Advertisement

Journal of Low Temperature Physics

, Volume 156, Issue 3–6, pp 116–131 | Cite as

Transition to Turbulence for a Quartz Tuning Fork in Superfluid 4He

  • D. I. Bradley
  • M. J. Fear
  • S. N. Fisher
  • A. M. Guénault
  • R. P. Haley
  • C. R. Lawson
  • P. V. E. McClintock
  • G. R. Pickett
  • R. Schanen
  • V. Tsepelin
  • L. A. Wheatland
Article

Abstract

We have studied the resonance of a commercial quartz tuning fork immersed in superfluid 4He, at temperatures between 5 mK and 1 K, and at pressures between zero and 25 bar. The force-velocity curves for the tuning fork show a linear damping force at low velocities. On increasing velocity we see a transition corresponding to the appearance of extra drag due to quantized vortex lines in the superfluid. We loosely call this extra contribution “turbulent drag”. The turbulent drag force, obtained after subtracting a linear damping force, is independent of pressure and temperature below 1 K, and is easily fitted by an empirical formula. The transition from linear damping (laminar flow) occurs at a well-defined critical velocity that has the same value for the pressures and temperatures that we have measured. Later experiments using the same fork in a new cell revealed different behaviour, with the velocity stepping discontinuously at the transition, somewhat similar to previous observations on vibrating wire resonators and oscillating spheres. We compare and contrast the observed behaviour of the superfluid drag and inertial forces with that measured for vibrating wires.

