The Prevalence of Similarity of the Turbulent Wall-bounded Velocity Profile

TL;DR

This paper critically examines the claimed universality of scaled turbulent velocity profiles in wall-bounded flows, revealing that previous evidence for similarity is flawed due to a fundamental scaling problem, challenging established paradigms.

Contribution

It identifies a flaw in the previous methodology for demonstrating velocity profile similarity, questioning the widespread assumption of similarity in turbulent boundary layers.

Findings

The similarity of turbulent velocity profiles is less prevalent than previously claimed.

A fundamental flaw exists in the scaling approach used in earlier studies.

The results challenge the accepted paradigm of boundary layer scaling.

Abstract

Castillo and George (Castillo, L. and George, W., AIAA J. 39, 41(2001)) developed a flow governing equation approach for describing the turbulent outer boundary layer region. The approach was used to develop similarity criteria for the mean velocity and Reynolds shear stress profiles. Using the criteria as a guide, Castillo, George, and coworkers examined an extensive set of experimental datasets and claim that most of these turbulent velocity boundary layers appear to be similar boundary layers when scaled with the Zagarola and Smits (Zagarola, M. and Smits, A., J. Fluid Mech. 373, 33(1998)) velocity parameter. In the work herein it is shown that their success at showing scaled profile similarity in many of those datasets is flawed due to a similarity problem that occurs when one combines the defect profile and the Zagarola and Smits type of velocity scaling parameter. The same problem has been identified in other papers in the literature and may in fact be widespread. We conclude that similarity of the turbulent velocity profile is not as prevalent as was claimed by Castillo, George, and coworkers. The result has implications as to the accepted paradigm of the scaling of the turbulent boundary layer.