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Spontaneous vortex crystal formation in classical rotating flows

Gabriel Marchetti and Pablo D. Mininni

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Phys. Rev. Fluids 10, 084603 – Published 21 August, 2025

DOI: https://doi.org/10.1103/t6fj-cvtz

Abstract

Vortex crystals, ordered structures observed in superconductors and rotating superfluids, have also been hypothesized to form in classical fluids, based on numerical simulations and observations of the Jovian polar atmospheres. We perform direct numerical simulations of the Navier-Stokes equations in rotating frames, to investigate the spontaneous emergence of metastable vortex crystals. We analyze the energy spectrum, vortex morphology, and spatiotemporal dynamics to understand their roles in crystal formation and evolution. In addition, we explore domains with varying aspect ratios to examine their impact on the vortex lattice. Our results indicate a relationship between the crystal lifespan and dissipation, and we propose a scaling law linking the rotation rate, domain geometry, and vortex lattice periodicity. Finally, we identify a critical threshold in the control parameter, the Rossby number, suggesting a behavior similar to that found in phase transitions.

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References (58)

  1. R. H. Kraichnan and D. Montgomery, Two-dimensional turbulence, Rep. Prog. Phys. 43, 547 (1980).
  2. X.-P. Huang and C. F. Driscoll, Relaxation of 2D turbulence to a metaequilibrium near the minimum enstrophy state, Phys. Rev. Lett. 72, 2187 (1994).
  3. K. S. Fine, A. C. Cass, W. G. Flynn, and C. F. Driscoll, Relaxation of 2D turbulence to vortex crystals, Phys. Rev. Lett. 75, 3277 (1995).
  4. J. Jiménez and A. Guegan, Spontaneous generation of vortex crystals from forced two-dimensional homogeneous turbulence, Phys. Fluids 19, 085103 (2007).
  5. H. Xia, D. Byrne, G. Falkovich, and M. Shats, Upscale energy transfer in thick turbulent fluid layers, Nat. Phys. 7, 321 (2011).
  6. A. Sen, P. D. Mininni, D. Rosenberg, and A. Pouquet, Anisotropy and nonuniversality in scaling laws of the large-scale energy spectrum in rotating turbulence, Phys. Rev. E 86, 036319 (2012).
  7. A. Adriani, A. Mura, G. Orton et al., Clusters of cyclones encircling Jupiter's poles, Nature (London) 555, 216 (2018).
  8. A. Pouquet, R. Marino, P. D. Mininni, and D. Rosenberg, Dual constant-flux energy cascades to both large scales and small scales, Phys. Fluids 29, 111108 (2017).
  9. A. Alexakis, R. Marino, P. D. Mininni, A. van Kan, R. Foldes, and F. Feraco, Large-scale self-organization in dry turbulent atmospheres, Science 383, 1005 (2024).
  10. G. Boffetta and R. E. Ecke, Two-dimensional turbulence, Annu. Rev. Fluid Mech. 44, 427 (2012).
  11. M. Hossain, Inverse energy cascades in three-dimensional turbulence, Phys. Fluids B 3, 511 (1991).
  12. P. D. Mininni, D. C. Montgomery, and A. G. Pouquet, A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows, Phys. Fluids 17, 035112 (2005).
  13. A. Alexakis, P. D. Mininni, and A. Pouquet, On the inverse cascade of magnetic helicity, Astrophys. J. 640, 335 (2006).
  14. P. D. Mininni, Inverse cascades and α effect at a low magnetic Prandtl number, Phys. Rev. E 76, 026316 (2007).
  15. L. Biferale, M. Buzzicotti, and M. Linkmann, From two-dimensional to three-dimensional turbulence through two-dimensional three-component flows, Phys. Fluids 29, 111101 (2017).
  16. A. Alexakis and L. Biferale, Cascades and transitions in turbulent flows, Phys. Rep. 767–769, 1 (2018).
  17. A. van Kan, B. Favier, K. Julien, and E. Knobloch, From a vortex gas to a vortex crystal in instability-driven two-dimensional turbulence, J. Fluid Mech. 984, A41 (2024).
  18. F. Waleffe, Inertial transfers in the helical decomposition, Phys. Fluids 5, 677 (1993).
  19. C. Cambon, N. N. Mansour and F. S. Godeferd, Energy transfer in rotating turbulence, J. Fluid Mech. 337, 303 (1997).
  20. C. Cambon, R. Rubinstein, and F. S. Godeferd, Advances in wave turbulence: Rapidly rotating flows, New J. Phys. 6, 73 (2004).
  21. P. D. Mininni, P. Dmitruk, W. H. Matthaeus, and A. Pouquet, Large-scale behavior and statistical equilibria in rotating flows, Phys. Rev. E 83, 016309 (2011).
  22. L. M. Smith and F. Waleffe, Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence, Phys. Fluids 11, 1608 (1999).
  23. A. Campagne, B. Gallet, F. Moisy, and P.-P. Cortet, Direct and inverse energy cascades in a forced rotating turbulence experiment, Phys. Fluids 26, 125112 (2014).
  24. M. Buzzicotti, P. Clark Di Leoni, and L. Biferale, On the inverse energy transfer in rotating turbulence, Eur. Phys. J. E 41, 131 (2018).
  25. P. Davidson, Turbulence in Rotating, Stratified and Electrically Conducting Fluids (Cambridge University Press, Cambridge, UK, 2013).
  26. H. Aref, P. Newton, M. Stremler, T. Tokieda, and D. Vainchtein, Vortex crystals, Adv. Appl. Mech. 39, 1 (2003).
