Journal of Low Temperature Physics

, Volume 196, Issue 1–2, pp 211–217 | Cite as

Spectrum in the Strong Turbulence Region of Gross–Pitaevskii Turbulence

  • Kyo YoshidaEmail author
  • Hideaki Miura
  • Yoshiyuki Tsuji


Numerical simulations of the Gross–Pitaevskii equation which describes the dynamics of quantum fluids are performed focusing on scales larger than the healing length. Dissipation and pumping of the mass are applied in high and low wavenumber ranges, respectively, in order to achieve turbulent states. In this setting of dissipation and pumping, it is found that the mass, or the particle number, cascades from low to high wavenumbers and a constant flux of the particle number is observed in the cascading wavenumber range. The spectrum F(k) (k is the wavenumber) of the order parameter field at the turbulent state is analyzed, and it is found that the obtained F(k) is consistent with the form \(\propto k^{-1}[\ln (k/k_0)]^{-1}\) (\(k_0\) is the lower-end wavenumber of the scaling range) which is derived from a closure approximation of the particle-number transfer range of strong turbulence (Yoshida and Arimitsu in J Phys A Math Theor 46(33):335501, 2013).


Quantum fluid Turbulence Gross–Pitaevskii equation Bose–Einstein condensate 



This work was performed on “Plasma Simulator” (FUJITSU FX100) of NIFS with the support and under the auspices of the NIFS Collaboration Research programs (NIFS15KNSS064, NIFS18KNSS106). Development of some numerical codes used in this work was supported in part by the “Code development support program” of Numerical Simulation Reactor Research Project (NSRP), NIFS. The authors are grateful to N. Ohno and H. Ontani for the permission to use the visualization tool VISMO in this work.


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Authors and Affiliations

  1. 1.Division of Physics, Faculty of Pure and Applied SciencesUniversity of TsukubaTsukubaJapan
  2. 2.National Institute for Fusion ScienceTokiJapan
  3. 3.Graduate School of EngineeringNagoya UniversityNagoyaJapan

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