Generalized Scaling of the Turbulence Structure in Wall-Bounded Flows

TL;DR

This paper proposes a universal scaling framework for turbulence structures in wall-bounded flows, revealing self-similarity in derivatives of Reynolds stresses and a universal velocity profile applicable across various flow conditions.

Contribution

It introduces a new self-similar scaling in gradient space and a universal integral scaling for mean velocity profiles, extending understanding of turbulence universality.

Findings

Universal scaling in gradient space for Reynolds stresses

Self-similarity across boundary layers

Universal velocity profile applicable to compressible flows

Abstract

Scaling of the Reynolds stresses has been sought by many researchers, since it provides a template of universal dynamical patterns across a range of Reynolds numbers. Various statistical and normalization schemes have been attempted, but without complete or convincing similarity properties. Our prior work on the transport processes in wall-bounded flows point toward self-similarity in the gradient space, where the first and second derivatives of the Reynolds stress components exhibit universal scaling across the entire boundary layer. This scaling is extendable to compressible flows. Finally, a universal, integral scaling for the mean velocity profiles is discovered and presented.