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The flow of superfluid helium-4 at very low temperatures around an oscillating microsphere has been studied in detail. At small oscillation amplitudes the drag force is linear in velocity amplitude. Above a critical velocity vc a transition from potential flow to turbulent flow is signaled by a large and nonlinear drag force that scales as (v^2 - vc^2), where vc is independent of temperature (below 1 K) and driving force. Interestingly, vc is found to scale as (k f)^(1/2), where k=h/m is the circulation quantum (h is Planck's constant and m is the mass of a helium-4 atom) and f is the oscillation frequency. We also observe slightly above vc that the flow pattern is unstable and switches intermittently between potential flow and turbulence. From time series recorded at constant drive and temperature we have investigated the statistical properties of this switching phenomenon. In this talk the universal law vc~(k f)^(1/2) will be discussed in detail. It can be derived theoretically in various ways: firstly, from a qualitative but very general argument based on the "superfluid Reynolds number" Rs = vl/k, where v is the flow velocity and l is a characteristic length scale, secondly, and in more detail, from Kopnin's equation of the time dependence of the vortex line density, and, finally, we have obtained this law rigorously by dynamical scaling of the equations of motion of vortex dynamics.
Author(s):
Risto Hänninen
O.V. Lounasmaa Laboratory, Aalto University
Finland
Michael Niemetz
University of Applied Sciences, Regensburg
Germany
Wilfried Schoepe
Regensburg University
Germany