Acta Applicandae Mathematicae

, Volume 122, Issue 1, pp 407–418 | Cite as

Turbulent Superfluid Profiles and Vortex Density Waves in a Counterflow Channel

Article
First Online:
Received:
Accepted:

Abstract

In this paper we study the two-dimensional profiles of the superfluid component velocity and the quantized vortex-points density in a counterflow channel where the influence of the walls cannot be neglected. The numerical results obtained show the presence of vortex density waves in the channel, as shown in a recent paper by means of the one-fluid model.

Keywords

Superfluid helium Quantized vortices Vortex waves Counterflow channels One-fluid model 
This is a preview of subscription content, log in to check access.

References

  1. 1.
    Landau, L.: J. Phys. USSR 5, 71 (1941) Google Scholar
  2. 2.
    Landau, L.: J. Phys. USSR 11, 91 (1947) Google Scholar
  3. 3.
    Landau, L.: Phys. Rev. 75, 884 (1949) CrossRefGoogle Scholar
  4. 4.
    London, F.: Superfluids, vol. 2. Wiley, New York (1954) MATHGoogle Scholar
  5. 5.
    Andronikashvili, E.L.: J. Phys. USSR 10, 21 (1946) Google Scholar
  6. 6.
    Allen, J.F., Jones, H.: Nature 141, 243 (1938) CrossRefGoogle Scholar
  7. 7.
    Mehl, J.B., Zimmermann, W.: Phys. Rev. 167, 214 (1968) CrossRefGoogle Scholar
  8. 8.
    Langer, J.S., Reppy, J.D.: Progress in Low Temperature Physics, vol. VI. North Holland, Amsterdam (1970) Google Scholar
  9. 9.
    Hall, H., Vinen, W.: Proc. R. Soc. Lond. A 238, 204 (1956) CrossRefGoogle Scholar
  10. 10.
    Hall, H., Vinen, W.: Proc. R. Soc. Lond. A 238, 215 (1956) MATHCrossRefGoogle Scholar
  11. 11.
    Onsager, L.: Nuovo Cimento 6, 249 (1949) MathSciNetGoogle Scholar
  12. 12.
    Feynman, R.: Prog. Low Temp. Phys. 1, 36 (1955) Google Scholar
  13. 13.
    Childers, R.K., Tough, J.T.: Phys. Rev. B 13, 1040 (1976) CrossRefGoogle Scholar
  14. 14.
    Ladner, D.R., Tough, J.T.: Phys. Rev. B 20, 2690 (1979) CrossRefGoogle Scholar
  15. 15.
    Martin, K.P., Tough, J.T.: Phys. Rev. B 27, 2788 (1983) CrossRefGoogle Scholar
  16. 16.
    Melotte, D.J., Barenghi, C.F.: Phys. Rev. Lett. 80, 4181 (1998) CrossRefGoogle Scholar
  17. 17.
    Mongioví, M.S., Jou, D.: J. Phys., Condens. Matter 17, 4423 (2005) CrossRefGoogle Scholar
  18. 18.
    Jou, D., Lebon, G., Mongiovì, M.S.: Phys. Rev. B 66, 224509 (2002) CrossRefGoogle Scholar
  19. 19.
    Mongioví, M.S., Jou, D.: Phys. Rev. B 75, 024507 (2007) CrossRefGoogle Scholar
  20. 20.
    Müller, I., Ruggeri, T.: Rational Extended Thermodynamics. Springer, New York (1998) MATHCrossRefGoogle Scholar
  21. 21.
    Jou, D., Casas-Vázquez, J., Lebon, G.: Extended Irreversible Thermodynamics. Springer, Berlin (2010) MATHCrossRefGoogle Scholar
  22. 22.
    Bewley, G.P., Lathrop, D.P., Sreenivasan, K.: Nature 441, 588 (2006) CrossRefGoogle Scholar
  23. 23.
    Zhang, T., Van Sciver, S.W.: Nat. Phys. 1, 36 (2005) CrossRefGoogle Scholar
  24. 24.
    Guo, W., Cahn, S.B., Nikkel, J.A., Vinen, W.F., McKinsey, D.N.: Phys. Rev. Lett. 105, 045301 (2010) CrossRefGoogle Scholar
  25. 25.
    Galantucci, L., Barenghi, C.F., Sciacca, M., Quadrio, M., Luchini, P.: J. Low Temp. Phys. 162, 354 (2011) CrossRefGoogle Scholar
  26. 26.
    Schwarz, K.: Phys. Rev. B 38, 2398 (1988) CrossRefGoogle Scholar
  27. 27.
    Hills, R.N., Roberts, P.H.: Arch. Ration. Mech. Anal. 66, 43 (1977) MathSciNetMATHCrossRefGoogle Scholar
  28. 28.
    Greengard, L.: SIAM J. Sci. Stat. Comput. 11, 603 (1990) MathSciNetMATHCrossRefGoogle Scholar
  29. 29.
    Schwarz, K.: Phys. Rev. Lett. 49, 283 (1982) CrossRefGoogle Scholar
  30. 30.
    Schwarz, K.: Phys. Rev. B 31, 5782 (1985) CrossRefGoogle Scholar
  31. 31.
    Koplik, J., Levine, H.: Phys. Rev. Lett. 71, 1375 (1993) CrossRefGoogle Scholar
  32. 32.
    Geurst, J.A.: Phys. Lett. 71, 78 (1979) CrossRefGoogle Scholar
  33. 33.
    Liu, I.: Arch. Ration. Mech. Anal. 46, 131 (1972) MATHGoogle Scholar
  34. 34.
    Jou, D., Mongioví, M.S., Sciacca, M.: Phys. Lett. A 368, 7 (2007) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria StrutturalePolitecnico di MilanoMilanoItaly
  2. 2.Dipartimento SAgAUniversità degli studi di PalermoPalermoItaly

Personalised recommendations