Double Kelvin Wave Cascade in Superfluid Helium

TL;DR

This paper introduces a simplified model for superfluid vortex filaments that predicts a double cascade of energy and wave action, confirmed by numerical simulations, advancing understanding of superfluid turbulence.

Contribution

The paper develops a minimal local model supporting six-wave interactions, predicting a double cascade spectrum in superfluid vortex turbulence, validated by numerical simulations.

Findings

Prediction of two distinct power-law spectra for energy and wave action cascades

Confirmation of theoretical predictions through numerical simulations in weak turbulence regime

Model offers a simpler alternative to the Biot-Savart model with similar validity

Abstract

We study the double cascade of energy and wave action in a local model of superfluid vortex filaments. The model is obtained from a truncated expansion of the 2D Local Induction Approximation and it is shown to support six-wave interactions. We argue that, because of the uncertainty in the vortex core profile, this model has the same status of validity as the traditionally used Biot-Savart model with cutoff, but it has advantage of being much simpler. Our minimal model leads to a wave kinetic equation for which we predict existence of two distinct power-law scaling in the spectrum, corresponding to a direct cascade of energy and an inverse one of wave action. Direct numerical simulations confirm the theoretical predictions in the weak turbulence regime.