Large-scale normal fluid circulation in helium superflows

We perform fully coupled numerical simulations of helium II pure superflows in a channel, with vortex-line density typical of experiments. Peculiar to our model is the computation of the back-reaction of the superfluid vortex motion on the normal fluid and the presence of solid boundaries. We recover the uniform vortex-line density experimentally measured employing second sound resonators and we show that pure superflow in helium II is associated with a large-scale circulation of the normal fluid which can be detected using existing particle-tracking visualization techniques.

Figure 1

Schematic of the normal-fluid (blue) and superfluid (red) velocity profiles in a pure superflow channel in a vortex-free flow (left). Middle and right: conjectures of normal-fluid large flow structures in the presence of a vortex tangle.

Figure 2

Left: coarse-grained profiles of superfluid velocity ${\overline{u}}_s$ (solid red line), normal fluid velocity ${\overline{u}}_n$ (solid blue line), and velocity difference ${\overline{u}}_{ns}={\overline{u}}_n-{\overline{u}}_s$ (solid green line) at $t=T_f$. Red and blue dot-dashed lines indicate the initial laminar velocity profiles of the superfluid and the normal fluid, respectively. Right: coarse-grained profile of the streamwise component of the mutual friction force ${\overline{F}}^x/{\rho }_n$ at $t=T_f$.

Figure 3

Left: vortex distribution at $t=T_f$, red empty (black filled) circles indicate positive (negative) vortices. Right: coarse-grained profiles of positive vortex density ${\overline{n}}^{+}$ (solid red line), negative vortex density ${\overline{n}}^{-}$ (dashed black line), and total vortex density $\overline{n}$ (dot-dashed green line) at $t=T_f$. In the inset, we report the corresponding coarse-grained profile of the polarization magnitude $\overline{p}$ (solid magenta line).

Figure 4

As in Fig. 1 (right) but with tracer particles, which are either free (light-grey circles) or trapped in vortices (black circles).