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We present a general construction of divergence-free knotted vector fieldsfrom complex scalar fields, whose closed field lines encode many kinds of knotsand links, including torus knots, their cables, the figure-8 knot and itsgeneralizations. As finite-energy physical fields they represent initial statesfor fields such as the magnetic field in a plasma, or the vorticity field in afluid. We give a systematic procedure for calculating the vector potential,starting from complex scalar functions with knotted zero filaments, thusenabling an explicit computation of the helicity of these knotted fields. Theconstruction can be used to generate isolated knotted flux tubes, filled byknots encoded in the lines of the vector field. Lastly we give examples ofmanifestly knotted vector fields with vanishing helicity. Our results providebuilding blocks for analytical models and simulations alike.

Weaving knotted vector fields with tunable helicity