Universal statistics of vortex tangles in three-dimensional random waves

Alexander Taylor*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

142 Downloads (Pure)


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.

Original languageEnglish
Article number075202
Number of pages18
JournalJournal of Physics A: Mathematical and Theoretical
Issue number7
Early online date19 Jan 2018
Publication statusPublished - 16 Feb 2018

Structured keywords



  • filamentary tangle
  • loop soup
  • optical vortex
  • reconnections
  • statistical physics
  • wave chaos


Dive into the research topics of 'Universal statistics of vortex tangles in three-dimensional random waves'. Together they form a unique fingerprint.

Cite this