Stability of Laminar and Turbulent Flow of Superfluid4He at mK Temperatures around an Oscillating Microsphere

Abstract

The flow of superfluid helium around a vibrating microsphere is investigated at temperatures between 1 K and 25 mK. At small oscillation amplitudes pure potential flow is observed, the linear drag force on the sphere being determined only by ballistic quasiparticle scattering below 0.7 K with phonons contributing exclusively below 0.5 K. At larger oscillation amplitudes a strongly nonlinear drag force gives evidence of stable turbulent flow if at least 0.6 pW are transferred from the sphere to the turbulent superfluid. In an intermediate range of amplitudes (or driving forces) both flow patterns are unstable and intermittent switching between both is observed below 0.5 K. We have recorded time series of this switching phenomenon at constant drives and temperatures lasting up to 36 hours. We have made a statistical analysis of the times series by means of reliability theory. The lifetime of the turbulent phases grows with increasing drive and diverges at a critical value (or at least becomes unmeasurably long). Stability of the laminar phases in the intermediate regime depends on the excess velocity of the sphere above the critical velocity. Metastable laminar phases are observed above the critical velocity having a mean lifetime limited to 25 minutes by natural background radioactivity which occasionally produces local vorticity due to ionization of the liquid. Finally, it is suggested that the breakdown of potential flow belongs to the class of “system failure” experiments which is well known in reliability testing and whose statistical properties are described by extreme-value theory.