A Cautionary Note on the Thermal Boundary Layer Similarity Scaling for the Turbulent Boundary Layer

TL;DR

This paper critically examines the validity of a previously proposed temperature profile scaling in turbulent boundary layers, revealing that what appeared as similarity was actually false similarity when properly analyzed.

Contribution

The paper demonstrates that the previously observed similarity in defect profiles does not hold for actual temperature profiles, highlighting a potential flaw in the scaling approach.

Findings

Defect profile similarity does not translate to temperature profile similarity.

False similarity can mislead interpretations of turbulent boundary layer data.

Proper analysis reveals the limitations of the proposed scaling parameters.

Abstract

Wang and Castillo have developed empirical parameters for scaling the temperature profile of the turbulent boundary layer flowing over a heated wall in the paper X. Wang and L. Castillo, J. Turbul., 4, 1(2003). They presented experimental data plots that showed similarity type behavior when scaled with their new scaling parameters. However, what was actually plotted, and what actually showed similarity type behavior, was not the temperature profile but the defect profile formed by subtracting the temperature in the boundary layer from the temperature in the bulk flow. We show that if the same data and same scaling is replotted as just the scaled temperature profile, similarity is no longer prevalent. This failure to show both defect profile similarity and temperature profile similarity is indicative of false similarity. The nature of this false similarity problem is discussed in detail.