Irreversibility of the two-dimensional enstrophy cascade

TL;DR

This paper investigates the time irreversibility of the two-dimensional enstrophy cascade using numerical simulations, revealing that irreversibility increases with Reynolds number and is influenced by forcing statistics.

Contribution

It introduces the metenstrophy as a new measure for analyzing time irreversibility in 2D turbulence and compares its behavior to 3D turbulence, highlighting the role of forcing.

Findings

Irreversibility increases with Reynolds number.

Forcing statistics significantly affect irreversibility.

Distinct enstrophy budget contributions differ from 3D turbulence.

Abstract

We study the time irreversibility of the direct cascade in two-dimensional turbulence by looking at the time derivative of the square vorticity along Lagrangian trajectories, a quantity which we call metenstrophy. By means of extensive numerical simulations we measure the time irreversibility from the asymmetry of the PDF of the metenstrophy and we find that it increases with the Reynolds number of the cascade, similarly to what found in three-dimensional turbulence. A detailed analysis of the different contributions to the enstrophy budget reveals a remarkable difference with respect to what observed for the direct cascade, in particular the role of the statistics of the forcing to determine the degree of irreversibility.