Statistics of Fourier Modes of Velocity and Vorticity in Turbulent Flows : Intermittency and Long-Range Correlations

TL;DR

This paper analyzes the statistical properties of Fourier modes in turbulent flows, revealing long-range correlations and intermittency differences between velocity and vorticity through experimental data and cascade models.

Contribution

It establishes a link between velocity structure functions and Fourier mode flatness, and compares intermittency in velocity and vorticity in turbulence.

Findings

Vorticity exhibits stronger intermittency than velocity.

Fourier modes show long-range correlations.

Statistical behaviors are consistent across velocity and vorticity data.

Abstract

We perform a statistical analysis of experimental fully developed turbulence longitudinal velocity data in the Fourier space. We address the controversial issue of statistical intermittency of spatial Fourier modes by acting on the finite spectral resolution. We derive a link between velocity structure functions and the flatness of Fourier modes thanks to cascade models. Similar statistical behaviors are recovered in the analysis of spatial Fourier modes of vorticity obtained in an acoustic scattering experiment. We conclude that vorticity is long-range correlated and found more intermittent than longitudinal velocity.