Attached flow structure and streamwise energy spectra in a turbulent boundary layer

S. Srinath, J. C. Vassilicos, C. Cuvier, J.-P. Laval, M. Stanislas, and J.-M. Foucaut
Phys. Rev. E 97, 053103 – Published 14 May 2018

Abstract

On the basis of (i) particle image velocimetry data of a turbulent boundary layer with large field of view and good spatial resolution and (ii) a mathematical relation between the energy spectrum and specifically modeled flow structures, we show that the scalings of the streamwise energy spectrum E11(kx) in a wave-number range directly affected by the wall are determined by wall-attached eddies but are not given by the Townsend-Perry attached eddy model's prediction of these spectra, at least at the Reynolds numbers Reτ considered here which are between 103 and 104. Instead, we find E11(kx)kx1p where p varies smoothly with distance to the wall from negative values in the buffer layer to positive values in the inertial layer. The exponent p characterizes the turbulence levels inside wall-attached streaky structures conditional on the length of these structures. A particular consequence is that the skin friction velocity is not sufficient to scale E11(kx) for wave numbers directly affected by the wall.

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  • Received 13 November 2017

DOI:https://doi.org/10.1103/PhysRevE.97.053103

©2018 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

S. Srinath1, J. C. Vassilicos1,2, C. Cuvier1, J.-P. Laval1, M. Stanislas1, and J.-M. Foucaut1

  • 1CNRS, ONERA, Centrale Lille, Univ. Lille, Arts et Metiers ParisTech, FRE2017, Laboratoire de Mécanique des Fluides de Lille–Kampé de Fériet (LMFL), 59000 Lille, France
  • 2Department of Aeronautics, Imperial College London, London SW7 2AZ, United Kingdom

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Issue

Vol. 97, Iss. 5 — May 2018

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