The Kelvin-wave cascade in the vortex filament model

TL;DR

This paper presents comprehensive numerical simulations of Kelvin-wave interactions in superfluid helium-4 turbulence, supporting the nonlocal six-wave interaction theory as a key energy transfer mechanism at small scales.

Contribution

The study provides the most detailed numerical evidence to date for nonlocal six-wave Kelvin wave interactions, using a novel algorithm based on the full Biot-Savart equation.

Findings

Results are consistent with nonlocal six-wave Kelvin wave interactions.

Supports the hypothesis that Kelvin waves transfer energy to small scales in superfluid turbulence.

Numerical simulations align with the theory proposed by L'vov and Nazarenko.

Abstract

The energy transfer mechanism in zero temperature superfluid turbulence of helium-4 is still a widely debated topic. Currently, the main hypothesis is that weakly nonlinear interacting Kelvin waves transfer energy to sufficiently small scales such that energy is dissipated as heat via phonon excitations. Theoretically, there are at least two proposed theories for Kelvin-wave interactions. We perform the most comprehensive numerical simulation of weakly nonlinear interacting Kelvin-waves to date and show, using a specially designed numerical algorithm incorporating the full Biot-Savart equation, that our results are consistent with nonlocal six-wave Kelvin wave interactions as proposed by L'vov and Nazarenko.