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Energy Transfer of the Gross-Pitaevskii Turbulence in Weak-Wave-Turbulence and Strong-Turbulence Ranges

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Abstract

Numerical simulations of quantum fluid turbulence obeying the Gross-Pitaevskii equation are performed with the simulation sizes as large as the weak-wave-turbulence and the strong-turbulence wavenumber ranges coexist in one simulation. The energy cascade is observed within the simulated wavenumber range. The spectrum F(k) in the weak-wave-turbulence range agrees with the \(k^{-1}\) scaling without logarithmic correction suggested by a closure approximation (Yoshida and Arimitsu in J Phys A Math Theor 46(33):335501, 2013) and the slope of F(k) in the strong-turbulence range is steeper than that suggested in the same closure approximation. The energy flow from the interaction energy to the kinetic energy during the cascade is also observed.

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References

  1. C.F. Barehnghi, L. Skrbek, K.R. Sreenivasan, Introduction to quantum turbulence. Proc. Natl. Acad. Sci. USA 111, 4647–4652 (2014)

    Article  ADS  Google Scholar 

  2. M. Tsubota, K. Fujimoto, S. Yui, Numerical studies of quantum turbulence. J. Low Temp. Phys. 188, 119–189 (2017)

    Article  ADS  Google Scholar 

  3. L.P. Pitaevskii, Vortex lines in an imperferct Bose gas. Sov. Phys. JETP 13, 451–454 (1961)

    Google Scholar 

  4. E.P. Gross, Hydrodynamics of superfluid condensate. J. Math. Phys. 4, 195–207 (1963)

    Article  ADS  Google Scholar 

  5. L. Pitaevskii, S. Stringari, Bose-Einstain Condensation (Oxford University Press, Oxford, 2003)

    MATH  Google Scholar 

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

  7. S. Nazareko, Wave Turbulence. Lecture Notes in Physics, vol. 825. Springer (2011)

  8. S. Dyachenko, A.C. Newell, A. Pushkarev, V.E. Zakharov, Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation. Physica D 57, 96–160 (1992)

    Article  ADS  MATH  Google Scholar 

  9. K. Yoshida, T. Arimitsu, Inertial-range structure of Gross-Pitaevskii turbulence within a spectral closure approximation. J. Phys. A: Math. Theor. 46(33), 335501 (2013)

    Article  MATH  Google Scholar 

  10. Y. Zhou, Turbulence theories and statistical closure approaches. Physics Reports 935, 1–117 (2021). https://doi.org/10.1016/j.physrep.2021.07.001 Turbulence theories and statistical closure approaches

  11. C. Nore, M. Abid, M.E. Brachet, Decaying Kolmogorov turbulence in a model of superflow. Phys. Fluids 9, 2644–2669 (1997)

    Article  ADS  MATH  Google Scholar 

  12. M. Kobayashi, M. Tsubota, Kolmogorov spectrum of quantum turbulence. J. Phys. Soc. Jpn. 74, 3248–3258 (2005)

    Article  ADS  MATH  Google Scholar 

  13. G. Krstulovic, M. Brachet, Energy cascade with small-scale thermalization, counterflow metastability, and anomalous velocity rings in fourier-truncated gross-pitaveskii equation. Phys. Rev. E 83, 066311 (2011)

    Article  ADS  Google Scholar 

  14. D. Proment, S. Nazarenko, M. Onorato, Quantum turbulence cascades in the gross-pitaevskii model. Phys. Rev. A 80, 051603 (2009)

    Article  ADS  Google Scholar 

  15. K. Yoshida, H. Miura, Y. Tsuji, Specturm in the storing turbulence region of Gross-Pitaevskii turbulence. J. Low Temp. Phys. 196(1–2), 211–217 (2019)

    Article  ADS  Google Scholar 

  16. K. Yoshida, T. Arimitsu, Energy spectra in quantum fluid turbulence. J. Low Temp. Phys. 145(1–4), 219–230 (2006)

    Article  ADS  Google Scholar 

  17. M.C. Tsatsos, P.E.S. Tavares, A. Cidrim, A.R. Fritsch, M.A. Caracanhas, F.E.A. dos Santos, C.F. Barenghi, V.S. Bagnato, Quantum turbulence in trapped atomic bose-einstein condensates. Physics Reports 622, 1–52 (2016). https://doi.org/10.1016/j.physrep.2016.02.003 Quantum turbulence in trapped atomic Bose-Einstein condensates

  18. N. Navon, A.L. Gaunt, R.P. Smith, Z. Hadzibabic, Emergence of a turbulent cascade in a quantum gas. Nature 539, 72–75 (2016)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was performed on “Plasma Simulator” (FUJITSU FX100, NEC SX-Aurora TSUBASA) of NIFS with the support and under the auspices of the NIFS Collaboration Research program (NIFS18KNSS106, NIFS20KNSS144).

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Authors and Affiliations

  1. Faculty of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba, 305-8571, Ibaraki, Japan

    Kyo Yoshida

  2. Department of Helical Plasma Reserarch, National Institute for Fusion Science, 322-6 Oroshi-cho, Toki, 509-5292, Gifu, Japan

    Hideaki Miura

  3. Department of Energy Science and Engineering, Nagoya University, Furo-sho, Chikusa, Naoyga, 464-8601, Aichi, Japan

    Yoshiyuki Tsuji

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  1. Kyo Yoshida
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Correspondence to Kyo Yoshida.

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The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Yoshida, K., Miura, H. & Tsuji, Y. Energy Transfer of the Gross-Pitaevskii Turbulence in Weak-Wave-Turbulence and Strong-Turbulence Ranges. J Low Temp Phys 210, 103–112 (2023). https://doi.org/10.1007/s10909-022-02819-4

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  • DOI: https://doi.org/10.1007/s10909-022-02819-4

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