The conjecture that helicity (or knottedness) is a fundamental conserved quantity has a rich history in fluid mechanics, but the nature of this conservation in the presence of dissipation has proven difficult to resolve. Making use of recent advances, we create vortex knots and links in viscous fluids and simulated superfluids and track their geometry through topology-changing reconnections. We find that the reassociation of vortex lines through a reconnection enables the transfer of helicity from links and knots to helical coils. This process is remarkably efficient, owing to the antiparallel orientation spontaneously adopted by the reconnecting vortices. Using a new method for quantifying the spatial helicity spectrum, we find that the reconnection process can be viewed as transferring helicity between scales, rather than dissipating it. We also infer the presence of geometric deformations that convert helical coils into even smaller scale twist, where it may ultimately be dissipated. Our results suggest that helicity conservation plays an important role in fluids and related fields, even in the presence of dissipation.helicity | fluid topology | vortex reconnections | superfluid vortices | topological fields

Helicity, a topological measure of the intertwining of vortices in a fluid flow, is a conserved quantity in inviscid fluids but can be dissipated by viscosity in real flows. Despite its relevance across a range of flows, helicity in real fluids remains poorly understood because the entire quantity is challenging to measure. We measured the total helicity of thin-core vortex tubes in water. For helical vortices that are stretched or compressed by a second vortex, we found conservation of total helicity. For an isolated helical vortex, we observed evolution toward and maintenance of a constant helicity state after the dissipation of twist helicity by viscosity. Our results show that helicity can remain constant even in a viscous fluid and provide an improved basis for understanding and manipulating helicity in real flows.

In addition to mass, energy, and momentum, classical dissipationless flows conserve helicity, a measure of the topology of the flow. Helicity has far-reaching consequences for classical flows from Newtonian fluids to plasmas. Since superfluids flow without dissipation, a fundamental question is whether such a conserved quantity exists for superfluid flows. We address the existence of a "superfluid helicity" using an analytical approach based on the symmetry underlying classical helicity conservation: the particle relabeling symmetry. Furthermore, we use numerical simulations to study whether bundles of superfluid vortices which approximate the structure of a classical vortex, recover the conservation of classical helicity and find dynamics consistent with classical vortices in a viscous fluid. 1 From here on, we refer to classical inviscid isentropic flows as Euler flows 2 We shall only consider superfluids with a complex scalar order parameter as in 4 He and atomic Bose-Einstein condensates.arXiv:1708.01526v4 [cond-mat.quant-gas]

The idea that the knottedness (hydrodynamic Helicity) of a fluid flow is conserved has a long history in fluid mechanics. The quintessential example of a knotted flow is a knotted vortex filament, however, owing to experimental difficulties, it has not been possible until recently to directly generate knotted vortices in real fluids. Using 3D printed hydrofoils and high-speed laser scanning tomography, we generate vortex knots and links and measure their subsequent evolution. In both cases, we find that the vortices deform and stretch until a series 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 Division 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 topologylinked 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 arXiv:1310.3321v1 [physics.flu-dyn]

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