Emission of Discrete Vortex Rings by a Vibrating Grid In Superfluid ${}^3\mathrm{He}\mathrm{\text{−}}B$: A Precursor to Quantum Turbulence

We report a transition in the vorticity generated by a grid moving in the $B$ phase of superfluid ${}^3\mathrm{He}$ at $T\ll T_c$. The evolution of the vorticity after arresting the grid shows a dramatic change in the decay rate at a critical grid velocity. We believe this to reflect a sharp transition from ballistic vortex-ring production at low grid velocities to quantum turbulence at higher velocities and that independent isolated vortex rings provide the precursors to the developed turbulence. Furthermore we believe that this may be a feature of all quantum turbulence arising from repetitive mechanical agitation.

Figure 1

The arrangement of the experiment.

Figure 2

Top: The thermal damping of the thermometer VWR and VWR #1 spanning a period when the grid is oscillated with a peak velocity of $4.5\mathrm{mm}/\mathrm{s}$, indicated by the shaded band. Bottom: The ratio of the damping of VWR #1 to that of the thermometer VWR. The decrease in the damping ratio arises from quantum vortex lines generated by the grid.

Figure 3

The transient response of the fractional change in damping ratio for the VWR #1 closest to the grid as a function of time after stopping the grid motion for various initial grid velocities. The slow recovery at higher velocities corresponds to the decay/dispersion of quantum turbulence. At lower velocities the fast recovery reflects the rapid dispersion of ballistic vortex rings produced by the grid.

Figure 4

The decay time constant of the vortex signal versus grid velocity for VWRs #1 and #2. The time constants correspond to the roughly linear sections of the curves of Fig. 3 for #1 (and to those of similar curves for #2). Values are only indicative since the decays are not precisely exponential. The shaded band indicates the sudden collapse in the time constant. The velocity of $3.6\mathrm{mm}/\mathrm{s}$ has two plotted points since here both a long and a short time constant can be estimated.

Figure 5

The “vorticity signal” for the two VWRs while the grid is driven at $2.5\mathrm{mm}/\mathrm{s}$ as a function of quasiparticle damping (or inverse temperature) at 12 bar. The lines are only guides to the eye. The vertical arrows indicate the temperatures at which the range of the vortex rings is expected to match the distances from the grid to the VWRs.

Figure 6

A simplified schematic view of the configuration of vortex lines generated by the grid. Top: At low grid velocities the low density of vortex rings allows each to propagate at its (high) self-induced velocity. Bottom: At a critical density the vortex rings can no longer avoid each other. Reconnection creates more complex arrangements and a rapid cascade to quantum turbulence which then only evolves at a modest rate.