Depletion of nonlinearity in two-dimensional turbulence

TL;DR

This paper investigates how nonlinearity diminishes in decaying two-dimensional turbulence, revealing a two-step relaxation process that occurs independently of Reynolds number, with implications for understanding turbulence decay dynamics.

Contribution

It introduces a novel measurement of nonlinearity in 2D turbulence and characterizes its two-stage decay process, enhancing understanding of turbulence relaxation mechanisms.

Findings

Nonlinearity drops in two steps during decay.

Fast relaxation occurs during vortex formation.

Long-term relaxation involves eddy merging.

Abstract

The strength of the nonlinearity is measured in decaying two-dimensional turbulence, by comparing its value to that found in a Gaussian field. It is shown how the nonlinearity drops following a two-step process. First a fast relaxation is observed on a timescale comparable to the time of for-mation of vortical structures, then at long times the nonlinearity relaxes further during the phase when the eddies merge to form the final dynamic state of decay. Both processes seem roughly independent of the value of the Reynolds number.