{
  "id": "2105.13200",
  "version": "v1",
  "published": "2021-05-27T14:49:36.000Z",
  "updated": "2021-05-27T14:49:36.000Z",
  "title": "Self-similar mechanisms in wall turbulence, through the lens of resolvent analysis",
  "authors": [
    "U. Karban",
    "E. Martini",
    "A. V. G. Cavalieri",
    "L. Lesshafft",
    "P. Jordan"
  ],
  "comment": "31 pages, 20 figures, submitted to Journal of Fluid Mechanics",
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "Self-similarity of coherent structures in turbulent channels is explored by means of resolvent analysis. In this modelling framework, coherent structures are understood to arise as a response of the linearised mean-flow operator to generalised, frequency-dependent Reynolds stresses, considered to act as an external forcing. We assess the self-similarity of both the flow structures and the associated forcing. The former are educed from direct numerical simulation data using Spectral Proper Orthogonal Decomposition, whereas the latter are identified using a frequency space version of Extended Proper Orthogonal Decomposition (Bor\\'{e}e, J. 2003 Extended proper orthogonal decomposition: a tool to analyse correlated events in turbulent flows. Experiments in fluids 35 (2), 188-192). The forcing structures identified are compared to those obtained using the resolvent-based estimation introduced by Towne et al. (2020) (Towne, A., Lozano-Dur\\'{a}n, A. & Yang, X. 2020 Resolvent-based estimation of space-time flow statistics. Journal of Fluid Mechanics 883, A17). The analysis reveals self-similarity of both coherent structures$-$supporting Townsend's notion of attached eddies$-$and the underlying forcing, and it is observed for simulations in which $Re_\\tau$ varies from 180 to 1000, indicating self-similar dynamics over a broad range of turbulent scales.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-27T14:49:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "resolvent analysis",
      "wall turbulence",
      "self-similar mechanisms",
      "extended proper orthogonal decomposition",
      "coherent structures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}