Kelvin-wave cascade and dissipation in low-temperature superfluids vortices

TL;DR

This study investigates Kelvin waves on superfluid vortices using the Gross-Pitaevskii equation, confirming the predicted spectrum and revealing non-Gaussian fluctuations in the dissipative range.

Contribution

It provides direct numerical evidence supporting the Kelvin-wave spectrum prediction and characterizes the statistical properties of Kelvin waves without artificial forcing.

Findings

Kelvin-wave occupation-number spectrum matches theoretical predictions.

Kelvin modes are Gaussian in the inertial range.

Non-Gaussian fluctuations are observed in the dissipative range.

Abstract

We study the statistical properties of the Kelvin waves propagating along quantized superfluid vortices driven by the Gross-Pitaevskii equation. No artificial forcing or dissipation is added. Vortex positions are accurately tracked. This procedure directly allows us to obtain the Kevin-waves occupation-number spectrum. Numerical data obtained from long time integration and ensemble-average over initial conditions supports the spectrum proposed in [L'vov and Nazarenko, JETP Lett 91, 428 (2010)]. Kelvin wave modes in the inertial range are found to be Gaussian as expected by weak-turbulence predictions. Finally the dissipative range of the Kelvin-wave spectrum is studied. Strong non-Gaussian fluctuations are observed in this range.