Keywords

Superfluid Turbulence Critical velocity Tuning fork 

PACS

67.25.dk 67.25.dg 47.27.Cn 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D.I. Bradley, D.O. Clubb, S.N. Fisher, A.M. Guénault, R.P. Haley, C.J. Matthews, G.R. Pickett, K.L. Zaki, J. Low Temp. Phys. 138, 493 (2005) CrossRefADSGoogle Scholar
  2. 2.
    D.I. Bradley, S.N. Fisher, A.M. Guénault, R.P. Haley, V. Tsepelin, G.R. Pickett, K.L. Zaki, J. Low Temp. Phys. 154, 97 (2009) CrossRefADSGoogle Scholar
  3. 3.
    D.I. Bradley, Phys. Rev. Lett. 84, 1252 (2000) CrossRefADSGoogle Scholar
  4. 4.
    S.N. Fisher, A.J. Hale, A.M. Guénault, G.R. Pickett, Phys. Rev. Lett. 86, 244 (2001) CrossRefADSGoogle Scholar
  5. 5.
    D.I. Bradley, S.N. Fisher, A.M. Guénault, M.R. Lowe, G.R. Pickett, A. Rahm, R.C.V. Whitehead, Phys. Rev. Lett. 93, 235302 (2004) CrossRefADSGoogle Scholar
  6. 6.
    H. Yano, A. Handa, H. Nakagawa, K. Obara, O. Ishikawa, T. Hara, M. Nakagawa, J. Low Temp. Phys. 138, 561 (2005) CrossRefADSGoogle Scholar
  7. 7.
    H. Yano, A. Handa, H. Nakagawa, K. Obara, O. Ishikawa, T. Hata, J. Phys. Chem. Solids 66, 1501 (2005) CrossRefADSGoogle Scholar
  8. 8.
    H. Yano, N. Hashimoto, A. Handa, M. Nakagawa, K. Obara, O. Ishikawa, T. Hata, Phys. Rev. B 75, 012502 (2007) CrossRefADSGoogle Scholar
  9. 9.
    N. Hashimoto, R. Goto, H. Yano, K. Obara, O. Ishikawa, T. Hata, Phys. Rev. B 76, 020504 (2007) CrossRefADSGoogle Scholar
  10. 10.
    N. Hashimoto, A. Handa, M. Nakagawa, K. Obara, H. Yano, O. Ishikawa, T. Hata, J. Low Temp. Phys. 148, 299 (2007) CrossRefADSGoogle Scholar
  11. 11.
    R. Goto, S. Fujiyama, H. Yano, Y. Nago, N. Hashimoto, K. Obara, O. Ishikawa, M. Tsubota, T. Hata, Phys. Rev. Lett. 100, 045301 (2008) CrossRefADSGoogle Scholar
  12. 12.
    J. Martikainen, J. Tuoriniemi, T. Knuuttila, G.R. Pickett, J. Low Temp. Phys. 126, 139 (2002) CrossRefGoogle Scholar
  13. 13.
    D.I. Bradley, D.O. Clubb, S.N. Fisher, A.M. Guénault, C.J. Matthews, G.R. Pickett, J. Low Temp. Phys. 134, 381 (2004) CrossRefADSGoogle Scholar
  14. 14.
    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. 95, 035302 (2005) CrossRefADSGoogle Scholar
  15. 15.
    D.I. Bradley, D.O. Clubb, S.N. Fisher, A.M. Guénault, R.P. Haley, C.J. Matthews, G.R. Pickett, V. Tsepelin, K.L. Zaki, Phys. Rev. Lett. 96, 035301 (2006) CrossRefADSGoogle Scholar
  16. 16.
    D.I. Bradley, S.N. Fisher, A.M. Guénault, R.P. Haley, N. Mulders, S. O’Sullivan, G.R. Pickett, J. Roberts, V. Tsepelin, Phys. Rev. Lett. 101, 65302 (2008) CrossRefADSGoogle Scholar
  17. 17.
    H.A. Nichol, L. Skrbek, P.C. Hendry, P.V.E. McClintock, Phys. Rev. E 70, 056307 (2004) CrossRefADSGoogle Scholar
  18. 18.
    D. Charalambous, L. Skrbek, P.C. Hendry, P.V.E. McClintock, W.F. Vinen, Phys. Rev. E 74, 036307 (2006) CrossRefADSGoogle Scholar
  19. 19.
    J. Jäger, B. Schuderer, W. Schoepe, Phys. Rev. Lett. 74, 566 (1995) CrossRefADSGoogle Scholar
  20. 20.
    M. Niemetz, H. Kerscher, W. Schoepe, J. Low Temp. Phys. 126, 287 (2002) CrossRefGoogle Scholar
  21. 21.
    M. Niemetz, W. Schoepe, J. Low Temp. Phys. 135, 447 (2004) CrossRefADSGoogle Scholar
  22. 22.
    W. Schoepe, Phys. Rev. Lett. 92, 095301 (2004) CrossRefADSGoogle Scholar
  23. 23.
    R. Hänninen, W. Schoepe, J. Low Temp. Phys. 153, 189 (2008) CrossRefADSGoogle Scholar
  24. 24.
    W. Schoepe, J. Low Temp. Phys. 150, 724 (2008) CrossRefADSGoogle Scholar
  25. 25.
    J. Luzuriaga, J. Low Temp. Phys. 108, 561 (1997) CrossRefGoogle Scholar
  26. 26.
    R. Blaauwgeers, M. Blaz̆ková, M. C̆lovec̆ko, 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) CrossRefADSGoogle Scholar
  27. 27.
    M. Blaz̆ková, M. C̆lovec̆ko, E. Gaz̆o, L. Skrbek, P. Skyba, J. Low Temp. Phys. 148, 305 (2007) CrossRefADSGoogle Scholar
  28. 28.
    M. Blaz̆ková, D. Schmoranzer, L. Skrbek, Phys. Rev. E 75, 025302 (2007) CrossRefADSGoogle Scholar
