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Acoustic Turbulence in Superfluid 4He

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Abstract

Recent work on nonlinear second sound wave propagation and acoustic turbulence in superfluid 4He is reviewed. Observations of direct and inverse turbulent energy cascades are described. The direct cascade arises due to the huge nonlinear dependence of the second sound wave velocity on its amplitude. The flux of energy injected at the driving frequency is transformed via successively higher harmonics until it is eventually attenuated by viscous dissipation at the short wavelength edge of the spectrum. The onset of the inverse cascade occurs above a critical driving energy density, and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomena is outlined and shown to be in good agreement with the experiments.

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References

  1. A.N. Kolmogorov, Dokl. Akad. Nauk SSSR 30, 299 (1941)

    ADS  Google Scholar 

  2. V.E. Zakharov, V.S. L’vov, G. Falkovich, Kolmogorov Spectra of Turbulence I (Springer, Berlin, 1992)

    MATH  Google Scholar 

  3. U. Frisch, Turbulence (Cambridge University Press, Cambridge, 1995)

    MATH  Google Scholar 

  4. P.A. Davidson, Turbulence: An Introduction for Scientists and Engineers (Oxford University Press, Oxford, 2004)

    MATH  Google Scholar 

  5. F.P. Incropera, D.P. DeWitt, Fundamentals of Heat Transfer (Wiley, New York, 1981)

    Google Scholar 

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

    Article  Google Scholar 

  7. W.F. Vinen, J. Low Temp. Phys. 145, 7 (2006)

    Article  ADS  Google Scholar 

  8. V.S. Tsoi, Cent. Eur. J. Phys. 1, 72 (2003)

    Article  Google Scholar 

  9. S.N. Gurbatov, V.V. Kurin, L.M. Kustov, N.V. Pronchatov-Rubtsov, Acoust. Phys. 51, 152 (2005)

    Article  ADS  Google Scholar 

  10. G.S. Bisnovatyi-Kogan, S.A. Silich, Rev. Mod. Phys. 67, 661 (1995)

    Article  ADS  Google Scholar 

  11. M. Ryutova, T. Tarbell, Phys. Rev. Lett. 90, 191101 (2003)

    Article  ADS  Google Scholar 

  12. G.V. Kolmakov, V.B. Efimov, A.N. Ganshin, P.V.E. McClintock, L.P. Mezhov-Deglin, Phys. Rev. Lett. 97, 155301 (2006)

    Article  ADS  Google Scholar 

  13. L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Butterworth and Heinemann, Oxford, 1987)

    MATH  Google Scholar 

  14. I.M. Khalatnikov, An Introduction to the Theory of Superfluidity (Benjamin, New York, 1965)

    Google Scholar 

  15. C.C. Ackerman, B. Bertman, H.A. Fairbank, R.A. Guyer, Phys. Rev. Lett. 16, 789 (1966)

    Article  ADS  Google Scholar 

  16. S.J. Putterman, Superfluid Hydrodynamics (North-Holland, Amsterdam, 1974)

    Google Scholar 

  17. A.Y. Iznankin, L.P. Mezhov-Deglin, Sov. Phys. JETP 57, 801 (1983)

    Google Scholar 

  18. I.Y. Borisenko, V.B. Efimov, L.P. Mezhov-Deglin, Sov. J. Low Temp. Phys. 14, 619 (1988)

    Google Scholar 

  19. L.P. Mezhov-Deglin, A.Y. Iznankin, V.P. Mineev, JETP Lett. 32, 199 (1980)

