Kelvin Wave Cascade and Decay of Superfluid Turbulence

TL;DR

This paper develops a weak-turbulence theory for Kelvin waves on vortex lines, deriving a kinetic equation that reveals a Kolmogorov cascade spectrum, supported by numerical analysis, advancing understanding of superfluid turbulence decay.

Contribution

It introduces a novel kinetic equation for kelvons beyond the local-induction approximation, demonstrating the existence of a Kolmogorov cascade in superfluid turbulence.

Findings

Existence of a Kolmogorov cascade spectrum for kelvons

Derivation of a kinetic equation governing kelvon interactions

Numerical validation of the cascade spectrum

Abstract

Kelvin waves (kelvons)--the distortion waves on vortex lines--play a key part in the relaxation of superfluid turbulence at low temperatures. We present a weak-turbulence theory of kelvons. We show that non-trivial kinetics arises only beyond the local-induction approximation and is governed by three-kelvon collisions; corresponding kinetic equation is derived. On the basis of the kinetic equation, we prove the existence of Kolmogorov cascade and find its spectrum. The qualitative analysis is corroborated by numeric study of the kinetic equation. The application of the results to the theory of superfluid turbulence is discussed.