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Irreversibility inversions in two-dimensional turbulence

Andrew D. Bragg*

Filippo De Lillo and Guido Boffetta

  • Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina 27708, USA

  • Department of Physics and INFN, University of Torino, Via Pietro Giuria 1, 10125 Torino, Italy

  • *andrew.bragg@duke.edu
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Phys. Rev. Fluids 3, 024302 – Published 12 February, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.024302

Abstract

In this paper, we consider a recent theoretical prediction [Bragg et al., Phys. Fluids 28, 013305 (2016)] that for inertial particles in two-dimensional (2D) turbulence, the nature of the irreversibility of the particle-pair dispersion inverts when the particle inertia exceeds a certain value. In particular, when the particle Stokes number, St, is below a certain value, the forward-in-time (FIT) dispersion should be faster than the backward-in-time (BIT) dispersion, but for St above this value, this should invert so that BIT becomes faster than FIT dispersion. This nontrivial behavior arises because of the competition between two physically distinct irreversibility mechanisms that operate in different regimes of St. In three-dimensional (3D) turbulence, both mechanisms act to produce faster BIT than FIT dispersion, but in 2D turbulence, the two mechanisms have opposite effects because of the flux of energy from the small to the large scales. We supplement the qualitative argument given by Bragg et al. [Phys. Fluids 28, 013305 (2016)] by deriving quantitative predictions of this effect in the short time limit. We confirm the theoretical predictions using results of inertial particle dispersion in a direct numerical simulation of 2D turbulence. A more general finding of this analysis is that in turbulent flows with an inverse energy flux, inertial particles may yet exhibit a net downscale flux of kinetic energy because of their nonlocal-in-time dynamics.

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Phys. Rev. Fluids 3, 024302– Published 12 February, 2018
  • Received 26 September 2017
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