Kelvin waves from vortex reconnection in superfluid helium at low temperatures

TL;DR

This paper investigates Kelvin waves generated by vortex reconnection in superfluid helium, challenging the Kelvin-wave cascade explanation and proposing an alternative interpretation based on curvature limitations.

Contribution

It provides a new explanation for observed scaling relations without invoking Kelvin-wave cascades and introduces a method to identify Kelvin spectra from decay patterns.

Findings

Scaling relation similar to previous studies but explained differently.

Kelvin spectrum is not a simple power law, varies with scale.

Proposes a method to identify Kelvin spectra via curvature decay.

Abstract

We report on the analysis of the root mean square curvature as a function of the numerical resolution for a single reconnection of two quantized vortex rings in superfluid helium. We find a similar scaling relation as reported in the case of decaying thermal counterflow simulations by L. Kondaurova et al. There the scaling was related to the existence of a Kelvin-wave cascade which was suggested to support the L'vov-Nazarenko spectrum. Here we provide an alternative explanation that does not involve the Kelvin-wave cascade but is due to the sharp cusp generated by a reconnection event in a situation where the maximum curvature is limited by the computational resolution. We also suggest a method for identifying the Kelvin spectrum based on the decay of the rms curvature by mutual friction. Our vortex filament simulation calculations show that the spectrum of Kelvin waves after the reconnection is not simply $n(k) \propto k^{-\eta}$ with constant $\eta$. At large scales the spectrum seems to be close to the Vinen prediction with $\eta$ = 3 but becomes steeper at smaller scales.