- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

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

Spatiotemporal Energy Cascade in Three-Dimensional Magnetohydrodynamic Turbulence

Giuseppe Arrò1, Hui Li1, and William H. Matthaeus2

PDF

Phys. Rev. Lett. 134, 235201 – Published 12 June, 2025

DOI: https://doi.org/10.1103/hx6s-8ns8

Abstract

We present a new scale decomposition method to investigate turbulence in wavenumber-frequency space. Using 3D magnetohydrodynamic turbulence simulations, we show that magnetic fluctuations with time scales longer than the nonlinear time exhibit an inverse cascade toward even smaller frequencies. Low frequency magnetic fluctuations support turbulence, acting as an energy reservoir that is converted into plasma kinetic energy, the latter cascading toward large wavenumbers and frequencies, where it is dissipated. Our results shed new light on the spatiotemporal properties of turbulence, potentially explaining the origin and role of low frequency turbulent fluctuations in the solar wind.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (78)

  1. R. Bruno and V. Carbone, Living Rev. Solar Phys. 10, 2 (2013).
  2. J. Armstrong, B. Rickett, and S. Spangler, Astrophys. J. 443, 209 (1995).
  3. S. A. Balbus and J. F. Hawley, Rev. Mod. Phys. 70, 1 (1998).
  4. I. Zhuravleva, E. Churazov, A. Schekochihin, S. Allen, P. Arévalo, A. Fabian, W. Forman, J. Sanders, A. Simionescu, R. Sunyaev et al., Nature (London) 515, 85 (2014).
  5. J. V. Shebalin, W. H. Matthaeus, and D. Montgomery, J. Plasma Phys. 29, 525 (1983).
  6. P. Goldreich and S. Sridhar, Astrophys. J. 438, 763 (1995).
  7. J. Cho and E. T. Vishniac, Astrophys. J. 539, 273 (2000).
  8. T. S. Horbury, M. Forman, and S. Oughton, Phys. Rev. Lett. 101, 175005 (2008).
  9. R. Wicks, T. Horbury, C. Chen, and A. Schekochihin, Mon. Not. R. Astron. Soc. 407, L31 (2010).
  10. S. S. Cerri, D. Grošelj, and L. Franci, Front. Astron. Space Sci. 6, 64 (2019).
  11. S. Oughton and W. H. Matthaeus, Astrophys. J. 897, 37 (2020).
  12. T. Parashar, S. Servidio, B. Breech, M. Shay, and W. Matthaeus, Phys. Plasmas 17 (2010).
  13. S. Markovskii and B. J. Vasquez, Astrophys. J. 903, 80 (2020).
  14. E. Papini, A. Cicone, L. Franci, M. Piersanti, S. Landi, P. Hellinger, and A. Verdini, Astrophys. J. Lett. 917, L12 (2021).
  15. X. Fu, H. Li, Z. Gan, S. Du, and J. Steinberg, Astrophys. J. 936, 127 (2022).
  16. Z. Gan, H. Li, X. Fu, and S. Du, Astrophys. J. 926, 222 (2022).
  17. Y. Narita, F. Sahraoui, M. Goldstein, and K.-H. Glassmeier, J. Geophys. Res. 115 (2010).
  18. L.-L. Zhao, G. Zank, M. Nakanotani, and L. Adhikari, Astrophys. J. 944, 98 (2023).
  19. O. Alexandrova, Nonlinear Processes Geophys. 15, 95 (2008).
  20. S. Lion, O. Alexandrova, and A. Zaslavsky, Astrophys. J. 824, 47 (2016).
  21. G. Zank, L.-L. Zhao, L. Adhikari, D. Telloni, J. Kasper, and S. Bale, Phys. Plasmas 28, 080501 (2021).