    ADS  Google Scholar 

  20. L.S. Goldner, G. Ahlers, R. Mehrotra, Phys. Rev. B 43, 12861 (1991)

    Article  ADS  Google Scholar 

  21. S.K. Nemirovskii, Sov. Phys. Usp. 33, 429 (1990)

    Article  ADS  Google Scholar 

  22. A.J. Dessler, W.H. Fairbank, Phys. Rev. 104, 6 (1956)

    Article  ADS  Google Scholar 

  23. H.N.V. Temperley, Proc. Phys. Soc. (Lond.) A 64, 105 (1951)

    Article  MATH  ADS  Google Scholar 

  24. D.V. Osborne, Proc. Phys. Soc. (Lond.) A 64, 114 (1951)

    Article  ADS  Google Scholar 

  25. R.J. Atkin, N. Fox, J. Phys. C: Solid State Phys. 18, 1585 (1985)

    Article  ADS  Google Scholar 

  26. V.B. Efimov, G.V. Kolmakov, E.V. Lebedeva, L.P. Mezhov-Deglin, A.B. Trusov, J. Low Temp. Phys. 119, 309 (2000)

    Article  Google Scholar 

  27. J.A. Tyson, D.H. Douglass Jr., Phys. Rev. Lett. 21, 1308 (1968)

    Article  ADS  Google Scholar 

  28. A.N. Ganshin, V.B. Efimov, G.V. Kolmakov, L.P. Mezhov-Deglin, P.V.E. McClintock, Phys. Rev. Lett. 101, 065303 (2008)

    Article  ADS  Google Scholar 

  29. A.I. Dyachenko, V.E. Zakharov, JETP Lett. 81, 255 (2005)

    Article  ADS  Google Scholar 

  30. D.R. Solli, C. Ropers, P. Koonath, B. Jalali, Nature 450, 1054 (2007)

    Article  ADS  Google Scholar 

  31. P.W. Anderson, H. Suhl, Phys. Rev. 100, 1788 (1955)

    Article  ADS  Google Scholar 

  32. V.S. L’vov, Wave Turbulence under Parametric Excitation. Application to Magnetics (Springer, Berlin, 1994)

    Google Scholar 

  33. T. Matsushita, R. Nomura, H.H. Hensley, H. Shiga, T. Mizusaki, J. Low Temp. Phys. 105, 67 (1996)

    Article  ADS  Google Scholar 

  34. S.R. Spangler, J.A. Leckband, I.H. Cairns, Phys. Plasmas 4, 846 (1997)

    Article  ADS  Google Scholar 

  35. D. Rinberg, V. Cherepanov, V. Steinberg, Phys. Rev. Lett. 76, 2105 (1996)

    Article  ADS  Google Scholar 

  36. V.B. Efimov, A.N. Ganshin, P.V.E. McClintock, G.V. Kolmakov, L.P. Mezhov-Deglin, J. Low Temp. Phys. 145, 155 (2006)

    Article  ADS  Google Scholar 

  37. H. Davidowitz, Y. L’vov, V. Steinberg, Physica D 84, 635 (1995)

    Article  Google Scholar 

  38. V.B. Efimov, G.V. Kolmakov, A.S. Kuliev, L.P. Mezhov-Deglin, Low Temp. Phys. 24, 81 (1998)

    Article  ADS  Google Scholar 

  39. I.Y. Borisenko, L.P. Mezhov-Deglin, V.Z. Rozenflantz, Prib. Tekh. Exp. 5, 137 (1987)

    Google Scholar 

  40. L.S. Goldner, N. Mulders, G. Ahlers, J. Low Temp. Phys. 93, 131 (1993)

    Article  ADS  Google Scholar 

  41. A. Ganshin, N. Mulders, Phys. Rev. B 69, 172502 (2004)

    Article  ADS  Google Scholar 

  42. P.V.E. McCintock, V.B. Efimov, A.N. Ganshin, G.V. Kolmakov, L.P. Mezhov-Deglin, J. Low Temp. Phys. 150, 394 (2008)

    Article  ADS  Google Scholar 

  43. V.B. Efimov, A.N. Ganshin, G.V. Kolmakov, P.V.E. McClintock, L.P. Mezhov-Deglin, in Let’s Face Chaos Through Nonlinear Dynamics, ed. by M. Robnik, V. Romanovski. Proc. of 7th Intern. Summer School and Conf. in Maribor. AIP Conf. Proc., vol. 1076 (AIP, Melville, 2008), pp. 53–62

