Hydrodynamic Entropy and Emergence of Order in Two-dimensional Euler Turbulence

TL;DR

This paper investigates how two-dimensional Euler turbulence develops large-scale structures and introduces hydrodynamic entropy to quantify order, revealing decreasing entropy over time despite the system's isolation.

Contribution

It introduces the concept of hydrodynamic entropy and demonstrates its decrease over time in 2D Euler turbulence, challenging traditional equilibrium predictions.

Findings

Large-scale flow structures emerge due to energy transfer among small wavenumber modes.

Hydrodynamic entropy decreases over time in isolated 2D Euler turbulence.

Asymptotic states depend on initial conditions and differ from Onsager and Kraichnan predictions.

Abstract

Using numerical simulations, we show that the asymptotic states of two-dimensional (2D) Euler turbulence exhibit large-scale flow structures due to nonzero energy transfers among small wavenumber modes. These asymptotic states, which depend on the initial conditions, are out of equilibrium, and they are different from the predictions of Onsager and Kraichnan. We propose ``hydrodynamic entropy'' to quantify order in 2D Euler turbulence; we show that this entropy decreases with time, even though the system is isolated with no dissipation and no contact with a heat bath.