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The conjecture that helicity (or knottedness) is a fundamental conservedquantity has a rich history in fluid mechanics, but the nature of thisconservation in the presence of dissipation has proven difficult to resolve.Making use of recent advances, we create vortex knots and links in viscousfluids and simulated superfluids and track their geometry through topologychanging reconnections. We find that the reassociation of vortex lines througha reconnection enables the transfer of helicity from links and knots to helicalcoils. This process is remarkably efficient, owing to the anti-parallelorientation spontaneously adopted by the reconnecting vortices. Using a newmethod for quantifying the spatial helicity spectrum, we find that thereconnection process can be viewed as transferring helicity between scales,rather than dissipating it. We also infer the presence of geometricdeformations which convert helical coils into even smaller scale twist, whereit may ultimately be dissipated. Our results suggest that helicity conservationplays an important role in fluids and related fields, even in the presence ofdissipation.

Helicity conservation by flow across scales in reconnecting vortex links and knots