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Analysis of the Energy Budget in Quantum Turbulence: HVBK Model

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Abstract

In this work, we analyze numerically the superfluid energy budget based on the Hall–Vinen–Bekarevich–Khalatnikov model, using a large eddy simulations (LES). First, LES predictions of freely decaying isotropic superfluid turbulence have shown the effect of different temperatures range and spatial resolutions. We furthermore investigate deviations from the KO-41 spectrum caused by intermittency effects. A second motivation of our work is the following: For homogeneous turbulence at very high Reynolds numbers, comparison of the terms in the spectral kinetic energy budget equation indicates, in the energy-containing range, that the production and energy-transfer effects become significant except for dissipation. In the inertial range, where the two fluids are perfectly locked, the mutual friction may be neglected with respect to other terms. Also, the LES results for the other terms of the energy balance are presented.

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References

  1. A. N. Kolmogorov, C. R. Acad. Sci. URSS 30, 301 (1941)

  2. A.N. Kolmogorov, C. R. Acad. Sci. URSS 32, 16 (1941)

    MATH  Google Scholar 

  3. W.F. Vinen, J. Phys. Chem. Solids 66, 1493 (2005)

    Article  ADS  Google Scholar 

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

  5. I.M. Khalatnikov, An Introduction to the Theory of Superfluidity (Perseus Publishing, Cambridge, UK, 1989)

    Google Scholar 

  6. C.F. Barenghi, C.J. Swanson, R.J. Donnelly, J. Low Temp. Phys. 100, 385 (1995)

    Article  ADS  Google Scholar 

  7. K.L. Henderson, C.F. Barenghi, J. Low Temp. Phys. 134, 959 (2004)

  8. L. Merahi, P. Sagaut, M. Abidat, J. Europhys. Lett. 75, 757 (2006)

    Article  ADS  Google Scholar 

  9. P.-E. Roche, C.F. Barenghi, E. Lévêque, EPL 87, 54006 (2009)

    Article  ADS  Google Scholar 

  10. J. Salort, P.-E. Roche, E. Lévêque, EPL 94, 24001 (2011)

    Article  ADS  Google Scholar 

  11. J. Tchoufag, P. Sagaut, Phys. Fluids 22, 125103 (2010)

    Article  ADS  Google Scholar 

  12. J.H. Silvestrini, E. Lamballais, M. Lesieur, Int. J. Heat Fluid Flow 19, 492 (1998)

    Article  Google Scholar 

  13. R. S. Rogallo, NASA Technical Report, TM-73, 203 (1977)

  14. C.F. Barenghi, V.S. L’vov, P.-E. Roche, arXiv:1306.6248v1 (2013)

  15. V.S. L’vov, S.V. Nazarenko, L. Skrbek, J. Low Temp. Phys. 145, 125 (2006)

  16. J.P. Chollet, M. Lesieur, J. Atmos. Sci. 38, 2747 (1981)

    Article  ADS  Google Scholar 

  17. A.W. Baggaley, C.F. Barenghi, A. Shukurov, Y.A. Sergeev, Europhys. Lett. 98, 26002 (2012)

    Article  ADS  Google Scholar 

  18. J.P. Chollet, M. Lesieur, La Météorologie 29–30, 183 (1982)

    Google Scholar 

  19. M. Kobayashi, M. Tsubota, J. Phys. Rev. Lett. 94, 065302 (2005)

    Article  ADS  Google Scholar 

  20. U. Frisch, Turbulence. The legacy of A.N. Kolmogorov (Cambridge University Press, Cambridge, UK, 1995)

    MATH  Google Scholar 

  21. J. Maurer, P. Tabeling, Europhys. Lett. 43, 29 (1998)

    Article  ADS  Google Scholar 

  22. J. Salort, B. Chabaud, E. Lévêque, and P.-E. Roche, in Proceedings of the 13th EUROMECH European Turbulence Conference, Journal of Physics: Conference Series, vol. 318, Sept 12–15, 2011, Warsaw (IOP Publishing, Warsaw, 2011), p. 042014

  23. J. Salort, B. Chabaud, E. Lévêque, P.-E. Roche, Europhys. Lett. 97, 34006 (2012)

    Article  ADS  Google Scholar 

  24. L. Boué, V. L’vov, A. Pomyalov, I. Procaccia, Phys. Rev. Lett. 110, 014502 (2013)

    Article  ADS  Google Scholar 

  25. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, UK, 2003)

    Google Scholar 

  26. G.K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge University Press, London, UK, 1953)

    MATH  Google Scholar 

  27. D.H. Wacks, C.F. Barenghi, Phys. Rev. B 84, 184505 (2011)

    Article  ADS  Google Scholar 

  28. P. Bradshaw, D.H. Ferriss, The Spectral Energy Balance in a Turbulent Mixing Layer (Her Majesty’s Stationery Office, London, 1967)

  29. N.N. Mansour, J. Kim, P. Moin, J. Fluid Mech. 194, 15 (1988)

  30. C.W. Van Atta, W.Y. Chen, J. Fluid Mech. 38, 743 (1969)

    Article  ADS  Google Scholar 

  31. J.L. Lumley, Phys. Fluids 7, 190 (1964)

  32. W.F. Vinen, J. Low Temp. Phys. 121, 367 (2000)

    Article  ADS  Google Scholar 

  33. C.F. Barenghi, R.J. Donnelly, W.F. Vinen, LNP 571, 17 (2001)

    Google Scholar 

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Acknowledgments

We are extremely grateful to Professor M. Abidat, laboratory director, for the opportunity to have this remarkable gathering here and for his contribution to various aspects of this work.

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Authors and Affiliations

  1. Laboratoire de Mécanique Appliquée, Université des sciences et de la Technologie (USTMB), BP 1505, El Mnouar Oran, Algeria

    M. Bakhtaoui & L. Merahi

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  1. M. Bakhtaoui
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  2. L. Merahi
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Correspondence to L. Merahi.

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Bakhtaoui, M., Merahi, L. Analysis of the Energy Budget in Quantum Turbulence: HVBK Model. J Low Temp Phys 178, 129–141 (2015). https://doi.org/10.1007/s10909-014-1256-8

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  • DOI: https://doi.org/10.1007/s10909-014-1256-8

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