Statistical equilibria of large scales in dissipative hydrodynamic turbulence

TL;DR

This paper investigates the statistical properties of large-scale turbulent flows in 3D dissipative turbulence, showing they align with absolute equilibrium theory predictions under certain scale conditions.

Contribution

It demonstrates that large-scale flows in dissipative turbulence can be effectively described by truncated Euler equations and absolute equilibrium theory.

Findings

Large-scale spectra match absolute equilibrium predictions.

Deviations from theory are analyzed and discussed.

Results apply to scales larger than forcing but smaller than domain size.

Abstract

We present a numerical study of the statistical properties of three-dimensional dissipative turbulent flows at scales larger than the forcing scale. Our results indicate that the large scale flow can be described to a large degree by the truncated Euler equations with the predictions of the zero flux solutions given by absolute equilibrium theory, both for helical and non-helical flows. Thus, the functional shape of the large scale spectra can be predicted provided that scales sufficiently larger than the forcing length scale but also sufficiently smaller than the box size are examined. Deviations from the predictions of absolute equilibrium are discussed.