  29. 29.
    M. Blaz̆ková, M. C̆lovec̆ko, V.B. Eltsov, E. Gaz̆o, R. de Graaf, J.J. Hosio, M. Krusius, D. Schmoranzer, W. Schoepe, L. Skrbek, P. Skyba, R.E. Solntsev, W.F. Vinen, J. Low Temp. Phys. 150, 525 (2008) CrossRefADSGoogle Scholar
  30. 30.
    M. Blaz̆ková, T.V. Chagovets, M. Rotter, D. Schmoranzer, L. Skrbek, J. Low Temp. Phys. 150, 194 (2008) CrossRefADSGoogle Scholar
  31. 31.
    G.A. Sheshin, A.A. Zadorozhko, E.Y. Rudavskii, V.K. Chagovets, L. Skrbek, M. Blaz̆ková, Low Temp. Phys. 34, 875 (2008) CrossRefADSGoogle Scholar
  32. 32.
    E.M. Pentti, J.T. Tuoriniemi, A.J. Salmela, A.P. Sebedash, J. Low Temp. Phys. 150, 555 (2008) CrossRefADSGoogle Scholar
  33. 33.
    M. Blaz̆ková, D. Schmoranzer, L. Skrbek, W.F. Vinen, Phys. Rev. B 79, 054522 (2009) CrossRefADSGoogle Scholar
  34. 34.
    S.N. Fisher, A.M. Guénault, C.J. Kennedy, G.R. Pickett, Phys. Rev. Lett. 63, 2566 (1989) CrossRefADSGoogle Scholar
  35. 35.
    S.N. Fisher, G.R. Pickett, R.J. Watts-Tobin, J. Low Temp. Phys. 83, 225 (1991) CrossRefADSGoogle Scholar
  36. 36.
    M.P. Enrico, S.N. Fisher, R.J. Watts-Tobin, J. Low Temp. Phys. 98, 81 (1995) CrossRefADSGoogle Scholar
  37. 37.
    C. Bauerle, Y.M. Bunkov, S.N. Fisher, H. Godfrin, Phys. Rev. B 57, 14381 (1998) CrossRefADSGoogle Scholar
  38. 38.
    D.O. Clubb, O.V.L. Buu, R.M. Bowley, R. Nyman, J.R. Owers-Bradley, J. Low Temp. Phys. 136, 1 (2004) CrossRefADSGoogle Scholar
  39. 39.
    M. Tsubota, T. Araki, S.K. Nemirovskii, Phys. Rev. B 62, 11751 (2000) CrossRefADSGoogle Scholar
  40. 40.
    D. Kivotides, J.C. Vassilicos, D.C. Samuels, C.F. Barenghi, Phys. Rev. Lett. 86, 3080 (2001) CrossRefADSGoogle Scholar
  41. 41.
    T. Araki, M. Tsubota, S.K. Nemirovskii, Phys. Rev. Lett. 89, 145301 (2002) CrossRefADSGoogle Scholar
  42. 42.
    W.F. Vinen, M. Tsubota, A. Mitani, Phys. Rev. Lett. 91, 135301 (2003) CrossRefADSGoogle Scholar
  43. 43.
    M. Tsubota, M. Kobayashi, AIP Conf. Proc. 850, 219 (2006) CrossRefADSGoogle Scholar
  44. 44.
    R. Hänninen, M. Tsubota, W.F. Vinen, Phys. Rev. B 75, 064502 (2007) CrossRefADSGoogle Scholar
  45. 45.
    S. Fujiyama, M. Tsubota, Phys. Rev. B 79, 094513 (2009) CrossRefADSGoogle Scholar
  46. 46.
    W.F. Vinen, Phys. Rev. B 71, 024513 (2005) CrossRefADSGoogle Scholar
  47. 47.
    C.F. Barenghi, D.C. Samuels, Phys. Rev. Lett. 89, 155302 (2002) CrossRefADSGoogle Scholar
  48. 48.
    W.F. Vinen, Phys. Rev. B. 71, 024513 (2005) CrossRefADSGoogle Scholar
  49. 49.
    C.F. Barenghi, Y.A. Sergeev, N. Suramlishvili, Phys. Rev. B 77, 104512 (2008) CrossRefADSGoogle Scholar
  50. 50.
    P.E. Roche, C.F. Barenghi, Europhys. Lett. 81, 36002 (2008) CrossRefADSGoogle Scholar
  51. 51.
    W.F. Vinen, J.J. Niemela, J. Low Temp. Phys. 128, 167 (2002) CrossRefGoogle Scholar
  52. 52.
    M. Tsubota, W.P. Halperin (eds.), Quantum Turbulence, Progress in Low Temperature Physics, vol. 16 (Elsevier, Amsterdam, 2009) Google Scholar
  53. 53.
    Quartz Tuning Forks, part label “KDS5M”, from KDS America/Daishinku Corporation Google Scholar
  54. 54.
    P. Skyba, S.M. Holt, Private communication, and to be published Google Scholar
  55. 55.
  56. 56.
    T. Sarpkaya, J. Fluid Mech. 165, 61 (1986) CrossRefADSGoogle Scholar
  57. 57.
    J.R. Morison, M.P. O’Brien, J.W. Johnson, S.A. Schaaf, Trans. Am. Inst. Min. Metall. Eng. 189, 149 (1950) Google Scholar
  58. 58.
    C.H.K. Williamson, J. Fluid Mech. 155, 141 (1985) CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • D. I. Bradley
    • 1
  • M. J. Fear
    • 1
  • S. N. Fisher
    • 1
  • A. M. Guénault
    • 1
  • R. P. Haley
    • 1
  • C. R. Lawson
    • 1
  • P. V. E. McClintock
    • 1
  • G. R. Pickett
    • 1
  • R. Schanen
    • 1
  • V. Tsepelin
    • 1
  • L. A. Wheatland
    • 1
  1. 1.Department of PhysicsLancaster UniversityLancasterUK

Personalised recommendations