Velocity matching and Poiseuille pipe flow of superfluid helium

We show that in laminar pipe flow of helium II with the average normal-fluid and superfluid velocities in the same direction, a single superfluid vortex filament can form a series of large vortex rings oriented with the flow. These rings interact to form an array of vortex rings that gives the superfluid a parabolic velocity profile matching the normal-fluid velocity profile. We conclude with some generalizations of this behavior to other flow geometries.