Does the Outer Region of the Turbulent Boundary Layer Display Similar Behavior?

TL;DR

This study investigates whether the outer region of turbulent boundary layers exhibits similarity behavior using various scaling parameters, finding limited but notable cases of 'similar-like' behavior aligned with theoretical predictions.

Contribution

The paper introduces an integral area method combined with traditional analysis to identify similarity in turbulent boundary layer velocity profiles, highlighting the effectiveness of displacement thickness and boundary velocity as scaling parameters.

Findings

No strict similarity observed in the datasets.

Ten datasets show 'similar-like' behavior based on the inner/outer thickness ratio.

Displacement thickness and boundary velocity are the preferred scaling parameters for similar-like cases.

Abstract

Recent theoretical results together with established theory have identified the displacement thickness and the velocity at the boundary layer edge as similarity scaling parameter candidates for the wall-bounded turbulent boundary layer. In the work described herein, we examine these scaling parameters along with the Prandtl Plus scaling's and the Zagarola and Smits scaling's to search for similarity in the outer region of experimental turbulent boundary layer velocity profile datasets. A new integral area method combined with the traditional chi-by-eye method is used to search for similar velocity profiles. The results indicate that strict whole profile similarity is not evident in any of the datasets we searched. However, ten datasets are found that display "similar-like" behavior using the ratio of the inner to outer thickness ratio as a search criterion. In alignment with theory, the preferred similarity scaling parameters for the similar-like behavior case are the displacement thickness and the velocity at the boundary layer edge. It was found that there are a few datasets for which the Prandtl Plus scaling and the Zagarola and Smits scaling also work.