Local energy flux of turbulent flows

Alexandros Alexakis and Sergio Chibbaro
Phys. Rev. Fluids 5, 094604 – Published 18 September 2020

Abstract

We investigate the local energy flux rate Π(x) towards small scales in isotropic turbulent flows using direct numerical simulations and applying different low-pass filters. Two different filters are examined: A sharp Fourier filter and a Gaussian filter. The probability density function (PDF) of the local energy flux is calculated for the different filters and for different filtering scales. It is shown that the local energy flux is a largely fluctuating quantity taking both negative and positive values and this is more pronounced for the sharp filter. The variance, skewness, and kurtosis of these fluctuations are shown to increase as the filtering scale is decreased. Furthermore, we calculate the joint PDF of Π(x) with the local filtered strain rate S and the enstrophy Ω. The flux shows a good correlation with the strain, but not with the enstrophy. It is shown that its conditional mean value scales like ΠS2S3 in support of the Smagorinsky eddy viscosity model. Nonetheless, strong fluctuations exist around this value that also need to be modeled. We discuss the implications of our results for subgrid scale models and propose new modeling directions.

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  • Received 4 May 2020
  • Accepted 27 August 2020

DOI:https://doi.org/10.1103/PhysRevFluids.5.094604

©2020 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Fluid DynamicsNonlinear Dynamics

Authors & Affiliations

Alexandros Alexakis*

  • Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France

Sergio Chibbaro

  • Sorbonne Université, CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France

  • *alexakis@phys.ens.fr
  • sergio.chibbaro@upmc.fr

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Issue

Vol. 5, Iss. 9 — September 2020

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