Reconnection Dynamics for Quantized Vortices

TL;DR

This study analyzes the dynamics of vortex reconnections in superfluid helium, confirming the predicted asymptotic behavior and highlighting the role of local fluctuations and boundary conditions in the reconnection process.

Contribution

It provides experimental evidence supporting the asymptotic form of vortex separation dynamics and introduces a correction-factor model accounting for environmental fluctuations.

Findings

Strong support for the $ au^{1/2}$ asymptotic behavior of vortex separation.

Identification of fluctuations influencing reconnection dynamics.

Statistical time-reversibility observed in vortex reconnection events.

Abstract

By analyzing trajectories of solid hydrogen tracers in superfluid $^4$He, we identify tens of thousands of individual reconnection events between quantized vortices. We characterize the dynamics by the minimum separation distance $\delta(t)$ between the two reconnecting vortices both before and after the events. Applying dimensional arguments, this separation has been predicted to behave asymptotically as $\delta(t) \approx A(\kappa |t-t_0|)^{1/2}$, where $\kappa=h/m$ is the quantum of circulation. The major finding of the experiments and their analysis is strong support for this asymptotic form with $\kappa$ as the dominant controlling feature, although there are significant event to event fluctuations. At the three-parameter level the dynamics may be about equally well-fit by two modified expressions: (a) an arbitrary power-law expression of the form $\delta(t)=B|t-t_0|^{\alpha}$ and (b) a correction-factor expression $\delta(t)=A(\kappa|t-t_0|)^{1/2}(1+c|t-t_0|)$. In light of possible physical interpretations we regard the correction-factor expression (b), which attributes the observed deviations from the predicted asymptotic form to fluctuations in the local environment and in boundary conditions, as best describing our experimental data. The observed dynamics appear statistically time-reversible, which suggests that an effective equilibrium has been established in quantum turbulence on the time scales investigated. We discuss the impact of reconnection on velocity statistics in quantum turbulence and, as regards classical turbulence, we argue that forms analogous to (b) could well provide an alternative interpretation of the observed deviations from Kolmogorov scaling exponents of the longitudinal structure functions.