The Life of a Vortex Knot Dustin Kleckner

The idea that the knottedness (hydrodynamic Helicity) of a fluid flow is conserved has a long history in fluid mechanics. The quintessen-tial example of a knotted flow is a knotted vortex filament, however, owing to experimental difficulties, it has not been possible until re-cently to directly generate knotted vortices in real fluids. Using 3D printed hydrofoils and high-speed laser scanning tomography, we gen-erate vortex knots and links and measure their subsequent evolution. In both cases, we find that the vortices deform and stretch until a se-ries of vortex reconnections occurs, eventually resulting several disjoint vortex rings. This article accompanies a fluid dynamics video entered into the Gallery of Fluid Motion at the 66th Annual Meeting of the APS Divi-sion of Fluid Dynamics. Smoke rings are an everyday example of filamental vortex loops that are found in many complex flows. Vortex loops with non-trivial topology – linked or knotted together – should be conserved in ideal fluids, as first noted by Lord Kelvin[1]. In real fluids, even superfluids, the situation is more complicated, and linking can change through reconnection events, whose detailed dynamics are challenging to resolve in both theory and experiment. As a result, the dynamics of knots in non-ideal fluids is largely unresolved. Previous methods for generating vortex loops are difficult or impossible to generalize to creating vortex links and knots, so we developed a new technique based on accelerating specially shaped hydrofoils[2]. Using this method, we were able to generate linked and knotted vortices for the first 1 a