Disentangling the triadic interactions in Navier-Stokes equations

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, $|\mathbf{k}|\sim k_m$. 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.

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Cited by in corpus (12)

• Cascades and transitions in turbulent flows
• Helically Decomposed Turbulence
• Energy Cascade and Intermittency in Helically Decomposed Navier-Stokes Equations
• Condensates in thin-layer turbulence
• Critical transition in fast-rotating turbulence within highly elongated domains
• Helicity statistics in homogeneous and isotropic turbulence and turbulence models
• Energy cascades in rapidly rotating and stratified turbulence within elongated domains
• Sign singularity of the local energy transfer in space plasma turbulence
• A closure theory for the split energy-helicity cascades in homogeneous isotropic homochiral turbulence
• Chaotic and regular instantons in helical shell models of turbulence
• Partial invariants, large-scale dynamo action, and the inverse transfer of magnetic helicity
• From Triadic Interactions to Kolmogorov Scaling: A Deterministic, Scale-Resolved Formulation of Energy Flux