Defining the mean turbulent boundary layer thickness based on streamwise velocity skewness

TL;DR

This paper introduces a novel, threshold-independent method for defining the mean turbulent boundary layer thickness based on streamwise velocity skewness sign change, applicable across various experimental and numerical datasets.

Contribution

It proposes a new statistical definition of boundary layer thickness based on velocity skewness, validated through extensive experiments, simulations, and modeling, and offers practical estimation methods.

Findings

The new definition aligns with traditional thickness measures.

It is robust across different boundary layer conditions.

Two estimation methods are effective in diverse datasets.

Abstract

A new statistical definition for the mean turbulent boundary layer thickness is introduced, based on identification of the point where the streamwise velocity skewness changes sign, from negative to positive, in the outermost region of the boundary layer. Importantly, this definition is independent of arbitrary thresholds, and broadly applicable, including to past single-point measurements. Further, this definition is motivated by the phenomenology of streamwise velocity fluctuations near the turbulent/non-turbulent interface, whose local characteristics are shown to be universal for turbulent boundary layers under low freestream turbulence conditions (i.e., with or without pressure gradients, surface roughness, etc.) through large-scale experiments, simulations and coherent structure-based modelling. The new approach yields a turbulent boundary layer thickness that is consistent with previous definitions, such as those based on Reynolds shear stress or `composite' mean velocity profiles, and which can be used practically e.g., to calculate integral thicknesses. Two methods are proposed for estimating the turbulent boundary layer thickness using this definition: one based on simple linear interpolation and the other on fitting a generalised Fourier model to the outer skewness profile. The robustness and limitations of these methods are demonstrated through analysis of several published experimental and numerical datasets, which cover a range of canonical and non-canonical turbulent boundary layers. These datasets also vary in key characteristics such as wall-normal resolution and measurement noise, particularly in the critical turbulent/non-turbulent interface region.