Equilibrium and nonequilibrium properties of Euler turbulence

TL;DR

This paper investigates the equilibrium and nonequilibrium behaviors of 2D and 3D Euler turbulence through simulations, confirming theoretical predictions and revealing persistent order in certain conditions.

Contribution

It provides direct simulation-based verification of equilibrium turbulence theory and explores the nonequilibrium evolution of 2D Euler turbulence with ordered initial conditions.

Findings

Equilibrium spectra match Maxwell-Boltzmann distribution

2D Euler turbulence remains out of equilibrium with ordered initial conditions

Hydrodynamic entropy decreases over time in 2D turbulence

Abstract

In this article, we report the equilibrium and nonequilibrium features of two-dimensional (2D) and three-dimensional (3D) Euler turbulence. To obtain a full range of equilibrium spectra, we perform pseudo-spectral simulations of Euler turbulence using $\delta$-correlated velocity field as an initial condition. These simulations provide zero energy flux and Maxwell-Boltzmann distribution for the velocity field, thus providing direct verification of the absolute equilibrium theory of turbulence. However, for ordered initial condition, 2D Euler turbulence remains out of equilibrium, with flow getting more ordered with time. We show that the hydrodynamic entropy of 2D Euler turbulence decreases with time, even though the system is isolated.