The life of vortex knots and links: the flow of knottiness across scales

James Franck Institute, University of Chicago

What happens if you take a vortex loop - akin to a smoke ring in air - and tie it into a knot or a link? The possibility of such knottiness in a fluid has fascinated physicists and mathematicians ever since Kelvin's 'vortex atom' hypothesis, in which the atoms of the periodic table were hypothesized to correspond to closed vortex loops of different knot types.

More recently, knottiness (hydrodynamic or magnetic helicity) of fluids and plasmas has re-emerged as a conserved quantity in dissipationless flows, offering the potential for fundamental insights.

Progress in understanding its implications has been hindered by lack of accessible experimental systems and explicit models. I will tell of how to make a vortex knot and link in water (in experiment), in the wave function of a superfluid (on a computer) and in light fields (in theory) and of what happens thence. In particular, I will talk about how linking coiling and twisting interplay across scales.