  22. G. Arrò, F. Pucci, F. Califano, M. E. Innocenti, and G. Lapenta, Astrophys. J. 958, 11 (2023).
  23. G. Arrò, F. Califano, F. Pucci, T. Karlsson, and H. Li, Astrophys. J. Lett. 970, L6 (2024).
  24. G. P. Zank, L.-L. Zhao, L. Adhikari, D. Telloni, P. Baruwal, P. Baruwal, X. Zhu, M. Nakanotani, A. Pitňa, J. C. Kasper et al., Astrophys. J. 966, 75 (2024).
  25. W. H. Matthaeus, M. L. Goldstein, and D. A. Roberts, J. Geophys. Res. 95, 20673 (1990).
  26. G. Zank and W. Matthaeus, J. Geophys. Res. 97, 17189 (1992).
  27. G. Zank, A. Dosch, P. Hunana, V. Florinski, W. Matthaeus, and G. Webb, Astrophys. J. 745, 35 (2011).
  28. C. Ng and A. Bhattacharjee, Astrophys. J. 465, 845 (1996).
  29. S. Galtier, S. Nazarenko, A. C. Newell, and A. Pouquet, J. Plasma Phys. 63, 447 (2000).
  30. P. Dmitruk and W. Matthaeus, Phys. Plasmas 16, 062304 (2009).
  31. K. H. Yuen, H. Li, and H. Yan, arXiv:2310.03806.
  32. P. Dmitruk and W. H. Matthaeus, Phys. Rev. E 76, 036305 (2007).
  33. P. Dmitruk, P. D. Mininni, A. Pouquet, S. Servidio, and W. H. Matthaeus, Phys. Rev. E 83, 066318 (2011).
  34. W. H. Matthaeus, G. P. Zank, S. Oughton, D. Mullan, and P. Dmitruk, Astrophys. J. 523, L93 (1999).
  35. P. Dmitruk, W. H. Matthaeus, L. Milano, S. Oughton, G. P. Zank, and D. Mullan, Astrophys. J. 575, 571 (2002).
  36. S. R. Cranmer, A. A. Van Ballegooijen, and R. J. Edgar, Astrophys. J. Suppl. Ser. 171, 520 (2007).
  37. S. R. Cranmer, M. Asgari-Targhi, M. P. Miralles, J. C. Raymond, L. Strachan, H. Tian, and L. N. Woolsey, Phil. Trans. R. Soc. A 373, 20140148 (2015).
  38. W. H. Matthaeus and M. L. Goldstein, Phys. Rev. Lett. 57, 495 (1986).
  39. W. Matthaeus, B. Breech, P. Dmitruk, A. Bemporad, G. Poletto, M. Velli, and M. Romoli, Astrophys. J. 657, L121 (2007).
  40. J. Giacalone and J. Jokipii, Astrophys. J. 520, 204 (1999).
  41. H. Yan and A. Lazarian, Phys. Rev. Lett. 89, 281102 (2002).
  42. H. Yan and A. Lazarian, Astrophys. J. 614, 757 (2004).
  43. H. H. Klahr and P. Bodenheimer, Astrophys. J. 582, 869 (2003).
  44. T. Sano, S.-i. Inutsuka, N. J. Turner, and J. M. Stone, Astrophys. J. 605, 321 (2004).
  45. R. B. Larson, Mon. Not. R. Astron. Soc. 194, 809 (1981).
  46. N. Schneider, S. Bontemps, R. Simon, V. Ossenkopf, C. Federrath, R. S. Klessen, F. Motte, P. André, J. Stutzki, and C. Brunt, Astron. Astrophys. 529, A1 (2011).
  47. A. A. Schekochihin, S. C. Cowley, S. F. Taylor, J. L. Maron, and J. C. McWilliams, Astrophys. J. 612, 276 (2004).
  48. Y. Ponty, H. Politano, and J.-F. Pinton, Phys. Rev. Lett. 92, 144503 (2004).
  49. A. Beresnyak, Phys. Rev. Lett. 108, 035002 (2012).
  50. Y. Yang, Y. Shi, M. Wan, W. H. Matthaeus, and S. Chen, Phys. Rev. E 93, 061102(R) (2016).
  51. Y. Yang, W. H. Matthaeus, T. N. Parashar, C. C. Haggerty, V. Roytershteyn, W. Daughton, M. Wan, Y. Shi, and S. Chen, Phys. Plasmas 24, 102308 (2017).
  52. W. H. Matthaeus, Y. Yang, M. Wan, T. N. Parashar, R. Bandyopadhyay, A. Chasapis, O. Pezzi, and F. Valentini, Astrophys. J. 891, 101 (2020).
