Logarithmic Behavior of Wall-Attached Structures in Wall-Bounded Turbulent Flows

Abstract

We summarize the results of our recent work that show the logarithmic region of the streamwise turbulent intensity in wall-bounded turbulent flows. We extract the three-dimensional structures of the intense streamwise velocity fluctuations in the instantaneous flow field obtained from direct numerical simulation data of turbulent boundary layer at \(Re_\tau \approx 1000\). The identified structures are physically attached to the wall, and their height (\(l_y\)) spans from the buffer layer to the boundary layer thickness. Their length and width scale with \(l_y\) and the population density function of the tall attached structures (\(290< l_y^+ < 550\)) is inversely proportional to \(l_y\), reflecting Townsend’s attached-eddy hypothesis. We conditionally average the streamwise turbulent intensity associated with the tall attached structures and show the existence of the logarithmic region. This logarithmic behavior is further verified by examining the diagnostic function.