Abstract
The critical velocity v c for the onset of turbulent drag of small spheres oscillating in superfluid 4He is frequency dependent (ω/2π from 100 Hz to 700 Hz) and is described by \(v_{c}=2.6\sqrt{\kappa \omega}\) , where κ is the circulation quantum. A qualitative analysis based on a recent theory of the onset of superfluid turbulence gives \(v_{c}\approx \sqrt{8\kappa \omega/\beta}\) , where β∼1 depends on the coefficients of mutual friction. This agrees well with the data and implies that v c is a universal critical velocity that is independent of geometry, size, and surface properties of the oscillating body. This is confirmed by comparing our data on spheres with v c obtained with other oscillating structures by other groups. Numerical simulations indicate somewhat larger critical velocity, above which a rapid increase in vortex length is observed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R.J. Donnelly, Quantized Vortices in Helium II (Cambridge University Press, Cambridge, 1991)
R. Hänninen, M. Tsubota, W.F. Vinen, Phys. Rev. B 75, 064502 (2007); see for a recent review on critical velocities of oscillating structures
R. Hänninen, W. Schoepe, A preliminary analysis of our results was published in arXiv:0801.2521 [cond-mat.other]
M. Niemetz, W. Schoepe, J. Low Temp. Phys. 135, 447 (2004)
J. Jäger, B. Schuderer, W. Schoepe, Physica B 210, 201 (1995)
J. Jäger, B. Schuderer, W. Schoepe, Phys. Rev. Lett. 74, 566 (1995)
W. Schoepe, Phys. Rev. Lett. 92, 095301 (2004)
D.I. Bradley, D.O. Clubb, S.N. Fisher, A.M. Guénault, R.P. Haley, C.J. Matthews, G.R. Pickett, K. Zaki, J. Low Temp. Phys. 138, 493 (2005)
H. Yano, N. Hashimoto, A. Handa, M. Nakagawa, K. Obara, O. Ishikawa, T. Hata, Phys. Rev. B 75, 012502 (2007)
H. Yano, Private communication, to be published
H.A. Nichol, L. Skrbek, P.C. Hendry, P.V.E. McClintock, Phys. Rev. Lett. 92, 244501 (2004)
H.A. Nichol, L. Skrbek, P.C. Hendry, P.V.E. McClintock, Phys. Rev. E 70, 056307 (2004)
D. Charalambous, L. Skrbek, P.C. Hendry, P.V.E. McClintock, W.F. Vinen, Phys. Rev. E 74, 036307 (2006)
J. Hosio, Private communication, Low Temperature Laboratory, Helsinki University of Technology
M. Blažková, D. Schmoranzer, L. Skrbek, Phys. Rev. E 75, 025302 (2007)
R. Blaauwgeers, M. Blazkova, M. Človečko, V.B. Eltsov, R. de Graaf, J. Hosio, M. Krusius, D. Schmoranzer, W. Schoepe, L. Skrbek, P. Skyba, R.E. Solntsev, D.E. Zmeev, J. Low Temp. Phys. 146, 537 (2007)
G.E. Volovik, JETP Lett. 78, 553 (2003)
L. Skrbek, JETP Lett. 80, 474 (2004)
N.B. Kopnin, Phys. Rev. Lett. 92, 135301 (2004)
W.F. Vinen, Proc. R. Soc. Lond. Ser. A 242, 493 (1957)
K.W. Schwarz, J.R. Rozen, Phys. Rev. B 44, 7563 (1991)
R. Goto, S. Fujiyama, H. Yano, Y. Nago, N. Hashimoto, K. Obara, O. Ishikawa, M. Tsubota, T. Hata, Phys. Rev. Lett. 100, 045301 (2008)
R.J. Donnelly, C.F. Barenghi, J. Phys. Chem. Ref. Data 27, 1217 (1998)
D. Kivotides, C. Barenghi, Y.A. Sergeev, Phys. Rev. B 77, 014527 (2008)
A.P. Finne, T. Araki, R. Blaauwgers, V.B. Eltsov, N.B. Kopnin, M. Krusius, L. Skrbek, M. Tsubota, G.E. Volovik, Nature (Lond.) 424, 1022 (2003)
D.I. Bradley, D.O. Clubb, S.N. Fisher, A.M. Guénault, R.P. Haley, C.J. Matthews, G.R. Pickett, V. Tsepelin, K. Zaki, Phys. Rev. Lett. 96, 035301 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hänninen, R., Schoepe, W. Universal Critical Velocity for the Onset of Turbulence of Oscillatory Superfluid Flow. J Low Temp Phys 153, 189–196 (2008). https://doi.org/10.1007/s10909-008-9834-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10909-008-9834-2