Geometry and scaling of tangled vortex lines in three-dimensional random wave fields

TL;DR

This paper investigates the geometric properties and scaling behavior of tangled vortex lines in 3D random wave fields through numerical simulations, revealing their statistical characteristics and self-similarity.

Contribution

It provides new numerical analysis of vortex line geometry and scaling in 3D random wave fields, comparing results with analytical models and other filament systems.

Findings

Probability distributions of curvature and torsion match analytical predictions.

Vortex lines exhibit self-similar scaling behavior.

Tangled vortex structures share properties with other filament systems.

Abstract

The short- and long-scale behaviour of tangled wave vortices (nodal lines) in random three-dimensional wave fields is studied via computer experiment. The zero lines are tracked in numerical simulations of periodic superpositions of three-dimensional complex plane waves. The probability distribution of local geometric quantities such as curvature and torsion are compared to previous analytical and new Monte Carlo results from the isotropic Gaussian random wave model. We further examine the scaling and self-similarity of tangled wave vortex lines individually and in the bulk, drawing comparisons with other physical systems of tangled filaments.