  27. L. Siegelman, W. R. Young, and A. P. Ingersoll, Polar vortex crystals: Emergence and structure, Proc. Natl. Acad. Sci. USA 119, e2120486119 (2022).
  28. T. Sakajo, Vortex crystals on the surface of a torus, Philos. Trans. R. Soc. A 377, 20180344 (2019).
  29. A. A. Abrikosov, On the Magnetic properties of superconductors of the second group, Sov. Phys. JETP 5, 1174 (1957).
  30. W. H. Kleiner, L. M. Roth, and S. H. Autler, Bulk solution of Ginzburg-Landau equations for type II superconductors: Upper critical field region, Phys. Rev. 133, A1226 (1964).
  31. V. K. Tkachenko, Stability of vortex lattices, Sov. J. Exp. Theor. Phys. 23, 1049 (1966).
  32. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Harcourt College, San Diego, CA, 1976).
  33. P. Clark Di Leoni, A. Alexakis, L. Biferale, and M. Buzzicotti, Phase transitions and flux-loop metastable states in rotating turbulence, Phys. Rev. Fluids 5, 104603 (2020).
  34. P. K. Newton and G. Chamoun, Vortex lattice theory: A particle interaction perspective, SIAM Rev. 51, 501 (2009).
  35. A. L. Fetter, Rotating trapped Bose-Einstein condensates, Rev. Mod. Phys. 81, 647 (2009).
  36. E. H. Brandt, Elastic and plastic properties of the flux-line lattice in type-II superconductors, Phys. Rev. B 34, 6514 (1986).
  37. J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, Observation of vortex lattices in Bose-Einstein condensates, Science 292, 476 (2001).
  38. C. Peretti, J. Vessaire, É. Durozoy, and M. Gibert, Direct visualization of the quantum vortex lattice structure, oscillations, and destabilization in rotating He4, Sci. Adv. 9, eadh2899 (2023).
  39. J. A. Estrada, M. E. Brachet, and P. D. Mininni, Thermalized Abrikosov lattices from decaying turbulence in rotating BECs, AVS Quantum Sci. 4, 046201 (2022).
  40. V. Fernandez-Gonzalez, M. Clerc, G. González-Cortés, P. Hidalgo, and J. Vergara, Abrikosov clusters in chiral liquid crystal droplets, Rep. Prog. Phys. 87, 120502 (2024).
  41. X. M. de Wit, M. Fruchart, T. Khain, F. Toschi, and V. Vitelli, Pattern formation by turbulent cascades, Nature (London) 627, 515 (2024).
  42. M. James, D. Suchla, J. Dunkel et al., Emergence and melting of active vortex crystals, Nat. Commun. 12, 5630 (2021).
  43. A. van Kan, Phase transitions in anisotropic turbulence, Chaos 34, 122103 (2024).
  44. B. M. Boubnov and G. S. Golitsyn, Experimental study of convective structures in rotating fluids, J. Fluid Mech. 167, 503 (1986).
  45. B. M. Boubnov and G. S. Golitsyn, Temperature and velocity field regimes of convective motions in a rotating plane fluid layer, J. Fluid Mech. 219, 215 (1990).
  46. B. M. Boubnov and G. S. Golitsyn, Convection in Rotating Fluids, Fluid Mechanics and Its Applications (Springer, Dordrecht, 2012).
  47. F. Zhong, R. Ecke, and V. Steinberg, Asymmetric modes and the transition to vortex structures in rotating Rayleigh-Bénard convection, Phys. Rev. Lett. 67, 2473 (1991).
  48. A. Alexakis, Helically decomposed turbulence, J. Fluid Mech. 812, 752 (2017).
  49. P. D. Mininni, D. Rosenberg, R. Reddy, and A. Pouquet, A hybrid MPI–OpenMP scheme for scalable parallel pseudospectral computations for fluid turbulence, Parallel Comput. 37, 316 (2011).
  50. D. Rosenberg, P. D. Mininni, R. Reddy, and A. Pouquet, GPU parallelization of a hybrid pseudospectral geophysical turbulence framework using CUDA, Atmosphere 11, 178 (2020).
  51. L. M. Smith and Y. Lee, On near resonances and symmetry breaking in forced rotating flows at moderate Rossby number, J. Fluid Mech. 535, 111 (2005).
  52. F. Moisy, C. Morize, M. Rabaud, and J. Sommeria, Decay laws, anisotropy and cyclone–anticyclone asymmetry in decaying rotating turbulence, J. Fluid Mech. 666, 5 (2011).
  53. B. Gallet, A. Campagne, P.-P. Cortet, and F. Moisy, Scale-dependent cyclone-anticyclone asymmetry in a forced rotating turbulence experiment, Phys. Fluids 26, 035108 (2014).
  54. F. Aurenhammer, Voronoi diagrams—A survey of a fundamental geometric data structure, ACM Comput. Surv. 23, 345 (1991).
  55. R. Chalmeta, F. Hurtado, V. Sacristán, and M. Saumell, Measuring regularity of convex polygons, Comput. Aided Des. 45, 93 (2013).
  56. J. Meijering, Interface area, edge length, and number of vertices in crystal aggregates with random nucleation, Philips Res. Rep. 8, 270 (1953).
  57. A. Hinde and R. Miles, Monte Carlo estimates of the distributions of the random polygons of the Voronoi tessellation with respect to a Poisson process, J. Stat. Comput. Simul. 10, 205 (1980).
  58. P. Clark di Leoni and P. D. Mininni, Quantifying resonant and near-resonant interactions in rotating turbulence, J. Fluid Mech. 809, 821 (2016).

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Phys. Rev. Fluids 10, 084603– Published 21 August, 2025
  • Received 8 April 2025
  • Accepted 29 July 2025
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