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Perturbative model for the second-order velocity structure function tensor in turbulent shear flows

Samvit Kumar1, Charles Meneveau1, and Gregory Eyink1,2

  • 1Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
  • 2Department of Applied Mathematics, Johns Hopkins University, Baltimore, Maryland 21218, USA

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Phys. Rev. Fluids 7, 064601 – Published 14 June, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.064601

Abstract

A model for the structure function tensor is proposed, incorporating the effect of anisotropy as a linear perturbation to the standard isotropic form. The analysis extends the spectral approach of Ishihara et al. [T. Ishihara, Phys. Rev. Lett. 88, 154501 (2002)] to physical space based on Kolmogorov's theory and is valid in the inertial range of turbulence. Previous results for velocity cospectra are used to obtain estimates of the model coefficients. Structure functions measured from direct numerical simulations of channel flow and from experimental measurements in turbulent boundary layers are compared with predicted behavior and reasonable agreement is found. We note that power-law scaling is more evident in the cospectra than for the mixed structure functions. Observations are made about countergradient correlation between Fourier modes of wall-normal and streamwise velocity components for wave numbers approaching the Kolmogorov scale.

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Phys. Rev. Fluids 7, 064601– Published 14 June, 2022
  • Received 6 January 2022
  • Accepted 23 May 2022
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