Irreversibility and small-scale generation in 3D turbulent flows

TL;DR

This paper links the irreversibility in 3D turbulence, characterized by asymmetry in force power distribution, to small-scale vorticity amplification, supported by analytical and numerical evidence.

Contribution

It establishes a quantitative connection between power distribution asymmetry and small-scale vorticity amplification in turbulence.

Findings

Negative third moment of force power distribution observed.

Analytical and numerical evidence supports the link.

First quantitative connection between irreversibility and small-scale generation.

Abstract

In three-dimensional turbulent flows energy is supplied at large scales and cascades down to the smallest scales where viscosity dominates. The flux of energy through scales implies the generation of small scales from larger ones, which is the fundamental reason for the irreversibility of the dynamics of turbulent flows. As we showed recently, this irreversibility manifests itself by an asymmetry of the probability distribution of the instantaneous power $p$ of the forces acting on fluid elements. In particular, the third moment of $p$ was found to be negative. Yet, a physical connection between the irreversibility manifested in the distribution of $p$ and the energy flux or small-scale generation in turbulence has not been established. Here, with analytical calculations and support from numerical simulations of fully developed turbulence, we connect the asymmetry in the power distribution, {\it i.e.}, the negative value of $\langle p^3 \rangle$, to the generation of small scales, or more precisely, to the amplification (stretching) of vorticity in turbulent flows. Our result is the first step towards a quantitative understanding of the origin of the irreversibility observed at the level of individual Lagrangian trajectories in turbulent flows.