- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Turbulent diffusion and dispersion in a superfluid

Yuan Tang, Sosuke Inui, Yiming Xing, Yinghe Qi, and Wei Guo*

  • *Contact author: wguo@magnet.fsu.edu
PDF

Phys. Rev. Research 7, 043215 – Published 24 November, 2025

DOI: https://doi.org/10.1103/2hdj-qnw3

Abstract

Single-body diffusion and two-body dispersion are fundamental processes in classical turbulence, governing particle mixing and transport. However, their behaviors in superfluid turbulence remain largely unexplored. In this study, we numerically investigate the diffusion and relative dispersion of both quantized vortices and superfluid parcels in the 0 K limit in two distinct turbulence regimes: ultraquantum turbulence, characterized by a randomized vortex tangle, and quasiclassical turbulence, in which locally polarized vortices create large-scale flows resembling classical turbulence. Our results reveal that while vortex segments exhibit similar superdiffusion behavior at short times in both regimes, superfluid parcels behave differently—following the same superdiffusion scaling in ultraquantum turbulence but deviating significantly in quasiclassical turbulence. This contrast provides a key clue to the origin of short-time superdiffusion, a puzzle since its recent discovery. Additionally, we show that two-body dispersion of both vortex segments and superfluid parcels exhibits distinct scaling behaviors in ultraquantum and quasiclassical turbulence, highlighting fundamental differences in these two turbulence regimes. Our findings bridge a critical gap in superfluid turbulence research, offering useful insights into turbulent transport in inviscid quantum fluids.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (48)

