Logarithmic Behavior of Wall-Attached Structures in a Turbulent Boundary Layer

Abstract

Wall turbulence is a ubiquitous phenomenon in nature and engineering applications, yet predicting such turbulence is difficult due to its complexity. High-Reynolds-number turbulence, which includes most practical flows, is particularly complicated because of its wide range of scales. Although the attached-eddy hypothesis postulated by Townsend can be used to predict turbulence intensities and serves as a unified theory for the asymptotic behaviors of turbulence, the presence of attached structures has not been confirmed. Here, we demonstrate the logarithmic region of the turbulent intensity by identifying wall-attached structures of streamwise velocity fluctuations through direct numerical simulation of a moderate-Reynolds-number boundary layer. The wall-attached structures are self-similar and composed of multiple uniform momentum zones. The population density of the structures scales inversely with their height, which is reminiscent of the hierarchy of attached eddies. These findings suggest that the identified structures are prime candidates for Townsend’s attached-eddy hypothesis and serve as conerstones for understanding the multiscale phenomena of high-Reynolds-number boundary layers.