Energy Cascade and Intermittency in Helically Decomposed Navier-Stokes Equations

TL;DR

This paper investigates how helicity-based triadic interactions in Fourier space influence energy transfer and intermittency in 3D Navier-Stokes turbulence, revealing that certain helicity configurations can reverse energy cascade and suppress intermittency.

Contribution

It introduces a helical Fourier decomposition approach to analyze the specific effects of helicity sign combinations on turbulence dynamics.

Findings

Triads with only one helicity sign cause inverse energy cascade and reduce intermittency.

Absence of such triads does not significantly affect the energy cascade or intermittency.

Helical interactions with mixed signs do not alter the forward cascade or intermittency.

Abstract

We study the nature of the triadic interactions in Fourier space for three-dimensional Navier-Stokes equations based on the helicity content of the participating modes. Using the tool of helical Fourier decomposition we are able to access the effects of a group of triads on the energy cascade process and on the small-scale intermittency. We show that while triadic interactions involving modes with only one sign of helicity results to an inverse cascade of energy and to a complete depletion of the intermittency, absence of such triadic interactions has no visible effect on the energy cascade and on the inertial-range intermittency of the three-dimensional Navier-Stokes equations.