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 (and). Employing the Karhunen-Loève decomposition and a novel approach based on the Voronoi diagram, we identify and classify statistically coherent structures based on their location, dimensions and. With increasing, 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, the attached eddies scale linearly with the wall-normal distance with a slope of approximately, while the detached eddies remain constant at the size of, 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.