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Analysis of the dissipative range of the energy spectrum in grid turbulence and in direct numerical simulations

Anastasiia Gorbunova1,2, Guillaume Balarac2,4, Mickaël Bourgoin3, Léonie Canet1,4, Nicolas Mordant2, and Vincent Rossetto1

  • 1Université Grenoble Alpes, Centre National de la Recherche Scientifique, LPMMC, 38000 Grenoble, France
  • 2Université Grenoble Alpes, Centre National de la Recherche Scientifique, LEGI, 38000 Grenoble, France
  • 3ENS Lyon and Centre National de la Recherche Scientifique, Physics Department, 69000 Lyon, France
  • 4Institut Universitaire de France, 1 rue Descartes, 75231 Paris, France

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Phys. Rev. Fluids 5, 044604 – Published 29 April, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.044604

Abstract

We present a statistical analysis of the behavior of the kinetic-energy spectrum in the dissipative range of fully developed three-dimensional turbulence, with the aim of testing a recent prediction obtained from the nonperturbative renormalization group. Analyzing spectra recorded in experiments of grid turbulence, generated in the Modane wind tunnel, and spectra obtained from high-resolution direct numerical simulations (DNSs) of the forced Navier-Stokes equation, we observe that the spectra decay as a stretched exponential in the dissipative range. The theory predicts a stretching exponent α=2/3, and the data analyses of the numerical and experimental spectra are in close agreement with this value. This result also corroborates previous DNS studies which found that the spectrum in the near-dissipative range is best modeled by a stretched exponential with α<1.

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Phys. Rev. Fluids 5, 044604– Published 29 April, 2020
  • Received 6 September 2019
  • Accepted 24 March 2020
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