Attached eddies in wall-bounded turbulent flows: streak instability and skin-friction generation

Abstract

The goal of this study is to answer some lingering questions that pertain the nature of wall-bounded turbulent flows. Building on the ‘attached-eddy’ hypothesis first proposed by A.A. Townsend, the main aim is to better understand the mechanisms governing their behaviour. In order to do so, several numerical experiments are performed in a turbulent channel flow. First, we seek for a better description of the mechanism behind the generation of the vortical structures: a body forcing is introduced in the flow to drive an amplified streak, and this process is carried out for several different streaks, ranging from the logarithmic to the outer region. All streaks are shown to undergo a sinuous-type instability; furthermore, they trigger the appearance of cross-streamwise structures, the streamwise wavelength scale of which is observed to be proportional to the spanwise spacing of the amplified streak. Application of dynamic mode decomposition reveals that the amplified streak can be considered the seeding mechanism for these vortical structures. Furthermore, the contribution of attached eddies to skin-friction drag is studied at relatively large Reynolds numbers. It is found that the outer-layer structures are responsible for a significant amount of skin-friction, but their removal does not result in comparable savings. Conversely, the self-similar structures populating the logarithmic layer are shown to generate a substantial amount of skin friction, and their contribution appears to increase with the Reynolds number. This outcome can explain the reduction in effectiveness of many drag-reducing devices, and is potentially useful to design novel techniques for flow control.