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

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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.

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References

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  3. D.I. Bradley, Phys. Rev. Lett. 84, 1252 (2000)

    Article  ADS  Google Scholar 

  4. S.N. Fisher, A.J. Hale, A.M. Guénault, G.R. Pickett, Phys. Rev. Lett. 86, 244 (2001)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  6. H. Yano, A. Handa, H. Nakagawa, K. Obara, O. Ishikawa, T. Hara, M. Nakagawa, J. Low Temp. Phys. 138, 561 (2005)

    Article  ADS  Google Scholar 

  7. H. Yano, A. Handa, H. Nakagawa, K. Obara, O. Ishikawa, T. Hata, J. Phys. Chem. Solids 66, 1501 (2005)

    Article  ADS  Google Scholar 

  8. H. Yano, N. Hashimoto, A. Handa, M. Nakagawa, K. Obara, O. Ishikawa, T. Hata, Phys. Rev. B 75, 012502 (2007)

    Article  ADS  Google Scholar 

  9. N. Hashimoto, R. Goto, H. Yano, K. Obara, O. Ishikawa, T. Hata, Phys. Rev. B 76, 020504 (2007)

    Article  ADS  Google Scholar 

  10. N. Hashimoto, A. Handa, M. Nakagawa, K. Obara, H. Yano, O. Ishikawa, T. Hata, J. Low Temp. Phys. 148, 299 (2007)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  12. J. Martikainen, J. Tuoriniemi, T. Knuuttila, G.R. Pickett, J. Low Temp. Phys. 126, 139 (2002)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  17. H.A. Nichol, L. Skrbek, P.C. Hendry, P.V.E. McClintock, Phys. Rev. E 70, 056307 (2004)

    Article  ADS  Google Scholar 

  18. D. Charalambous, L. Skrbek, P.C. Hendry, P.V.E. McClintock, W.F. Vinen, Phys. Rev. E 74, 036307 (2006)

    Article  ADS  Google Scholar 

  19. J. Jäger, B. Schuderer, W. Schoepe, Phys. Rev. Lett. 74, 566 (1995)

    Article  ADS  Google Scholar 

  20. M. Niemetz, H. Kerscher, W. Schoepe, J. Low Temp. Phys. 126, 287 (2002)

    Article  Google Scholar 

  21. M. Niemetz, W. Schoepe, J. Low Temp. Phys. 135, 447 (2004)

    Article  ADS  Google Scholar 

  22. W. Schoepe, Phys. Rev. Lett. 92, 095301 (2004)

    Article  ADS  Google Scholar 

  23. R. Hänninen, W. Schoepe, J. Low Temp. Phys. 153, 189 (2008)

    Article  ADS  Google Scholar 

  24. W. Schoepe, J. Low Temp. Phys. 150, 724 (2008)

    Article  ADS  Google Scholar 

  25. J. Luzuriaga, J. Low Temp. Phys. 108, 561 (1997)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  27. M. Blaz̆ková, M. C̆lovec̆ko, E. Gaz̆o, L. Skrbek, P. Skyba, J. Low Temp. Phys. 148, 305 (2007)

    Article  ADS  Google Scholar 

  28. M. Blaz̆ková, D. Schmoranzer, L. Skrbek, Phys. Rev. E 75, 025302 (2007)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  30. M. Blaz̆ková, T.V. Chagovets, M. Rotter, D. Schmoranzer, L. Skrbek, J. Low Temp. Phys. 150, 194 (2008)

    Article  ADS  Google Scholar 

  31. G.A. Sheshin, A.A. Zadorozhko, E.Y. Rudavskii, V.K. Chagovets, L. Skrbek, M. Blaz̆ková, Low Temp. Phys. 34, 875 (2008)

