Modal decomposition of high-Reynolds-number pipe flow

Large-scale coherent structures in incompressible turbulent pipe flow are studied for a wide range of Reynolds numbers (Reτ rangin from 180 to 10000), based on the recent data from high-order direct numerical simulations. Employing three-dimensional proper orthogonal decomposition (POD) and a novel weighting approach based on the Voronoi diagram, we identify and classify statistically coherent structures based on their location, dimensions, and Reynolds number. With increasing Reτ, two distinct classes of structures become most energetic, associated to wall-attached and detached eddies. We will discuss in detail the procedure of extraction of the modes, and the weighting based on energy, and the interaction between modes. The described two classes of structures are described in terms of their spatial characteristics, including radial size, helix angle, and azimuthal self-similarity. Eventually, the spatial distribution may 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), as it becomes clear that channel flows will have very different structures in the channel centre, as the geometrical confinement is very different. In addition, we will also discuss a new data set for pipe flow, obtained at the comparably high Ret of 10000, and make initial steps towards modal decomposition.