Attached structures in wall-bounded turbulent flows

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. The present thesis demonstrates the logarithmic region of the turbulence intensity by identifying wall-attached structures of velocity fluctuations through direct numerical simulation of a moderate-Reynolds-number boundary layer. The wall-attached structures are self-similar with respect to their heights ($l_y$), and in particular the population density of the streamwise component scales inversely with $l_y$, which is reminiscent of the hierarchy of attached eddies. The turbulent intensities contained within the wall-parallel components (u and w) exhibit the logarithmic behavior. The tall attached structures ($l_y^+ > 100$) of u are composed of multiple uniform momentum zones (UMZs) with a long streamwise extent, whereas those of the cross-stream components (v and w) are relatively short with a comparable width, suggesting the presence of tall vortical structures associated with multiple UMZs. The magnitudes of the near-wall peak observed in the streamwise turbulent intensity increase with increasing ly, reflecting nested hierarchies of the attached u structures. These findings suggest that the identified structures are prime candidates for Townsend’s attached-eddy hypothesis and serve as cornerstones for understanding the multiscale phenomena of high-Reynolds-number boundary layers.