- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Turbulence and large-scale structures in self-gravitating superfluids

Sanjay Shukla*

  • *Contact author: s.shukla@tue.nl
PDF

Phys. Rev. Fluids 10, 114601 – Published 3 November, 2025

DOI: https://doi.org/10.1103/7jtd-kybt

Abstract

I study turbulence in self-gravitating superfluids by performing direct numerical simulations of the three-dimensional (3D) Gross-Pitaevskii-Poisson (GPP) equation, which is also a model for dark-matter halos around galaxies. In the absence of self-gravity, the spectrally truncated Gross-Pitaevskii (GP) equation shows the emergence of Kolmogorov's 5/3 scaling in the incompressible kinetic-energy spectrum. Introducing self-gravity, I observe the formation of different structures, from sheetlike to spherically collapsed structures, which introduce a minimum in the kinetic-energy spectrum that corresponds to the sizes of these structures. The system shows early convergence towards statistically stationary states, which I show by the onset of thermalization in the compressible kinetic-energy spectrum, where Ekinc∝k2. I also show that the formation of such large-scale structures suggests that the particles (bosons) move from small to large scales through an inverse cascade, supporting a mechanism for the formation of large-scale structures, such as dark-matter halos, around our galaxy Milky Way.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (47)

  1. C. Cichowlas, P. Bonaïti, F. Debbasch, and M. Brachet, Effective dissipation and turbulence in spectrally truncated euler flows, Phys. Rev. Lett. 95, 264502 (2005).
  2. J. Maurer and P. Tabeling, Local investigation of superfluid turbulence, Europhys. Lett. 43, 29 (1998).
  3. M. S. Paoletti and D. P. Lathrop, Quantum turbulence, Annu. Rev. Condens. Matter Phys. 2, 213 (2011).
  4. E. A. L. Henn, J. A. Seman, G. Roati, K. M. F. Magalhães, and V. S. Bagnato, Emergence of turbulence in an oscillating bose-einstein condensate, Phys. Rev. Lett. 103, 045301 (2009).
  5. N. G. Berloff, M. Brachet, and N. P. Proukakis, Modeling quantum fluid dynamics at nonzero temperatures, Proc. Natl. Acad. Sci. USA 111, 4675 (2014).
  6. M. Kobayashi and M. Tsubota, Kolmogorov spectrum of superfluid turbulence: Numerical analysis of the Gross-Pitaevskii equation with a small-scale dissipation, Phys. Rev. Lett. 94, 065302 (2005).
  7. M. Kobayashi and M. Tsubota, Thermal dissipation in quantum turbulence, Phys. Rev. Lett. 97, 145301 (2006).
  8. G. Krstulovic, Kelvin-wave cascade and dissipation in low-temperature superfluid vortices, Phys. Rev. E 86, 055301(R) (2012).
  9. A. K. Verma, R. Pandit, and M. E. Brachet, Rotating self-gravitating Bose-Einstein condensates with a crust: A model for pulsar glitches, Phys. Rev. Res. 4, 013026 (2022).
  10. L. V. Drummond and A. Melatos, Stability of interlinked neutron vortex and proton flux-tube arrays in a neutron star – II. Far-from-equilibrium dynamics, Mon. Not. R. Astron. Soc. 475, 910 (2018).
  11. S. Shukla, M. E. Brachet, and R. Pandit, Neutron-superfluid vortices and proton-superconductor flux tubes: Development of a minimal model for pulsar glitches, Phys. Rev. D 110, 083002 (2024).
  12. P.-H. Chavanis, Mass-radius relation of Newtonian self-gravitating Bose-Einstein condensates with short-range interactions. I. analytical results, Phys. Rev. D 84, 043531 (2011).
  13. E. J. M. Madarassy and V. T. Toth, Evolution and dynamical properties of Bose-Einstein condensate dark matter stars, Phys. Rev. D 91, 044041 (2015).
  14. A. Suárez, V. H. Robles, and T. Matos, A review on the scalar field/Bose-Einstein condensate dark matter model, Astrophys. Space Sci. Proc. 38, 107 (2014).
  15. P.-H. Chavanis, Phase transitions between dilute and dense axion stars, Phys. Rev. D 98, 023009 (2018).
  16. S. Shukla, A. K. Verma, M. E. Brachet, and R. Pandit, Gravity- and temperature-driven phase transitions in a model for collapsed axionic condensates, Phys. Rev. D 109, 063009 (2024).
  17. J. Skipp, V. L'vov, and S. Nazarenko, Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics, Phys. Rev. A 102, 043318 (2020).
  18. J. Koplik and H. Levine, Vortex reconnection in superfluid helium, Phys. Rev. Lett. 71, 1375 (1993).
  19. J. Koplik and H. Levine, Scattering of superfluid vortex rings, Phys. Rev. Lett. 76, 4745 (1996).
