Are Defect Profile Similarity Criteria Different Than Velocity Profile Similarity Criteria for the Turbulent Boundary Layer?

TL;DR

This paper investigates whether defect profile and velocity profile similarity criteria in turbulent boundary layers are theoretically different, concluding they are identical and that the velocity profile is preferable for experimental analysis.

Contribution

It provides a theoretical derivation showing that defect and velocity profile similarity criteria are identical, clarifying their relationship in turbulent boundary layer analysis.

Findings

Similarity criteria for defect and velocity profiles are identical.

Velocity profile is preferable for experimental investigations.

Defect profile similarity must be accompanied by velocity profile similarity.

Abstract

The use of the defect profile instead of the experimentally observed velocity profile for the search for similarity parameters has become firmly imbedded in the turbulent boundary layer literature. However, a search of the literature reveals that there are no theoretical reasons for this defect profile preference over the more traditional velocity profile. In the report herein, we use the flow governing equation approach to develop similarity criteria for the two profiles. Results show that the derived similarity criteria are identical. Together with previous work that found that defect profile similarity must be accompanied by velocity profile similarity, then ones expectations must be that either profile can be used to search for similarity in experimental datasets. The choice should therefore be dictated by which one works best for experimental investigations, which in this case is the velocity profile.