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Time irreversibility and multifractality of power along single particle trajectories in turbulence

Massimo Cencini1,2,*, Luca Biferale3, Guido Boffetta4, and Massimo De Pietro3

  • 1Istituto dei Sistemi Complessi, CNR, Via dei Taurini 19, 00185 Roma, Italy
  • 2INFN, Università di Roma “Tor Vergata,” Via Ricerca Scientifica 1, 00133 Roma, Italy
  • 3Dipartimento di Fisica and INFN, Università di Roma “Tor Vergata,” Via Ricerca Scientifica 1, 00133 Roma, Italy
  • 4Dipartimento di Fisica and INFN, Università di Torino, Via P. Giuria 1, 10125 Torino, Italy

  • *Corresponding author: massimo.cencini@cnr.it
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Phys. Rev. Fluids 2, 104604 – Published 27 October, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.104604

Abstract

The irreversible turbulent energy cascade epitomizes strongly nonequilibrium systems. At the level of single fluid particles, time irreversibility is revealed by the asymmetry of the rate of kinetic energy change, the Lagrangian power, whose moments display a power-law dependence on the Reynolds number, as recently shown by Xu et al. [H. Xu et al., Proc. Natl. Acad. Sci. USA 111, 7558 (2014)]. Here Lagrangian power statistics are rationalized within the multifractal model of turbulence, whose predictions are shown to agree with numerical and empirical data. Multifractal predictions are also tested, for very large Reynolds numbers, in dynamical models of the turbulent cascade, obtaining remarkably good agreement for statistical quantities insensitive to the asymmetry and, remarkably, deviations for those probing the asymmetry. These findings raise fundamental questions concerning time irreversibility in the infinite-Reynolds-number limit of the Navier-Stokes equations.

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Phys. Rev. Fluids 2, 104604– Published 27 October, 2017
  • Received 27 July 2017

©2017 American Physical Society

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