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Scaling of turbulence intensities up to Reτ=106 with a resolvent-based quasilinear approximation

Nikolaos Skouloudis and Yongyun Hwang*

  • Department of Aeronautics, Imperial College London, SW7 2AZ, United Kingdom

  • *y.hwang@imperial.ac.uk
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Phys. Rev. Fluids 6, 034602 – Published 3 March, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.034602

Abstract

A minimal form of quasilinear approximation (QLA), recently proposed with a stochastic forcing and proper orthogonal decomposition modes [Hwang and Ekchardt, J. Fluid Mech. 894, A23 (2020)], has been extended by employing a resolvent framework. A particular effort is made to reach an extremely high Reynolds number by carefully controlling the approximation without loss of the general scaling properties in the spectra, while setting out the main limitations and accuracy of the proposed QLA with possibility of further improvement. The QLA is subsequently applied to turbulent channel flow up to Reτ=106 (Reτ is the friction Reynolds number). While confirming that the logarithmic wall-normal dependence in streamwise and spanwise turbulence intensities robustly appears, it reveals some nontrivial difference from the scaling of the classical attached eddy model based on inviscid flow assumption. First, the spanwise wave number spectra do not show any clearly visible inverse-law behavior due to the viscous wall effect prevailing in a significant portion of the lower part of the logarithmic layer. Second, the near-wall peak streamwise and spanwise turbulence intensities are found to deviate from lnReτ scaling for Reτ≳104. Importantly, the near-wall streamwise turbulence intensity is inversely proportional to 1/Ucl+ (Ucl+ is the inner-scaled channel centreline velocity), consistent with the scaling obtained from an asymptotic analysis of the Navier-Stokes equations [Monkewitz and Nagib, J. Fluid Mech. 783, 474 (2015)]. The same behavior was also observed for the streamwise turbulence intensity in the logarithmic region, as was predicted with the asymptotic analysis. Finally, the streamwise turbulence intensity in the logarithmic region is found to become greater than the near-wall one at Reτ≃O(105). It is shown that this behavior originates from the near-wall spectra associated with large-scale inactive motions, the intensity of which gradually decays as Reτ→∞.

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Outline

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Phys. Rev. Fluids 6, 034602– Published 3 March, 2021
  • Received 7 September 2020
  • Accepted 10 February 2021
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