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Reynolds and Prandtl number scaling of viscous heating in isotropic turbulence

Andrey Pushkarev1, Guillaume Balarac1, and Wouter J. T. Bos2

  • 1LEGI, CNRS, Grenoble INP, 38000 Grenoble, France
  • 2LMFA, CNRS, Ecole Centrale de Lyon, Université de Lyon, 69134 Ecully, France

Phys. Rev. Fluids 2, 084606 – Published 21 August, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.084606

Abstract

Viscous heating is investigated using high-resolution direct numerical simulations. Scaling relations are derived and verified for different values of the Reynolds and Prandtl numbers. The scaling of the heat fluctuations is shown to depend on Lagrangian correlation times and on the scaling of dissipation-rate fluctuations. The convergence of the temperature spectrum to asymptotic scaling is observed to be slow, due to the broadband character of the temperature production spectrum and the slow convergence of the dissipation-rate spectrum to its asymptotic form.

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