Reconnections of Vortex Loops in the Superfluid Turbulent HeII. Rates of the Breakdown and Fusion processes

TL;DR

This paper evaluates the rates of vortex loop reconnections, including merging and breakdown processes, in superfluid helium II, using a Gaussian vortex tangle model to quantify these dynamic events.

Contribution

It introduces a method to calculate reconnection rates of vortex loops in superfluid helium using Gaussian vortex tangle statistics, providing explicit coefficients for merging and breakdown processes.

Findings

Derived coefficients for vortex loop reconnection rates.

Quantified the frequency of merging and breakdown events.

Applied Gaussian model to vortex tangle statistics.

Abstract

Kinetics of merging and breaking down vortex loops is the important part of the whole vortex tangle dynamics. Another part is the motion of individual lines, which obeys the Biot-Savart law in presence of friction force and of applied external velocity fields if any. In the present work we evaluate the coefficients of the reconnection rates $A(l_{1},l_{2},l)$ and $B(l,l_{1},l_{2})$. Quantity $A$ is a number (per unit of time and per unit of volume) of events, when two loops with lengths $l_{1}$and $l_{2}$ collide and form the single loop of length $ l=l_{1}+l_{2}$. Quantity $% B(l,l_{1},l_{2}) $ describes the rate of events, when the single loop of the length $l$ breaks down into two the daughter loops of lengths $ l_{1}$ and $l_{2}$. These quantities ave evaluated as the averaged numbers of zeroes of vector $\mathbf{S}%_{s}(\xi_{2},\xi_{1},t)$ connecting two points on the loops of $\xi_{2}$ and $ \xi_{1}$ at moment of time $t$. Statistics of the individual loops is taken from the Gaussian model of vortex tangle. PACS-number 67.40