- 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

Solar wind magnetohydrodynamic turbulence energy transfer rate ordered by magnetic field topology

B. Hnat*, S. C. Chapman, and C. M. Liptrott

N. W. Watkins

  • *Contact author: B.Hnat@warwick.ac.uk
PDF

Phys. Rev. Research 7, 043058 – Published 16 October, 2025

DOI: https://doi.org/10.1103/9wb2-r437

Abstract

The magnetic field fluctuations that mediate a magnetohydrodynamic turbulent cascade have distinct magnetic topologies and associated energy transfer rates. Magnetic field topology is classified by the magnetic field gradient tensor constructed from solar wind in situ observations by the four Cluster spacecraft tetrahedron on a scale of ∼40 proton gyroradii. Energy transfer rates are estimated instantaneously from the third-order term. We find on average 25% and up to 60% larger forward energy transfer rates in hyperbolic topology compared to flux ropes/plasmoids. Hyperbolic topology, consistent with reconnection, preferentially contributes to the forward energy cascade in magnetohydrodynamic turbulence in the solar wind. This forward cascade is a candidate mechanism for heating the solar wind.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (55)

  1. R. Bruno and V. Carbone, The solar wind as a turbulence laboratory, Living Rev. Solar Phys. 10, 2 (2013).
  2. K. H. Kiyani, K. T. Osman, and S. C. Chapman, Dissipation and heating in solar wind turbulence: From the macro to the micro and back again, Philos. Trans. R. Soc. A 373, 20140155 (2015).
  3. L. Sorriso-Valvo et al., Intermittency in the solar wind turbulence through probability distribution functions of fluctuations, Geophys. Res. Lett. 26, 1801 (1999).
  4. B. Hnat, S. C. Chapman, and G. Rowlands, Intermittency, scaling, and the Fokker-Planck approach to fluctuations of the solar wind bulk plasma parameters as seen by the WIND spacecraft, Phys. Rev. E 67, 056404 (2003).
  5. S. C. Chapman and B. Hnat, Quantifying scaling in the velocity field of the anisotropic turbulent solar wind, Geophys. Res. Lett. 34, L17103 (2007).
  6. R. Marino and L. Sorriso-Valvo, Scaling laws for the energy transfer in space plasma turbulence, Phys. Rep. 1006, 1 (2023).
  7. E. Marsch, Turbulence in the solar wind, in Reviews in Modern Astronomy, edited by G. Klare (Springer, Berlin, 1991), Vol. 4, p. 145.
  8. C. H. K. Chen, Recent progress in astrophysical plasma turbulence from solar wind observations, J. Plasma Phys. 82, 535820602 (2016).
  9. E. Marsch, Kinetic physics of the solar corona and solar wind, Living Rev. Solar Phys. 3, 1 (2006).
  10. G. G. Howes, S. C. Cowley, W. Dorland, G. W. Hammett, E. Quataert, and A. A. Schekochihin, A model of turbulence in magnetized plasmas: Implications for the dissipation range in the solar wind, J. Geophys. Res. 113, A05103 (2008).
  11. K. H. Kiyani et al., Global scale-invariant dissipation in collisionless plasma turbulence, Phys. Rev. Lett. 103, 075006 (2009).
  12. S. R. Cranmer, W. H. Matthaeus, B. A. Breech, and J. C. Kasper, Empirical constraints on proton and electron heating in the fast solar wind, Astrophys. J. 702, 1604 (2009).
  13. J. E. Stawarz, C. W. Smith, B. J. Vasquez, M. A. Forman, and B. T. MacBride, The turbulent cascade and proton heating in the solar wind at 1 AU, Astrophys. J. 697, 1119 (2009).
  14. M. K. Verma, D. A. Roberts, and M. L. Goldstein, Turbulent heating and temperature evolution in the solar wind plasma, J. Geophys. Res.: Space Phys. 100, 19839 (1995).
  15. A. N. Yaglom, On local temperature field structure in a turbulent flow, Dokl. Akad. Nauk SSSR 69, 743 (1949).
  16. H. Politano and A. Pouquet, Dynamical length scales for turbulent magnetized flows, Geophys. Res. Lett. 25, 273 (1998);.
  17. G. Gogoberidze, S. Perri, and V. Carbone, The Yaglom law in the expanding solar wind, Astrophys. J. 769, 111 (2013).
  18. T. de Kármán and L. Howarth, On the statistical theory of isotropic turbulence, Proc. R. Soc. A 164, 192 (1938); P. Hellinger et al., von Kármán–Howarth equation for Hall magnetohydrodynamics: Hybrid simulations, Astrophys. J. Lett. 857, L19 (2018); Spectral transfer and Kármán–Howarth–Monin equations for compressible Hall magnetohydrodynamics, Astrophys J. 917, 101 (2021).
