Weaving knotted vector fields with tunable helicity

Hridesh Kedia, David Foster, Mark R. Dennis, William T. M. Irvine

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

20 Citations (Scopus)
340 Downloads (Pure)


We present a general construction of divergence-free knotted vector fields from complex scalar fields, whose closed field lines encode many kinds of knots and links, including torus knots, their cables, the figure-8 knot and its generalizations. As finite-energy physical fields they represent initial states for fields such as the magnetic field in a plasma, or the vorticity field in a fluid. We give a systematic procedure for calculating the vector potential, starting from complex scalar functions with knotted zero filaments, thus enabling an explicit computation of the helicity of these knotted fields. The construction can be used to generate isolated knotted flux tubes, filled by knots encoded in the lines of the vector field. Lastly we give examples of manifestly knotted vector fields with vanishing helicity. Our results provide building blocks for analytical models and simulations alike.
Original languageEnglish
Article number274501
Number of pages6
JournalPhysical Review Letters
Issue number27
Publication statusPublished - 30 Dec 2016

Structured keywords



  • Fluid dynamics
  • helicity
  • knot theory
  • applied topology

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