Self-Similar Intermediate Structures in Turbulent Boundary Layers At Large Reynolds Numbers

TL;DR

This study shows that a Reynolds-number–dependent scaling law for the mean velocity distribution in the self-similar intermediate region adjacent to the viscous sublayer accurately describes zero-pressure-gradient boundary-layer flows at large $Re$, once an appropriate length scale $oxed{ ext{Lambda}}$ is defined so that $ ext{Re} = U oxed{ ext{Lambda}}/ u$. The authors demonstrate the existence of a second self-similar region under weak external turbulence and reveal how free-stream turbulence and wall roughness shift or diminish this structure. By replotting data from numerous experiments in transformed coordinates, they establish a universal collapse onto a bisectrix, confirming the scaling law’s robustness and supporting the framework of incomplete similarity and vanishing-viscosity asymptotics for wall-bounded turbulence. The findings imply broader applicability to other turbulent shear flows and offer a sensitive diagnostic for wall-roughness effects in experimental data.

Abstract

Processing the data from a large variety of zero-pressure-gradient boundary layer flows shows that the Reynolds-number-dependent scaling law, which the present authors obtained earlier for pipes, gives an accurate description of the velocity distribution in a self-similar intermediate region of distances from the wall adjacent to the viscous sublayer. The appropriate length scale that enters the definition of the boundary layer Reynolds number is found for all the flows under investigation. Another intermediate self-similar region between the free stream and the first intermediate region is found under conditions of weak free stream turbulence. The effects of turbulence in the free stream and of wall roughness are assessed, and conclusions are drawn.