  19. H. Politano and A. Pouquet, von Karman-Howarth equation for magnetohydrodynamics and its consequences on third-order longitudinal structure and correlation functions, Phys. Rev. E 57, R21(R) (1998).
  20. B. T. MacBride, C. W. Smith, and M. A. Forman, The turbulent cascade at 1 AU: Energy transfer and the third-order scaling for MHD, Astrophys. J. 679, 1644 (2008).
  21. L. Sorriso-Valvo, R. Marino, V. Carbone, A. Noullez, F. Lepreti, P. Veltri, F. R. Bruno, B. Bavassano, and E. Pietropaolo, Observation of inertial energy cascade in interplanetary space plasma, Phys. Rev. Lett. 99, 115001 (2007).
  22. K. T. Osman, W. H. Matthaeus, K. H. Kiyani, B. Hnat, and S. C. Chapman, Proton kinetic effects and turbulent energy cascade rate in the solar wind, Phys. Rev. Lett. 111, 201101 (2013).
  23. L. Z. Hadid, F. Sahraoui, and S. Galtier, Energy cascade rate in compressible fast and slow solar wind turbulence, Astrophys. J. 838, 9 (2017).
  24. R. Bandyopadhyay, L. Sorriso-Valvo, A. Chasapis, P. Hellinger, W. H. Matthaeus, A. Verdini, S. Landi, L. Franci, L. Matteini, B. L. Giles, and D. J. Gershman, In situ observation of Hall magnetohydrodynamic cascade in space plasma, Phys. Rev. Lett. 124, 225101 (2020).
  25. F. Pecora, Y. Yang, W. H. Matthaeus, A. Chasapis, K. G. Klein, M. Stevens, S. Servidio, A. Greco, D. J. Gershman, B. L. Giles, and J. L. Burch, Three-dimensional energy transfer in space plasma turbulence from multipoint measurement, Phys. Rev. Lett. 131, 225201 (2023).
  26. H. Politano and A. Pouquet, Model of intermittency in magnetohydrodynamic turbulence, Phys. Rev. E 52, 636 (1995); W. H. Matthaeus et al., Intermittency, nonlinear dynamics and dissipation in the solar wind and astrophysical plasmas, Philos. Trans. R. Soc. A 373, 20140154 (2015).
  27. G. Consolini and P. De Michelis, A joint multifractal approach to solar wind turbulence, Fractal Fract. 7, 748 (2023); H. Wu, Honghong et al., Intermittency of magnetic discontinuities in the near-Sun solar wind turbulence, Astrophys. J. Lett. 947, L22 (2023).
  28. A. Bendt and S. C. Chapman, Ubiquitous threshold for coherent structures in solar wind turbulence, Phys. Rev. R 7, 023176 (2025).
  29. M. Wan, W. H. Matthaeus, V. Roytershteyn, H. Karimabadi, T. Parashar, P. Wu, and M. Shay, Intermittent dissipation and heating in 3D kinetic plasma turbulence, Phys. Rev. Lett. 114, 175002 (2015); A. Greco, P. Chuychai, W. H. Matthaeus, S. Servidio, and P. Dmitruk, Intermittent MHD structures and classical discontinuities, Geophys. Res. Lett. 35, 19 (2008).
  30. T. S. Chang, An Introduction to Space Plasma Complexity (Cambridge University Press, Cambridge, UK, 2015).
  31. A. Pouquet, D. Rosenberg, J. E. Stawarz, and R. Marino, Helicity dynamics, inverse, and bidirectional cascades in fluid and magnetohydrodynamic turbulence: A brief review, Earth Space Sci. 6, 351 (2019); O. Pezzi, D. Trotta, S. Benella, L. Sorriso-Valvo, F. Malara, F. Pucci, C. Meringolo, W. H. Matthaeus, and S. Servidio, Turbulence and particle energization in twisted flux ropes under solar-wind conditions, Astron. Astrophys. 686, A116 (2024).
  32. S. Boldyrev and N. F. Loureiro, Magnetohydrodynamic turbulence mediated by reconnection, Astrophys. J 844, 125 (2017); D. Vech, A. Mallet, K. G. Klein, and J. C. Kasper, Magnetic reconnection may control the ion-scale spectral break of solar wind turbulence, Astrophys. J. Lett. 855, L27 (2018).
  33. W. H. Matthaeus and D. Montgomery, Selective decay hypothesis at high mechanical and magnetic Reynolds numbers, Ann. N.Y. Acad. Sci. 357, 203 (1980).
  34. V. Carbone, P. Veltri, and A. Mangeney, Coherent structure formation and magnetic field line reconnection in magnetohydrodynamic turbulence, Phys. Fluids 2, 1487 (1990).
  35. S. Perri et al., Detection of small-scale structures in the dissipation regime of solar-wind turbulence, Phys. Rev. Lett. 109, 191101 (2012).
