Universal statistics of vortex tangle in three-dimensional wave chaos

TL;DR

This paper investigates the universal statistical properties of vortex tangles in three-dimensional wave chaos, revealing large-scale power law behaviors and boundary effects that are consistent across different physical systems.

Contribution

It provides numerical and analytical evidence for universal large-scale statistics of vortex tangles in 3D wavefields, emphasizing the role of boundary conditions and system connectedness.

Findings

Vortex conformations follow predicted power law scaling.

Large scale vortex statistics are influenced by boundary conditions.

Analytical results describe vortex reconnection in dynamic systems.

Abstract

The tangled nodal lines (wave vortices) in random, three-dimensional wavefields are studied as an exemplar of a fractal loop soup. Their statistics are a three-dimensional counterpart to the characteristic random behaviour of nodal domains in quantum chaos, but in three-dimensions the filaments can wind around one another to give distinctly different large scale behaviours. By tracing numerically the structure of the vortices, their conformations are shown to follow recent analytical predictions for random vortex tangles with periodic boundaries, where the local disorder of the model `averages out' to produce large scale power law scaling relations whose universality classes do not depend on the local physics. These results explain previous numerical measurements in terms of an explicit effect of the periodic boundaries, where the statistics of the vortices are strongly affected by the large scale connectedness of the system even at arbitrarily high energies. The statistics are investigated primarily for static (monochromatic) wavefields, but the analytical results are further shown to directly describe the reconnection statistics of vortices evolving in certain dynamic systems, or occurring during random perturbations of the static configuration.