Lagrangian view of time irreversibility of fluid turbulence

TL;DR

This paper explores how Lagrangian fluid particle data can reveal the time irreversibility of turbulence, linking energy flux across scales to observable statistical signatures in experiments and simulations.

Contribution

It introduces new insights into detecting flow irreversibility from Lagrangian data, especially through the energy change of particles over time.

Findings

Relative motion between particles reveals energy flux and irreversibility.

Single-particle velocity structure functions do not detect time asymmetry.

Kinetic energy change along particle trajectories is sensitive to flow irreversibility.

Abstract

A turbulent flow is maintained by an external supply of kinetic energy, which is eventually dissipated into heat at steep velocity gradients. The scale at which energy is supplied greatly differs from the scale at which energy is dissipated, the more so as the turbulent intensity (the Reynolds number) is larger. The resulting energy flux over the range of scales, intermediate between energy injection and dissipation, acts as a source of time irreversibility. As it is now possible to follow accurately fluid particles in a turbulent flow field, both from laboratory experiments and from numerical simulations, a natural question arises: how do we detect time irreversibility from these Lagrangian data? Here we discuss recent results concerning this problem. For Lagrangian statistics involving more than one fluid particle, the distance between fluid particles introduces an intrinsic length scale into the problem. The evolution of quantities dependent on the relative motion between these fluid particles, including the kinetic energy in the relative motion, or the configuration of an initially isotropic structure can be related to the equal-time correlation functions of the velocity field, and is therefore sensitive to the energy flux through scales, hence to the irreversibility of the flow. In contrast, for single-particle Lagrangian statistics, the most often studied velocity structure functions cannot distinguish the "arrow of time." Recent observations from experimental and numerical simulation data, however, show that the change of kinetic energy following the particle motion, is sensitive to time-reversal. We end the survey with a brief discussion of the implication of this line of work.