Spectral data-driven analysis of high Reynolds-number turbulent pipe flows

Accurate computation of high-Reynolds-number wall turbulence, relevant to many technological applications, presents unresolved questions about modelling, prediction, and the underlying mechanisms of generation and interaction of coherent structures. Smooth circular pipe flow of radius R and length of 10πR is studied. The analysis is based on the comprehensive dataset comprising well-resolved DNS up to Re_τ = 5200 by Yao et al. (2023). Using Fourier-based Proper Orthogonal Decomposition (POD), we identify the spatially coherent structures and classify them according to their location, spatial extent, and lifetime as functions of the Reynolds number. At the high Reynolds numbers, we observe two distinct characteristics. Firstly, there are very large-scale motions (VLSM) which dominate the rankings of the most energetic POD modes. Our findings suggest that these structures exhibit spatial correlation over a length greater than that of the pipe itself. Secondly, the POD classification directly identifies attached eddies with their size scaling linearly from the wall, as well as detached eddies located at roughly 0.5R away from the wall. We can thus draw a comprehensive picture of the structures in pipes using POD, and track the influence of the Reynolds number.