Spectrum of Kelvin-wave turbulence in superfluids

TL;DR

This paper derives a new kinetic equation for Kelvin-wave turbulence in superfluids, revealing a different energy spectrum that corrects previous models and impacts quantum turbulence decay predictions.

Contribution

It introduces a new local energy cascade spectrum for Kelvin waves, replacing the outdated nonlocal spectrum used in quantum turbulence models.

Findings

New energy spectrum $E_{LN}(k) \,\propto\, k^{-5/3}$ derived

Previous spectrum $E_{KS}(k) \,\propto\, k^{-7/5}$ shown to be inconsistent

Provides a basis for improved quantum turbulence decay rate calculations

Abstract

We derive a type of kinetic equation for Kelvin waves on quantized vortex filaments with random large-scale curvature, that describes step-by-step (local) energy cascade over scales caused by 4-wave interactions. Resulting new energy spectrum $E\Sb{LN}(k)\propto k^{-5/3}$ must replace in future theory (e.g. in finding the quantum turbulence decay rate) the previously used spectrum $E\Sb {KS}(k)\propto k^{-7/5}$, which was recently shown to be inconsistent due to nonlocality of the 6-wave energy cascade.