The Decay of a Quantized Vortex Ring and the Influence of Tracer Particles

Abstract

We capture the decay of a quantized vortex ring in superfluid helium-4 by imaging particles trapped on the vortex core. The ring shrinks in time, providing direct evidence for the dissipation of energy in the superfluid. The ring with trapped particles collapses more slowly than predicted by an available theory, but the collapse rate can be predicted correctly if the trapping of the particles on the core is taken into account. We theoretically explore the conditions under which particles may be considered passive tracers of quantized vortices and estimate, in particular, that their dynamics on the large-scale is largely unaffected by the burden of trapped particles if the latter are spaced by more than ten particle diameters along the vortex core, at temperatures between 1.5 K and 2.1 K.

Three-dimensional stability of leapfrogging quantum vortex rings

“…Since the expression in square bracket is effectively local, it approximately results in (1/2) ln(δ/a) n |X ′ n |dβ, thus confirming (12). In most simulations we used δ = 1/20, and only for verification we used δ = 1/40 in some cases.…”

“…where δ > a (of course, vortex configuration should be far from mutual and self-intersections). Fig.3 indicates that replacement (12) only weakly changes dispersion law at moderate wave numbers. A direct way to see weak sensitivity of the system under (12) is to write in Eq.…”

Velocity, energy, and helicity of vortex knots and unknots

“…For example, the fact that upon large amplitude Kelvin waves vortex rings can slow down and even reverse their translational motion has been recognised only recently [22,7]. Alongside the traditional interest for problems in classical fluid mechanics, additional interest is motivated by current work on superfluid helium [42,9,17,13] and atomic Bose-Einstein condensates [41,27,19].…”

Slowing down of vortex rings in Bose-Einstein condensates

“…Although streams of vortex rings can be generated using ions [9], and individual rings can be visualized by small tracers [10], helium vortex rings cannot be created individually in a controlled, reproducible way. Bose-Einstein condensed atomic gases are potentially a more fruitful context.…”