the helicity of a knotted vortex filament

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There is however a subtlety in relation to move I, as may be seen from consideration of figure 6 which represents the twisting of a loop through an angle 2r, thus ...
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T H E HELICITY OF A KNOTTED VORTEX FILAMENT

R.L. RICCA' and H.K.MOFFATT' Institute for Theoretical Physics University of California Santa Barbara, California 93106-4030 U.S.A. ABSTRACT. The helicity 31 associated with a knotted vortex filament is considered. The filament is first constructed starting from a circular tube, in three stages involving injection of (integer) twist, deformation and switching of crossings. This produces a vortex tube in the form of an arbitrary knot K; each vortex line in the tube is a (trivial) satellite of I

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