Scaling of Wall Turbulence at Finite Reynolds Number

TL;DR

This paper introduces new scaling relations for wall turbulence at finite Reynolds numbers using matched asymptotic expansions, highlighting the significance of the parameter Lambda+ in determining the velocity profile behavior.

Contribution

It proposes a novel scaling parameter Lambda+ and derives a power law for mean velocity, advancing understanding of turbulence behavior near walls.

Findings

Lambda+ is a key parameter for wall turbulence.

Power law for mean velocity derived from new scaling.

Similarity of Lambda+ influences velocity law form.

Abstract

New scaling relations for the mean velocity and Reynolds shear stress in viscous sublayer were proposed based on the application of matched asymptotic expansion method to the mean momentum balance. It was shown that the new parameter $\Lambda_+$ is relevant for the wall turbulence in addition to the friction velocity. From the proposed new scaling of the viscous sublayer the power law for the mean velocity in the overlap region was derived. The complete or incomplete similarity of the parameter $\Lambda_+$ was shown to be the key factor, which determines whether the mean velocity obeys the power law or log law in the overlap layer.