    Article  ADS  Google Scholar 

  32. E.M. Pentti, J.T. Tuoriniemi, A.J. Salmela, A.P. Sebedash, J. Low Temp. Phys. 150, 555 (2008)

    Article  ADS  Google Scholar 

  33. M. Blaz̆ková, D. Schmoranzer, L. Skrbek, W.F. Vinen, Phys. Rev. B 79, 054522 (2009)

    Article  ADS  Google Scholar 

  34. S.N. Fisher, A.M. Guénault, C.J. Kennedy, G.R. Pickett, Phys. Rev. Lett. 63, 2566 (1989)

    Article  ADS  Google Scholar 

  35. S.N. Fisher, G.R. Pickett, R.J. Watts-Tobin, J. Low Temp. Phys. 83, 225 (1991)

    Article  ADS  Google Scholar 

  36. M.P. Enrico, S.N. Fisher, R.J. Watts-Tobin, J. Low Temp. Phys. 98, 81 (1995)

    Article  ADS  Google Scholar 

  37. C. Bauerle, Y.M. Bunkov, S.N. Fisher, H. Godfrin, Phys. Rev. B 57, 14381 (1998)

    Article  ADS  Google Scholar 

  38. D.O. Clubb, O.V.L. Buu, R.M. Bowley, R. Nyman, J.R. Owers-Bradley, J. Low Temp. Phys. 136, 1 (2004)

    Article  ADS  Google Scholar 

  39. M. Tsubota, T. Araki, S.K. Nemirovskii, Phys. Rev. B 62, 11751 (2000)

    Article  ADS  Google Scholar 

  40. D. Kivotides, J.C. Vassilicos, D.C. Samuels, C.F. Barenghi, Phys. Rev. Lett. 86, 3080 (2001)

    Article  ADS  Google Scholar 

  41. T. Araki, M. Tsubota, S.K. Nemirovskii, Phys. Rev. Lett. 89, 145301 (2002)

    Article  ADS  Google Scholar 

  42. W.F. Vinen, M. Tsubota, A. Mitani, Phys. Rev. Lett. 91, 135301 (2003)

    Article  ADS  Google Scholar 

  43. M. Tsubota, M. Kobayashi, AIP Conf. Proc. 850, 219 (2006)

    Article  ADS  Google Scholar 

  44. R. Hänninen, M. Tsubota, W.F. Vinen, Phys. Rev. B 75, 064502 (2007)

    Article  ADS  Google Scholar 

  45. S. Fujiyama, M. Tsubota, Phys. Rev. B 79, 094513 (2009)

    Article  ADS  Google Scholar 

  46. W.F. Vinen, Phys. Rev. B 71, 024513 (2005)

    Article  ADS  Google Scholar 

  47. C.F. Barenghi, D.C. Samuels, Phys. Rev. Lett. 89, 155302 (2002)

    Article  ADS  Google Scholar 

  48. W.F. Vinen, Phys. Rev. B. 71, 024513 (2005)

    Article  ADS  Google Scholar 

  49. C.F. Barenghi, Y.A. Sergeev, N. Suramlishvili, Phys. Rev. B 77, 104512 (2008)

    Article  ADS  Google Scholar 

  50. P.E. Roche, C.F. Barenghi, Europhys. Lett. 81, 36002 (2008)

    Article  ADS  Google Scholar 

  51. W.F. Vinen, J.J. Niemela, J. Low Temp. Phys. 128, 167 (2002)

    Article  Google Scholar 

  52. M. Tsubota, W.P. Halperin (eds.), Quantum Turbulence, Progress in Low Temperature Physics, vol. 16 (Elsevier, Amsterdam, 2009)

    Google Scholar 

  53. Quartz Tuning Forks, part label “KDS5M”, from KDS America/Daishinku Corporation

  54. P. Skyba, S.M. Holt, Private communication, and to be published

  55. K. Karrai (eds.), Lecture notes (2000). At http://www.nano.physik.uni-muenchen.de/publikationen/Preprints/p-00-03_Karrai.pdf

  56. T. Sarpkaya, J. Fluid Mech. 165, 61 (1986)

    Article  ADS  Google Scholar 

  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. C.H.K. Williamson, J. Fluid Mech. 155, 141 (1985)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Lancaster University, Lancaster, UK

    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

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  1. D. I. Bradley
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  2. M. J. Fear
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Correspondence to R. P. Haley.

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Bradley, D.I., Fear, M.J., Fisher, S.N. et al. Transition to Turbulence for a Quartz Tuning Fork in Superfluid 4He. J Low Temp Phys 156, 116–131 (2009). https://doi.org/10.1007/s10909-009-9901-3

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