  36. T. D. Phan et al., Electron magnetic reconnection without ion coupling in Earth's turbulent magnetosheath, Nature (London) 557, 202 (2018); M. S. Davis, T. D. Phan, J. T. Gosling, and R. M. Skoug, Detection of oppositely directed reconnection jets in a solar wind current sheet, Geophys. Res. Lett. 33, 19 (2006).
  37. B. Hnat, S. C. Chapman, and N. W. Watkins, Topology of turbulence within collisionless plasma reconnection, Sci. Rep. 13, 18665 (2023).
  38. V. Dallas and A. Alexakis, Structures and dynamics of small scales in decaying magnetohydrodynamic turbulence, Phys. Fluids 25, 105106 (2013).
  39. M. Materassi and G. Consolini, The stochastic tetrad magneto-hydrodynamics via functional formalism, J. Plasma Phys. 81, 495810602 (2015).
  40. V. Quattrociocchi, G. Consolini, M. F. Marcucci, and M. Materassi, On geometrical invariants of the magnetic field gradient tensor in turbulent space plasmas: Scale variability in the inertial range, Astrophys. J. 878, 124 (2019).
  41. B. Hnat, S. C. Chapman, and N. W. Watkins, Magnetic topology of actively evolving and passively convecting structures in the turbulent solar wind, Phys. Rev. Lett. 126, 125101 (2021).
  42. L. Sorriso-Valvo et al., Local energy transfer rate and kinetic processes: The fate of turbulent energy in two-dimensional hybrid Vlasov–Maxwell numerical simulations, J. Plasma Phys. 84, 725840201 (2018).
  43. A. Balogh et al., The Cluster magnetic field investigation, Space Sci. Rev. 79, 65 (1997).
  44. H. Réme et al., First multispacecraft ion measurements in and near the Earth's magnetosphere with the identical Cluster ion spectrometry (CIS) experiment, Ann. Geophys. 19, 1303 (2001).
  45. G. Paschmann and P. W. Daly, Analysis methods for multi-spacecraft data, ISSI Scientific Reports Series SR-001, ESA/ISSI, Vol. 1 (1998).
  46. A. D. Johnstone et al., PEACE: A plasma electron and current experiment, Space Sci. Rev. 79, 351 (1997).
  47. B. J. Cantwell, Exact solution of a restricted Euler equation for the velocity gradient tensor, Phys. Fluids A 4, 782 (1992); C. Meneveau, Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows, Annu. Rev. Fluid Mech. 43, 219 (2011); M. S. Chong, A. E. Perry, and B. J. Cantwell, A general classification of three-dimensional flow fields, Phys. Fluids 2, 765 (1990).
  48. N. Andrés, S. Galtier, and F. Sahraoui, Exact law for homogeneous compressible Hall magnetohydrodynamics turbulence, Phys. Rev. E 97, 013204 (2018); N. Andrés et al., Energy cascade rate measured in a collisionless space plasma with MMS data and compressible Hall magnetohydrodynamic turbulence theory, Phys. Rev. Lett. 123, 245101 (2019).
  49. Y. Wang et al., Strategies for determining the cascade rate in MHD turbulence: Isotropy, anisotropy, and spacecraft sampling, Astrophys. J. 937, 76 (2022); K. T. Osman, M. Wan, W. H. Matthaeus, J. M. Weygand, and S. Dasso, Anisotropic third-moment estimates of the energy cascade in solar wind turbulence using multispacecraft data, Phys. Rev. Lett. 107, 165001 (2011); A. Verdini, R. Grappin, P. Hellinger, S. Landi, and W. C. Müller, Anisotropy of third-order structure functions in MHD turbulence, Astrophys. J. 804, 119 (2015).
  50. R. J. Hyndman and Y. Fan, Sample quantiles in statistical packages, Am. Stat. 54, 361 (1966).
  51. P. A. Davidson, Turbulence: An Introduction for Scientists and Engineers, 2nd ed. (Oxford University Press, 2015).
  52. K. G. Klein et al., HelioSwarm: A multipoint, multiscale mission to characterize turbulence, Space Sci. Rev. 219, 74 (2023).
  53. M. Chertkov, A. Pumir, and B. I. Shraiman, Lagrangian tetrad dynamics and the phenomenology of turbulence, Phys. Fluids 11, 2394 (1999).
  54. R. E. Denton et al., Polynomial reconstruction of the reconnection magnetic field observed by multiple spacecraft, J. Geophys. Res.: Space Phys. 125, e2019JA027481 (2020).
  55. S. S. Girimaji and C. G. Speziale, A modified restricted Euler equation for turbulent flows with mean velocity gradients, Phys. Fluids 7, 1438 (1995).

Outline

Information

Phys. Rev. Research 7, 043058– Published 16 October, 2025
  • Received 12 May 2025
  • Accepted 4 September 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