Fluctuations of large-scale jets in the stochastic 2D Euler equation

TL;DR

This paper investigates the fluctuations of large-scale jets in 2D turbulence, using a kinetic theory approach to relate jet dynamics to Reynolds stress statistics, with analytical predictions supported by numerical simulations.

Contribution

It introduces a multi-scale kinetic theory framework to analyze jet fluctuations and predicts their spatial covariance structure in stochastically forced 2D Euler turbulence.

Findings

Analytical Gaussian fluctuation predictions match qualitative simulation results.

Jets velocity fluctuations are enhanced away from stationary points.

Quantitative validation of predictions remains challenging with current computational capabilities.

Abstract

Two-dimensional turbulence in a rectangular domain self-organises into large-scale unidirectional jets. While several results are present to characterize the mean jets velocity profile, much less is known about the fluctuations. We study jets dynamics in the stochastically forced two-dimensional Euler equations. In the limit where the average jets velocity profile evolves slowly with respect to turbulent fluctuations, we employ a multi-scale (kinetic theory) approach, which relates jet dynamics to the statistics of Reynolds stresses. We study analytically the Gaussian fluctuations of Reynolds stresses and predict the spatial structure of the jets velocity covariance. Our results agree qualitatively well with direct numerical simulations, clearly showing that the jets velocity profile are enhanced away from the stationary points of the average velocity profile. A numerical test of our predictions at quantitative level seems out of reach at the present day.