Lagrangian Irreversibility and Eulerian Dissipation in Fully-Developed Turbulence

TL;DR

This paper investigates the relationship between Lagrangian irreversibility and Eulerian dissipation in turbulence, revealing that intense dissipation zones are dominated by energy gains, with irreversibility persisting even in non-intermittent flows.

Contribution

It demonstrates the connection between extreme Eulerian dissipation events and Lagrangian power fluctuations, introducing a pressure-gradient driven take-off mechanism in turbulence.

Findings

Particle trajectories in intense dissipation zones show dominant energy gains.

Lagrangian irreversibility persists even in non-intermittent flows.

Dissipation rate fluctuations follow exponential tail distributions.

Abstract

We revisit the issue of Lagrangian irreversibility in the context of recent results [Xu, et al., PNAS, 111, 7558 (2014)] on flight-crash events in turbulent flows and show how extreme events in the Eulerian dissipation statistics are related to the statistics of power-fluctuations for tracer trajectories. Surprisingly, we find that particle trajectories in intense dissipation zones are dominated by energy gains sharper than energy losses, contrary to flight-crashes, through a pressure-gradient driven take-off phenomenon. Our conclusions are rationalised by analysing data from simulations of three-dimensional intermittent turbulence, as well as from non-intermittent decimated flows. Lagrangian irreversibility is found to persist even in the latter case, wherein fluctuations of the dissipation rate are shown to be relatively mild and to follow probability distribution functions with exponential tails.