Numerical simulation of stochastic vortex tangles

TL;DR

This paper presents a numerical simulation of chaotic vortex dynamics in superfluid helium, incorporating stochastic forces and dissipation, to analyze vortex tangle characteristics like length distribution and energy spectrum.

Contribution

It introduces a new numerical algorithm for vortex reconnection processes within stochastic differential equations modeling superfluid vortices.

Findings

Chaotic vortex dynamics modeled with Langevin approach.

Distribution of vortex loop lengths analyzed.

Energy spectrum of vortex tangles computed.

Abstract

We present the results of simulation of the chaotic dynamics of quantized vortices in the bulk of superfluid He II. Evolution of vortex lines is calculated on the base of the Biot-Savart law. The dissipative effects appeared from the interaction with the normal component, or/and from relaxation of the order parameter are taken into account. Chaotic dynamics appears in the system via a random forcing, e.i. we use the Langevin approach to the problem. In the present paper we require the correlator of the random force to satisfy the fluctuation-disspation relation, which implies that thermodynamic equilibrium should be reached. In the paper we describe the numerical methods for integration of stochastic differential equation (including a new algorithm for reconnection processes), and we present the results of calculation of some characteristics of a vortex tangle such as the total length, distribution of loops in the space of their length, and the energy spectrum.