Identification of Kelvin waves: numerical challenges

TL;DR

This paper reviews numerical methods for identifying Kelvin waves in vortex tangles, testing their accuracy and exploring their relation to Kelvin spectra and energy distribution in superfluid turbulence.

Contribution

It introduces and evaluates several numerical techniques for Kelvin wave detection, clarifying their effectiveness and limitations in complex vortex configurations.

Findings

Certain numerical methods reliably identify Kelvin waves

The correlation dimension relates to Kelvin spectra

Energy spectrum E(k) follows 1/k in high-k region

Abstract

Kelvin waves are expected to play an essential role in the energy dissipation for quantized vortices. However, the identification of these helical distortions is not straightforward, especially in case of vortex tangle. Here we review several numerical methods that have been used to identify Kelvin waves within the vortex filament model. We test their validity using several examples and estimate whether these methods are accurate enough to verify the correct Kelvin spectrum. We also illustrate how the correlation dimension is related to different Kelvin spectra and remind that the 3D energy spectrum E(k) takes the form 1/k in the high-k region, even in the presence of Kelvin waves.