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

TL;DR

This paper investigates the time irreversibility and multifractal nature of power fluctuations along single particle trajectories in turbulence, linking theoretical models with numerical and empirical data to understand non-equilibrium energy cascades.

Contribution

It provides a multifractal model-based explanation for Lagrangian power statistics and tests these predictions against data at high Reynolds numbers, revealing insights into turbulence irreversibility.

Findings

Multifractal predictions match empirical data for turbulence power statistics.

Good agreement between models and data for quantities insensitive to asymmetry.

Deviations observed in asymmetry-sensitive quantities at high Reynolds numbers.

Abstract

The irreversible turbulent energy cascade epitomizes strongly non-equilibrium 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. U.S.A. 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.