units, and the vortical structures are progressively strengthened as Reynolds number increases, which is proposed as a possible mechanism responsible for the anomalous scaling behavior. Finally, it is found that a small-scale part of the outer large-scale footprint can be well scaled by the viscous units.