Analyzing a turbulent pipe flow via the one-point structure tensors: Vorticity crawlers and streak shadows

Abstract

Efforts to identify and visualize near-wall structures typically focus on the region y+≳5, where large-scale structures with significant turbulent kinetic energy content reside, such as the high-speed and low-speed streaks associated with sweep and ejection events. While it is true that the level of the turbulent kinetic energy drops to zero as one approaches the wall, the organization of near-wall turbulence does not end at y+≈5. Large-scale structures with significant streamwise extent and spatial organization exist even in the immediate proximity of the wall y+<5. These coherent structures have received less attention so far, but it would be both useful and enlightening to bring them to focus in order, on one hand, to understand them, but also to analyze their interaction with the energetic structures that reside at somewhat higher distances from the wall. We have recently developed a rigorous mathematical and computational framework that can be used for the calculation of the turbulence structure tensors in arbitrary flow configurations. In this work, we use this new framework to compute, for the first time, the structure tensors in a fully-developed turbulent pipe flow. We perform Direct Numerical Simulation (DNS) at Reynolds number Reb=5300, based on the bulk velocity and the pipe diameter. We demonstrate the diagnostic properties of the structure tensors, by analyzing the DNS results with a focus on the near-wall structure of the turbulence. We develop a new eduction technique, based on the instantaneous values of the structure tensors, for the identification of inactive structures (i.e. large-scale structures without significant turbulent kinetic energy). This leads to the visualization of “vorticity crawlers” and “streak shadows”, large-scale structures with low energy content in the extreme vicinity of the wall. Furthermore, comparison with traditional eduction techniques (such as instantaneous iso-surfaces of turbulent kinetic energy) shows that the structure-based eduction method seamlessly captures the large-scale energetic structures further away from the wall. We then show that the one-point structure tensors reflect the morphology of the inactive structures in the extreme vicinity of the wall and that of the energy-containing large-scale structures further away from the wall. The emerging complete picture of large-scale structures helps explain the near-wall profiles of all the one-point structure tensors and is likely to have an impact in the further development of Structure-Based Models (SBMs) of turbulence. "