  53. G. Arrò, F. Califano, and G. Lapenta, Astron. Astrophys. 668, A33 (2022).
  54. A. Favre, Soc. Indust. 231 (1969).
  55. See Supplemental Material at http://link.aps.org/supplemental/10.1103/hx6s-8ns8 for equations derivation and additional simulations information.
  56. G. L. Eyink, J. Fluid Mech. 549, 159 (2006).
  57. J. M. Stone, K. Tomida, C. J. White, and K. G. Felker, Astrophys. J. Suppl. Ser. 249, 4 (2020).
  58. J. TenBarge, G. G. Howes, W. Dorland, and G. W. Hammett, Comput. Phys. Commun. 185, 578 (2014).
  59. R. Bandyopadhyay, L. Sorriso-Valvo, A. Chasapis, P. Hellinger, W. H. Matthaeus, A. Verdini, S. Landi, L. Franci, L. Matteini, B. L. Giles et al., Phys. Rev. Lett. 124, 225101 (2020).
  60. S. Du, H. Li, X. Fu, and Z. Gan, Astrophys. J. 948, 72 (2023).
  61. P. Hellinger, A. Verdini, V. Montagud-Camps, L. Franci, E. Papini, L. Matteini, and S. Landi, Astron. Astrophys. 684, A120 (2024).
  62. V. Eswaran and S. B. Pope, Comput. Fluids 16, 257 (1988).
  63. J. TenBarge and G. Howes, Phys. Plasmas 19 (2012).
  64. U. Frisch, Turbulence: The Legacy of AN Kolmogorov (Cambridge University Press, Cambridge, England, 1995).
  65. O. Alexandrova, C. H. Chen, L. Sorriso-Valvo, T. S. Horbury, and S. D. Bale, Space Sci. Rev. 178, 101 (2013).
  66. J. Squire, R. Meyrand, M. W. Kunz, L. Arzamasskiy, A. A. Schekochihin, and E. Quataert, Nat. Astron. 6, 715 (2022).
  67. E. Papini, L. Franci, S. Landi, A. Verdini, L. Matteini, and P. Hellinger, Astrophys. J. 870, 52 (2019).
  68. G. Arrò, F. Califano, and G. Lapenta, Astron. Astrophys. 642, A45 (2020).
  69. B. K. Arbic, R. B. Scott, G. R. Flierl, A. J. Morten, J. G. Richman, and J. F. Shriver, J. Phys. Oceanogr. 42, 1577 (2012).
  70. B. K. Arbic, M. Müller, J. G. Richman, J. F. Shriver, A. J. Morten, R. B. Scott, G. Sérazin, and T. Penduff, J. Phys. Oceanogr. 44, 2050 (2014).
  71. A. K. O’Rourke, B. K. Arbic, and S. M. Griffies, J. Climate 31, 1789 (2018).
  72. G. Sérazin, T. Penduff, B. Barnier, J.-M. Molines, B. K. Arbic, M. Müller, and L. Terray, J. Phys. Oceanogr. 48, 1385 (2018).
  73. P. E. Martin, B. K. Arbic, and A. M. Hogg, J. Climate 34, 3975 (2021).
  74. A. Mondal, A. J. Morten, B. K. Arbic, G. R. Flierl, R. B. Scott, and J. Skitka, arXiv:2405.02259.
  75. F. Fraternale, L. Zhao, N. V. Pogorelov, L. Sorriso-Valvo, S. Redfield, M. Zhang, K. Ghanbari, V. Florinski, and T. Y. Chen, Front. Astron. Space Sci. 9, 1064098 (2022).
  76. C. Chen, S. Bale, J. Bonnell, D. Borovikov, T. Bowen, D. Burgess, A. Case, B. Chandran, T. D. de Wit, K. Goetz et al., Astrophys. J. Suppl. Ser. 246, 53 (2020).
  77. U. Frisch, A. Pouquet, J. Léorat, and A. Mazure, J. Fluid Mech. 68, 769 (1975).
  78. A. Alexakis, P. D. Mininni, and A. Pouquet, Astrophys. J. 640, 335 (2006).

Outline

Information

Phys. Rev. Lett. 134, 235201– Published 12 June, 2025
  • Received 7 December 2024
  • Accepted 20 May 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