Helicity conservation in classical vortex knots and links*

Vortex knots and links in an ideal fluid remain knotted or linked, ensuring that the topology of the vortex field lines is conserved. For a real fluid, however, this conservation is jeopardized by the presence of reconnection events, which allow vortex tubes to reconfigure their global topology; indeed, it has recently been observed that knotted and linked vortex tubes in classical fluids unknot or untie themselves via a series of these reconnection events. Remarkably, we observe that these reconnection processes conserve a measure of the vortex line topology (helicity) and do so through a geometric mechanism that efficiently transfers this topology across scales. The geometric nature of this topology transfer, along with its recent observation in superfluid vortices, suggests that helicity conservation may be a robust and generic feature of non-ideal flows.