  1. K. R. Sreenivasan, Turbulent mixing: A perspective, Proc. Natl. Acad. Sci. USA 116, 18175 (2019).
  2. P. A. Davidson, Turbulence: An Introduction for Scientists and Engineers (Oxford University Press, Oxford, UK, 2004).
  3. S. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, UK, 2000).
  4. L. F. Richardson, Atmospheric diffusion shown on a distance-neighbour graph, Proc. R. Soc. London A 110, 709 (1926).
  5. G. K. Batchelor, The effect of homogeneous turbulence on material lines and surfaces, Proc. R. Soc. London A 213, 349 (1952).
  6. R. Bitane, H. Homann, and J. Bec, Time scales of turbulent relative dispersion, Phys. Rev. E 86, 045302 (2012).
  7. P. K. Yeung, Direct numerical simulation of two‐particle relative diffusion in isotropic turbulence, Phys. Fluids 6, 3416 (1994).
  8. B. L. Sawford, Turbulent relative dispersion, Annu. Rev. Fluid Mech. 33, 289 (2001).
  9. G. Boffetta and I. M. Sokolov, Statistics of two-particle dispersion in two-dimensional turbulence, Phys. Fluids 14, 3224 (2002).
  10. F. Toschi and E. Bodenschatz, Lagrangian properties of particles in turbulence, Annu. Rev. Fluid Mech. 41, 375 (2009).
  11. J. P. Salazar and L. R. Collins, Two-particle dispersion in isotropic turbulent flows, Annu. Rev. Fluid Mech. 41, 405 (2009).
  12. S. Tan and R. Ni, Universality and intermittency of pair dispersion in turbulence, Phys. Rev. Lett. 128, 114502 (2022).
  13. R. Shnapp, S. Brizzolara, M. M. Neamtu-Halic, H. Xu, E. Ben-Naim, A. Pumir, H. Xu, and E. Bodenschatz, Universal alignment in turbulent pair dispersion, Nat. Commun. 14, 4195 (2023).
  14. W. F. Vinen and J. J. Niemela, Quantum turbulence, J. Low Temp. Phys. 128, 167 (2002).
  15. D. R. Tilley and J. Tilley, Superfluidity and Superconductivity, 3rd ed. (Institute of Physics Publishing, Bristol, 1990).
  16. J. Koplik and H. Levine, Vortex reconnection in superfluid helium, Phys. Rev. Lett. 71, 1375 (1993).
  17. G. E. Volovik, Classical and quantum regimes of superfluid turbulence, JETP Lett. 78, 533 (2003).
  18. P. Walmsley, D. Zmeev, F. Pakpour, and A. Golov, Dynamics of quantum turbulence of different spectra, Proc. Natl. Acad. Sci. USA 111, 4691 (2014).
  19. A. W. Baggaley, J. Laurie, and C. F. Barenghi, Vortex-density fluctuations, energy spectra, and vortical regions in superfluid turbulence, Phys. Rev. Lett. 109, 205304 (2012).
  20. Y. Tang, S. Bao, T. Kanai, and W. Guo, Statistical properties of homogeneous and isotropic turbulence in He ii measured via particle tracking velocimetry, Phys. Rev. Fluids 5, 084602 (2020).
  21. Y. Tang, W. Guo, V. S. L’vov, and A. Pomyalov, Eulerian and Lagrangian second-order statistics of superfluid He4 grid turbulence, Phys. Rev. B 103, 144506 (2021).
  22. P. M. Walmsley and A. I. Golov, Quantum and quasiclassical types of superfluid turbulence, Phys. Rev. Lett. 100, 245301 (2008).
  23. P. Z. Stasiak, Y. Xing, Y. Alihosseini, C. F. Barenghi, A. Baggaley, W. Guo, L. Galantucci, and G. Krstulovic, Experimental and theoretical evidence of universality in superfluid vortex reconnections, Proc. Natl. Acad. Sci. USA 122, e2426064122 (2025).
  24. E. Fonda, D. P. Meichle, N. T. Ouellette, S. Hormoz, and D. P. Lathrop, Direct observation of Kelvin waves excited by quantized vortex reconnection, Proc. Natl. Acad. Sci. USA 111, 4707 (2014).
  25. E. Kozik and B. Svistunov, Kelvin-wave cascade and decay of superfluid turbulence, Phys. Rev. Lett. 92, 035301 (2004).
  26. V. S. L’vov, S. V. Nazarenko, and O. Rudenko, Bottleneck crossover between classical and quantum superfluid turbulence, Phys. Rev. B 76, 024520 (2007).
  27. L. Boué, V. S. L’vov, A. Nagar, S. V. Nazarenko, A. Pomyalov, and I. Procaccia, Energy and vorticity spectra in turbulent superfluid helium from T=0 to T=Tλ, Phys. Rev. B 91, 144501 (2015).
  28. J. Gao, E. Varga, W. Guo, and W. F. Vinen, Energy spectrum of thermal counterflow turbulence in superfluid helium-4, Phys. Rev. B 96, 094511 (2017).
  29. E. Rickinson, N. G. Parker, A. W. Baggaley, and C. F. Barenghi, Inviscid diffusion of vorticity in low-temperature superfluid helium, Phys. Rev. B 99, 224501 (2019).
  30. M. Tsubota, T. Araki, and W. F. Vinen, Diffusion of an inhomogeneous vortex tangle, Phys. B: Condens. Matter 329-333, 224 (2003).
  31. Y. Tang, S. Bao, and W. Guo, Superdiffusion of quantized vortices uncovering scaling laws in quantum turbulence, Proc. Natl. Acad. Sci. USA 118, e2021957118 (2021).
  32. R. Boltnev, M. Vasiliev, and O. Petrov, Two-dimensional Brownian motion of an active particle on superfluid helium surface, Sci. Rep. 13, 22538 (2023).
  33. S. Yui, Y. Tang, W. Guo, H. Kobayashi, and M. Tsubota, Universal anomalous diffusion of quantized vortices in ultraquantum turbulence, Phys. Rev. Lett. 129, 025301 (2022).
  34. D. R. Poole and C. F. Barenghi, Two-dimensional turbulence in a finite-size domain, J. Low Temp. Phys. 134, 483 (2004).
  35. C. Callegari and W. E. Ernst, Helium droplets as nanocryostats for molecular spectroscopy—From the vacuum ultraviolet to the microwave regime, in Handbook of High‐resolution Spectroscopy, edited by M. Quack and F. Merkt (John Wiley & Sons, Ltd., Hoboken, New Jersey, USA, 2011).
  36. J. P. Toennies and A. F. Vilesov, Superfluid helium droplets: A uniquely cold nanomatrix for molecules and molecular complexes, Angew. Chem. Int. Ed. 43, 2622 (2004).
  37. P. Moroshkin, V. Lebedev, B. Grobety, C. Neururer, and E. B. Gordon, Nanowire formation by gold nano-fragment coalescence on quantized vortices in He ii, Europhys. Lett. 90, 34002 (2010).
  38. E. B. Gordon, A. V. Karabulin, V. I. Matyushenko, V. D. Sizov, and I. I. Khodos, Production of ultrathin nanowires from refractory metals (Nb, Re, W, Mo) by laser ablation in superfluid helium, Laser Phys. Lett. 12, 096002 (2015).
  39. E. B. Gordon, A. V. Karabulin, M. I. Kulish, V. I. Matyushenko, and M. E. Stepanov, Coagulation of metals in superfluid and normal liquid helium, J. Phys. Chem. A 121, 9185 (2017).
  40. K. W. Schwarz, Three-dimensional vortex dynamics in superfluid He4: Homogeneous superfluid turbulence, Phys. Rev. B 38, 2398 (1988).
  41. M. Tsubota, T. Araki, and S. K. Nemirovskii, Dynamics of vortex tangle without mutual friction in superfluid He4, Phys. Rev. B 62, 11751 (2000).
  42. H. Adachi, S. Fujiyama, and M. Tsubota, Steady-state counterflow quantum turbulence: Simulation of vortex filaments using the full Biot-Savart law, Phys. Rev. B 81, 104511 (2010).
  43. A. W. Baggaley, The sensitivity of the vortex filament method to different reconnection models, J. Low Temp. Phys. 168, 18 (2012).
  44. O. Yurkina and S. K. Nemirovskii, On the energy spectrum of the 3D velocity field, generated by an ensemble of vortex loops, Low Temp. Phys. 47, 652 (2021).
  45. K. R. Sreenivasan, On the universality of the Kolmogorov constant, Phys. Fluids 7, 2778 (1995).
  46. B. L. Sawford, P. K. Yeung, and J. F. Hackl, Reynolds number dependence of relative dispersion statistics in isotropic turbulence, Phys. Fluids 20, 065111 (2008).
  47. M. S. Borgas and B. L. Sawford, A family of stochastic models for two-particle dispersion in isotropic homogeneous stationary turbulence, J. Fluid Mech. 279, 69 (1994).
  48. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C. The Art of Scientific Computing (Cambridge University Press, Cambridge, 1992).

Outline

Information

Phys. Rev. Research 7, 043215– Published 24 November, 2025
  • Received 31 March 2025
  • Accepted 1 October 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation