Large-scale superfluid vortex rings at nonzero temperatures

We numerically model experiments in which large-scale vortex rings—bundles of quantized vortex loops—are created in superfluid helium by a piston-cylinder arrangement. We show that the presence of a normal-fluid vortex ring together with the quantized vortices is essential to explain the coherence of these large-scale vortex structures at nonzero temperatures, as observed experimentally. Finally we argue that the interaction of superfluid and normal-fluid vortex bundles is relevant to recent investigations of superfluid turbulence.

Figure 1

Motion of 3 vortex rings (initial condition: $R=0.0896\mathrm{cm},a=0.0075\mathrm{cm})$ at zero temperature (no friction). Left: $t=0$; middle: $t=3.6$; right: $t=7.2\mathrm{s}$. The vortex bundle is stable, and each ring leapfrogs around the others. Each vortex line is represented by a tube [23] whose thickness if for the sake of visualization only (vortex lines have infinitesimal thickness).

Figure 2

Motion of 3 vortex rings in the presence of friction at $T=2.02\mathrm{K}$ with ${\mathbf{v}}_n=0$. The initial condition is the same as in Fig. 1. Left: $t=0$; middle: $t=3.6$; right: $t=7.2\mathrm{s}$. The vortex bundle decays: one by one, all vortex rings shrink and vanish on the axis of propagation.

Figure 3

Motion of 3 vortex rings in the presence of friction at $T=2.02\mathrm{K}$ and normal-fluid ring $\left({\mathbf{v}}_n\ne 0\right)$. The initial condition is the same as in Fig. 1. Left: $t=0$; middle: $t=3.6$; right: $t=7.2\mathrm{s}$. It is apparent that the superfluid vortex bundle moves in a stable way as in the absence of friction (Fig. 1); the individual rings leapfrog around each other.

Figure 4

Vortex bundle at $T=0$ (no friction). Top: Side (left) and rear (right) view of vortex bundle with $N=19$ rings at time $t=40\mathrm{s}$.

Figure 5

Vortex bundle at $T=2.02\mathrm{K}$ in the presence of friction and normal-fluid ring ${\mathbf{v}}_n$. Top: Side (left) and rear (right) view of vortex bundle with $N=19$ rings at time $t=80\mathrm{s}$.