Coherent propagation of vortex rings at extremely high Reynolds numbers

Abstract

We take advantage of the extremely small kinematic viscosity of superfluid $^4$ He to investigate the propagation of macroscopic vortex rings at Reynolds numbers between $2 \times 10^4$ and $4 \times 10^6$ . These inhomogeneous flow structures are thermally generated by releasing short power pulses into a small volume of liquid, open to the surrounding bath through a vertical tube $2$  mm in diameter. We study specifically the ring behaviour between $1.30$ and $1.80$  K using the flow visualization and second sound attenuation techniques. From the obtained data sets, containing more than $2600$ realizations, we find that the rings remain well-defined in space and time for distances up to at least $40$ tube diameters, and that their circulation depends significantly on the travelled distance, in a way similar to that observed for turbulent vortex rings propagating in Newtonian fluids. Additionally, the ring velocity and circulation appear to be influenced solely by a single, experimentally accessible parameter, combining the liquid temperature with the magnitude and duration of the power pulse. Overall, our results support the view that macroscopic vortex rings moving in superfluid $^4$ He closely resemble their Newtonian analogues, at least in the absence of significant thermal effects and at sufficiently large flow scales.