Helicity in superfluids: Existence and the classical limit

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 we find dynamics consistent with classical vortices in a viscous fluid.