Energy-based characterisation of large-scale coherent structures in turbulent pipe flows

Large-scale coherent structures in incompressible turbulent pipe flow are studied for a wide range of Reynolds numbers (Re-tau = 180, 550, 1000, 2000 and 5200). Employing the Karhunen-Loeve decomposition and a novel approach based on the Voronoi diagram, we identify and classify statistically coherent structures based on their location, dimensions and Re-tau. With increasing Re-tau, two distinct classes of structures become more energetic, namely wall-attached and detached eddies. The Voronoi methodology is shown to delineate these two classes without the need for specific criteria or thresholds. At the highest Re-tau, the attached eddies scale linearly with the wall-normal distance with a slope of approximately l(y) similar to 1.2y/R, while the detached eddies remain constant at the size of l(y) approximate to 0.26R, with a progressive shift towards the pipe centre. We extract these two classes of structures and describe their spatial characteristics, including radial size, helix angle and azimuthal self-similarity. The spatial distribution could help explain the differences in mean velocity between pipe and channel flows, as well as in modelling large and very-large-scale motions (LSM and VLSM). In addition, a comprehensive description is provided for both wall-attached and detached structures in terms of LSM and VLSM.