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.
PACS numbers: 67.40.Vs, 47.27.Cn.
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REFERENCES
R.J. Donnelly, Quantized Vortices in Helium II (Cambridge University Press, Cambridge, 1991).
A.I. Ahonen, J. Kokko, O.V. Lounasmaa, M.A. Paalanen, R.C. Richardson, W. Schoepe, and Y. Takano, Phys. Rev. Lett. 37, 511(1976).
G. Baym, C.J. Pethick, and M. Salomaa, Phys. Rev. Lett. 38, 845(1977).
J.T. Simola, K.K. Nummila, A. Hirai, J.S. Korhonen, W. Schoepe, and L. Skrbek, Phys. Rev. Lett. 57, 1923(1986).
Juha Tuoriniemi, Diploma thesis, Helsinki University of Technology, 1989.
K. Gloos, J.H. Koivuniemi, W. Schoepe, J.T. Simola, and J.T. Tuoriniemi, Physica B 165&166, 119(1990); K. Gloos, W. Schoepe, J.T. Simola, and J.T. Tuoriniemi, Cryogenics 33, 791(1992).
R. Grosset, P. Höcherl, A. Martin, M. Niemetz, and W. Schoepe, J. Low Temp. Phys. 119, 723(1999).
J. Jäger, B. Schuderer, and W. Schoepe, Phys. Rev. Lett. 74, 566(1995); Physica B 210, 201(1995).
Michael Niemetz, Hubert Kerscher, and Wilfried Schoepe, in Quantized Vortex Dynamics and Superfluid Turbulence, p.87, ed. C. F. Barenghi, R.J. Donnelly and W. F. Vinen (Springer, Berlin, 2001).
M. Niemetz, H. Kerscher, W. Schoepe, J. Low Temp. Phys. 126, 287(2002).
W.F. Vinen, Proc. R. Soc. London, Ser. A 240, 114(1957); Proc. R. Soc. London, Ser. A 240, 128(1957); Proc. R. Soc. London, Ser. A 242, 493(1957); J.T. Tough, in Progress in Low Temperature Physics VIII, ed. D.F. Brewer (North-Holland, Amsterdam, 1982); K.W. Schwarz, Phys. Rev. B 38, 2389(1988); S.K. Nemirovskii and W. Fiszdon, Rev. Mod. Phys. 67, 37(1995).
Quantized Vortex Dynamics and Superfluid Turbulence, ed. C. F. Barenghi, R.J. Donnelly and W. F. Vinen (Springer, Berlin, 2001).
D.C. Samuels, Physica B 284–288, 73(2000); B.V. Svistunov, Phys. Rev. B 52, 3647(1995); W.F. Vinen, Phys. Rev. B 61 1410(2000).
J. Maurer and P. Tabeling, Europhys. Lett. 43, 29(1998).
S.R. Stalp, L. Skrbek, and R.J. Donnelly, Phys. Rev. Lett. 82, 4831(1999).
W. F. Vinen and J. J. Niemela, J. Low Temp. Phys. 128, 167(2002).
É. Varoquaux, O. Avenel, Yu. Mukharsky, and P. Hakonen, in Quantized Vortex Dynamics and Superfluid Turbulence, p.36, ed. C. F. Barenghi, R.J. Donnelly and W. F. Vinen (Springer,Berlin, 2001); É. Varoquaux, O. Avenel, Phys. Rev. B 68, 054515(2003).
R.E. Packard, Rev. Mod. Phys. 70,641(1998) and references therein.
S.I. Davis, P.C. Hendry, and P.V.E. McClintock, Physica B 280, 43(2000).
D.J. Bradley, Phys. Rev. Lett. 84, 1252(2000).
S.N. Fisher, A.J. Hale, A.M. Guénault, and G.R. Pickett, Phys. Rev. Lett. 86, 244(2001).
We used isotopically pure helium-4 (impurity concentration < 1 ppb) purchased from Campro Scientific GmbH, Berlin.
At temperatures above 1 K the temperature dependence of the superfluid density has to be taken into account, because turbulence is produced only in the superfluid component, see Ref. 8.
T. Winiecki, J.F. McCann, and C.S. Adams, Phys. Rev. Lett. 82, 51861(1999).
M. Niemetz, W. Schoepe, J.T. Simola, and J.T. Tuoriniemi, Physica B 280, 559(2000).
B.V. Gnedenko, Yu.K. Belyayev, and A.D. Solovyev, Mathematical Methods of Reliability Theory (Academic Press, New York, 1969).
W. Schoepe, to be published.
G.W. Rayfield, F. Reif, Phys. Rev. 136, A1194(1964).
M. Niemetz, Dissertation, Regensburg University (Der Andere Verlag, Osnabrück, 2001).
Actually, the reliability function R cannot level off at a positive constant value because it has to decrease from one to zero. This problem disappears when an additional failure rate is taken into account, see below.
E.J. Gumbel, Statistics of Extremes (Columbia University Press, New York 1958); J. Galambos, The Asymptotic Theory of Extreme Order Statistics (John Wiley&Sons, New York, 1978); M.R. Leadbetter, Georg Lindgren, Holger Rootzén, Extremes and Related Properties of Random Sequences and Processes (Springer-Verlag, New York, 1983).
At finite temperatures Δυ has also an upper bound Δυ max, see Eq. 7. Therefore, R has an endpoint. Strictly speaking, this truncated Rayleigh is not an EVD, but the truncation disappears in the limit T → 0.
The experiment is being performed with G. Eska at Bayreuth University.
H. Kerscher, M. Niemetz and W. Schoepe, J. Low Temp. Phys. 124, 163(2001).
H. Kerscher, Diploma Thesis, Regensburg University, 2000.
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Niemetz, M., Schoepe, W. Stability of Laminar and Turbulent Flow of Superfluid 4He at mK Temperatures Around an Oscillating Microsphere. Journal of Low Temperature Physics 135, 447–469 (2004). https://doi.org/10.1023/B:JOLT.0000029507.98543.1d
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DOI: https://doi.org/10.1023/B:JOLT.0000029507.98543.1d