  20. M. Leadbeater, T. Winiecki, D. C. Samuels, C. F. Barenghi, and C. S. Adams, Sound emission due to superfluid vortex reconnections, Phys. Rev. Lett. 86, 1410 (2001).
  21. R. M. Kerr, Vortex stretching as a mechanism for quantum kinetic energy decay, Phys. Rev. Lett. 106, 224501 (2011).
  22. C. Rorai, K. R. Sreenivasan, and M. E. Fisher, Propagating and annihilating vortex dipoles in the Gross-Pitaevskii equation, Phys. Rev. B 88, 134522 (2013).
  23. M. Kobayashi, P. Parnaudeau, F. Luddens, C. Lothodé, L. Danaila, M. Brachet, and I. Danaila, Quantum turbulence simulations using the Gross–Pitaevskii equation: High-performance computing and new numerical benchmarks, Comput. Phys. Commun. 258, 107579 (2021).
  24. S. Shukla, G. Krstulovic, and R. Pandit, Capture and release of quantum vortices using mechanical devices in low-temperature superfluids, Phys. Rev. B 111, L100504 (2025).
  25. R. Feynman, Chapter II Application of Quantum Mechanics to Liquid Helium in Progress in Low Temperature Physics, edited by C. J. Gorter (Elsevier, 1955), pp. 17–53.
  26. S.-i. Ogawa, M. Tsubota, and Y. Hattori, Study of reconnection and acoustic emission of quantized vortices in superfluid by the numerical analysis of the Gross–Pitaevskii equation, J. Phys. Soc. Jpn. 71, 813 (2002).
  27. C. Nore, M. Abid, and M. E. Brachet, Decaying Kolmogorov turbulence in a model of superflow, Phys. Fluids 9, 2644 (1997).
  28. C. Nore, M. Abid, and M. E. Brachet, Kolmogorov turbulence in low-temperature superflows, Phys. Rev. Lett. 78, 3896 (1997).
  29. T. Araki, M. Tsubota, and S. K. Nemirovskii, Energy spectrum of superfluid turbulence with no normal-fluid component, Phys. Rev. Lett. 89, 145301 (2002).
  30. J. I. Polanco, N. P. Müller, and G. Krstulovic, Vortex clustering, polarization and circulation intermittency in classical and quantum turbulence, Nat. Commun. 12, 7090 (2021).
  31. U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1995).
  32. C.-K. Chan, D. Mitra, and A. Brandenburg, Dynamics of saturated energy condensation in two-dimensional turbulence, Phys. Rev. E 85, 036315 (2012).
  33. G. Boffetta and R. E. Ecke, Two-dimensional turbulence, Annu. Rev. Fluid Mech. 44, 427 (2012).
  34. M. K.-H. Kiessling, The “Jeans swindle”: A true story—mathematically speaking, Adv. Appl. Math. 31, 132 (2003).
  35. M. Falco, S. H. Hansen, R. Wojtak, and G. A. Mamon, Why does the jeans swindle work? Mon. Not. R. Astron. Soc. Lett. 431, L6 (2013).
  36. N. P. Proukakis and B. Jackson, Finite-temperature models of Bose-Einstein condensation, J. Phys. B: At. Mol. Opt. Phys. 41, 203002 (2008).
  37. S.-J. Sin, Late-time phase transition and the galactic halo as a Bose liquid, Phys. Rev. D 50, 3650 (1994).
  38. Y. Sofue and V. Rubin, Rotation curves of spiral galaxies, Annu. Rev. Astron. Astrophys. 39, 137 (2001).
  39. T. Y. Hou and R. Li, Computing nearly singular solutions using pseudo-spectral methods, J. Comput. Phys. 226, 379 (2007).
  40. G. I. Taylor and A. E. Green, Mechanism of the production of small eddies from large ones, Proc. R. Soc. Lond. A 158, 499 (1937).
  41. Y. B. Zel'dovich, Gravitational instability: An approximate theory for large density perturbations, Astron. Astrophys. 5, 84 (1970).
  42. P. J. E. Peebles, The Large-Scale Structure of the Universe (Princeton University Press, 1980).
  43. C. F. Barenghi, L. Skrbek, and K. R. Sreenivasan, Introduction to quantum turbulence, Proc. Natl. Acad. Sci. USA 111, 4647 (2014).
  44. G. Krstulovic and M. Brachet, Dispersive bottleneck delaying thermalization of turbulent Bose-Einstein condensates, Phys. Rev. Lett. 106, 115303 (2011).
  45. K. Kirkpatrick, A. E. Mirasola, and C. Prescod-Weinstein, Relaxation times for Bose-Einstein condensation in axion miniclusters, Phys. Rev. D 102, 103012 (2020).
  46. M. Abid, C. Huepe, S. Metens, C. Nore, C. T. Pham, L. S. Tuckerman, and M. E. Brachet, Gross-Pitaevskii dynamics of Bose-Einstein condensates and superfluid turbulence, Fluid Dyn. Res. 33, 509 (2003).
  47. L. Warszawski and A. Melatos, Gross-Pitaevskii model of pulsar glitches, Mon. Not. R. Astron. Soc. 415, 1611 (2011).

Outline

Information

Phys. Rev. Fluids 10, 114601– Published 3 November, 2025
  • Received 28 February 2025
  • Accepted 14 October 2025
Crossmark - Check for updates button

©2025 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation