Statistics of Intermittent Switching between Potential Flow and Turbulence around an Oscillating Sphere in Superfluid 4He below 0.5 K

The flow of superfluid helium at very low temperatures around an oscillating microsphere is known to be unstable slightly above the critical velocity. The flow pattern switches intermittently between potential flow and turbulence. From time series recorded at constant temperature and driving force the statistical properties of the switching phenomenon are discussed. Based on our recent understanding of the critical velocity vc of oscillatory superflows, i.e., \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$v_{c}\sim \sqrt{\kappa\,\omega}$\end{document}, where κ is the circulation quantum and ω is the oscillation frequency, the analysis is being refined now. From the exponential distribution of the lifetimes of the turbulent phases quantitative information on the vortex density L can be inferred such as the distribution and the width of the fluctuations of L. The phases of potential flow show a Rayleigh distribution of the excess oscillation amplitude above the amplitude at turbulent flow. The rms value is found to scale as ω−3/2.