Vortices in Superfluid Helium

The conditions under which fluid flow becomes turbulent have been studied for over a century, and have implications for topics from aircraft flight to meteorology to water distribution systems. Even an exact solution for a special case may yield little insight into an apparently similar situation. Small initial discrepancies can lead to vastly different fluid flows at a later time. As a result, many theories of developed turbulence deal with random flow fields and their statistical properties. Yet a more detailed approach is needed to understand the onset of turbulence, with its complicated dependence on geometry and initial conditions.

When a single vortex line is partially trapped around a wire in superfluid helium, the motion of the untrapped portion can be observed through its effect on the normal modes of the wire's vibration. Such a microscopic probe of vortex motion provides a rare opportunity for detailed fluid flow studies. We are investigating the onset of turbulence by studying how the regular precession of the vortex reacts to perturbations from heat pulses, pinned vortices, geometrical obstructions, or fluid cross-flow.

On the computational side, the excellent agreement between K. Schwarz' superfluid hydrodynamics calculations and the experimental precession rate provides the best test to date for theories of superfluid vortex motion. These simulations describe the regular vortex motion in great detail and are a logical starting point for further computer simulations. In fact, Schwarz has already predicted characteristic features for rough walls or an extremely off-center wire. We have verified most of these predictions and are now extending the calculations to incorporate different perturbations.

Here are pretty pictures of our simulations of vortex motion. When the precessing vortex pins to a spot on the wall, it oscillates as it settles into a stable configuration. The four pictures show different stages of this process, with the color scale representing the magnitude of the velocity field. All four show the same cut through the cell. As the vortex oscillates, the attachment point to the wire moves up and down. We detect this motion in our measurements. Only part of the free vortex appears in bright colors because the core is not entirely in the plane of the screen. In the first picture the vortex curves away from the viewer. In the second it curves slightly away near the wire, then comes through the screen and towards the viewer. In the last two the vortex comes towards the viewer.

Using regular motion as a starting point greatly simplifies the initial conditions, making it possible to compare detailed computer simulations with actual experiments. By comparing experimental results with computer simulations I hope to improve microscopic models of these effects. Because many aspects of fluid flow are similar for superfluids and normal liquids, the results may have relevance to the very general problems of classical turbulence.

Further reading:

J.T. Tough, "Superfluid turbulence," in Progress in Low Temperature Physics, edited by D.F. Brewer (North-Holland, Amsterdam, 1982), Vol. VIII, p. 133.

K.W. Schwarz, "Three-dimensional vortex dynamics in superfluid He4: Homogeneous superfluid turbulence," Phys. Rev. B31, 5782 (1985).

R.J. Zieve et al., "Precession of a single vortex line in superfluid He3," Phys. Rev. Lett. 68, 1327 (1992).

K.W. Schwarz, "Unwinding of a single quantized vortex from a wire," Phys. Rev. B47, 12030 (1993).