Disentangling the triadic interactions in Navier-Stokes equations

TL;DR

This paper investigates how helicity influences energy transfer in modified Navier-Stokes equations by selectively removing helical modes, revealing conditions that lead to inverse or forward energy cascades.

Contribution

It introduces a novel approach of selectively removing helical Fourier modes at specific wavenumbers to study their impact on energy transfer in Navier-Stokes dynamics.

Findings

Inverse energy cascade occurs when negative helical modes are only at wavenumbers below the forcing scale.

Transition from backward to forward energy transfer when negative helical modes are only at wavenumbers above the forcing scale.

Presence of helical modes at specific scales determines the direction of energy transfer.

Abstract

We study the role of helicity in the dynamics of energy transfer in a modified version of the Navier-Stokes equations with explicit breaking of the mirror symmetry. We select different set of triads participating in the dynamics on the basis of their helicity content. In particular, we remove the negative helically polarized Fourier modes at all wavenumbers except for those falling on a localized shell of wavenumber, $|{\bf k}| \sim k_m$. Changing $k_m$ to be above or below the forcing scale, $k_f$, we are able to assess the energy transfer of triads belonging to different interaction classes. We observe that when the negative helical modes are present only at wavenumber smaller than the forced wavenumbers, an inverse energy cascade develops with an accumulation of energy on a stationary helical condensate. Vice versa, when negative helical modes are present only at wavenumber larger than the forced wavenumbers, a transition from backward to forward energy transfer is observed in the regime when the minority modes become energetic enough.