Local power fluctuations in two-dimensional turbulence

TL;DR

This paper investigates power fluctuations in two-dimensional turbulence, revealing non-Gaussian statistics, asymmetric exponential tails, and an empirical fluctuation relation, with implications for understanding entropy production.

Contribution

It provides a detailed statistical analysis of power fluctuations in 2D turbulence, including modeling the distribution and deriving entropy production from empirical data.

Findings

Power PDF exhibits asymmetric exponential tails.

Distribution modeled by product of correlated normal variables.

Empirical fluctuation relation observed and entropy rate matches measurements.

Abstract

The statistics of power fluctuations are studied in simulations of two-dimensional turbulence in both inverse (energy) and direct (enstrophy) cascade regimes from both Lagrangian and Eulerian perspectives. The probability density function (PDF) of the appropriately defined dimensionless power is strongly non-gaussian with asymmetric exponential tails. This distribution can be modeled by the distribution of the product of correlated normal variables allowing a derivation of the asymptotics of the tails. The PDF of the dimensionless power is shown to exhibit an empirical Fluctuation Relation. An expression for the entropy production rate is deduced from the asymptotic form of the power PDF and is found to agree very well with the measured entropy rate.