Irreversibility-inversions in 2 dimensional turbulence

TL;DR

This paper investigates how the irreversibility of inertial particle dispersion in 2D turbulence inverts at a certain Stokes number, supported by theoretical predictions and numerical simulations, revealing complex energy flux behaviors.

Contribution

It provides a quantitative prediction of the inversion of dispersion irreversibility in 2D turbulence based on particle inertia, extending previous qualitative insights.

Findings

Irreversibility inversion occurs at a critical Stokes number.

Numerical simulations confirm the theoretical predictions.

Inertial particles can exhibit a net downscale energy flux in inverse energy cascade flows.

Abstract

In this paper we consider a recent theoretical prediction (Bragg \emph{et al.}, Phys. Fluids \textbf{28}, 013305 (2016)) that for inertial particles in 2D turbulence, the nature of the irreversibility of the particle-pair dispersion inverts when the particle inertia exceeds a certain value. In particular, when the particle Stokes number, ${\rm St}$, is below a certain value, the forward-in-time (FIT) dispersion should be faster than the backward-in-time (BIT) dispersion, but for ${\rm St}$ above this value, this should invert so that BIT becomes faster than FIT dispersion. This non-trivial behavior arises because of the competition between two physically distinct irreversibility mechanisms that operate in different regimes of ${\rm St}$. In 3D turbulence, both mechanisms act to produce faster BIT than FIT dispersion, but in 2D turbulence, the two mechanisms have opposite effects because of the flux of energy from the small to the large scales. We supplement the qualitative argument given by Bragg \emph{et al.} (Phys. Fluids \textbf{28}, 013305 (2016)) by deriving quantitative predictions of this effect in the short time limit. We confirm the theoretical predictions using results of inertial particle dispersion in a direct numerical simulation of 2D turbulence. A more general finding of this analysis is that in turbulent flows with an inverse energy flux, inertial particles may yet exhibit a net downscale flux of kinetic energy because of their non-local in-time dynamics.