    Google Scholar 

  44. A.N. Ganshin, P.V.E. McClintock, V.B. Efimov, G.V. Kolmakov, L.P. Mezhov-Deglin, Low Temp. Phys. 34, 288 (2008)

    Article  ADS  Google Scholar 

  45. G.V. Kolmakov, M.Y. Brazhnikov, A.A. Levchenko, A.V. Abdurakhimov, P.V.E. McClintock, L.P. Mezhov-Deglin, in Progress in Low Temperature Physics: Quantum Turbulence, vol. 16, ed. by W.P. Halperin, M. Tsubota (Elsevier, Amsterdam, 2009), pp. 303–349

    Google Scholar 

  46. R.L. Devaney, An Introduction to Chaotic Dynamical Systems (Addison-Wesley, Reading, 2000)

    Google Scholar 

  47. G. Falkovich, M. Meyer, Phys. Rev. E 54, 4431 (1996)

    Article  ADS  Google Scholar 

  48. P.A. Franken, A.E. Hill, C.W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961)

    Article  ADS  Google Scholar 

  49. K.N. Zinov’eva, Sov. Phys. JETP 4, 36 (1957)

    Google Scholar 

  50. V.B. Efimov, A.N. Ganshin, P.V.E. McClintock, Phys. Rev. E 78, 066611 (2008)

    Article  ADS  Google Scholar 

  51. W. Chester, J. Fluid Mech. 18, 44 (1964)

    Article  MATH  ADS  Google Scholar 

  52. E. Falcon, C. Laroche, S. Fauve, Phys. Rev. Lett. 98, 094503 (2007)

    Article  ADS  Google Scholar 

  53. L.V. Abdurakhimov, M.Y. Brazhnikov, A.A. Levchenko, JETP Lett. 88, 19 (2008)

    Article  ADS  Google Scholar 

  54. V.L. Pokrovskii, I.M. Khalatnikov, Sov. Phys. JETP 44, 1036 (1976)

    ADS  Google Scholar 

  55. B.B. Kadomtsev, V.I. Petviashvili, Sov. Phys. Dokl. 15, 539 (1970)

    MATH  ADS  Google Scholar 

  56. V.E. Zakharov, R.Z. Sagdeev, Dokl. Akad. Nauk SSSR 15, 439 (1970)

    MATH  Google Scholar 

  57. L.S. Goldner, G. Ahlers, R. Mehrotra, Physica B 165, 539 (1990)

    ADS  Google Scholar 

  58. L. Mandelstam, N. Papalexi, Z. Phys. 73, 223 (1932)

    Article  ADS  Google Scholar 

  59. M. Onorato, A.R. Osborne, M. Serio, S. Bertone, Phys. Rev. Lett. 86, 5831 (2001)

    Article  ADS  Google Scholar 

  60. R.G. Dean, in Water Wave Kinetics, ed. by A. Torum, O.T. Gudmestad (Kluwer, Amsterdam, 1990), pp. 609–612

    Google Scholar 

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Author notes

  1. G. V. Kolmakov

    Present address: Department of Chemical and Petroleum Engineering, Pittsburgh University, Pittsburgh, PA, 15261, USA

Authors and Affiliations

  1. Department of Physics, Lancaster University, Lancaster, A1 4YB, UK

    V. B. Efimov, A. N. Ganshin & P. V. E. McClintock

  2. Institute of Solid State Physics RAS, 142432, Chernogolovka, Russia

    V. B. Efimov, G. V. Kolmakov & L. P. Mezhov-Deglin

Authors
  1. V. B. Efimov
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  2. A. N. Ganshin
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  3. G. V. Kolmakov
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  4. P. V. E. McClintock
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  5. L. P. Mezhov-Deglin
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Correspondence to P. V. E. McClintock.

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Efimov, V.B., Ganshin, A.N., Kolmakov, G.V. et al. Acoustic Turbulence in Superfluid 4He. J Low Temp Phys 156, 95–115 (2009). https://doi.org/10.1007/s10909-009-9894-y

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  • DOI: https://doi.org/10.1007/s10909-009-9894-y

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