JETP Letters

, Volume 110, Issue 5, pp 329–335 | Cite as

Nonlinear Transformations of the Kinetic and Magnetic Energies in Rotating Magnetohydrodynamic Turbulent Flows

  • R. A. SirazovEmail author
  • A. S. Petrosyan
Plasma, Hydro- and Gas Dynamics


Time-periodic imbalances in the kinetic and magnetic energies at the conservation of the total energy have been found for three-dimensional homogeneous magnetohydrodynamic turbulence in the presence of rotation and an external magnetic field. It has been shown that these imbalances are caused by the collisions of Alfvén wave packets that arise because of the external magnetic field. It has been shown that no periodic imbalances of the kinetic and magnetic energies occur in the system at certain threshold values of the angular velocity of rotation and external magnetic field.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This work was supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “Basis,” by the Presidium of the Russian Academy of Sciences (project no. KP19-270 “Problems of the Origin and Evolution of the Universe Using Ground-Based Observations and Space Research”), and by the Russian Foundation for Basic Research (project no. 19-02-00016).


  1. 1.
    L. M. Zelenyi, A. M. Bykov, Y. A. Uvarov, and A. V. Artemyev, J. Plasma Phys. 81, 395810401 (2015).CrossRefGoogle Scholar
  2. 2.
    A. Petrosyan, A. Balogh, M. L. Goldstein, J. Léorat, E. Marsch, K. Petrovay, B. Roberts, R. von Steiger, and J. C. Vial, Spac. Sci. Rev. 156, 135 (2010).ADSCrossRefGoogle Scholar
  3. 3.
    A. A. Chernyshov, K. V. Karelsky, and A. S. Petrosyan, Phys. Usp. 57, 421 (2014).ADSCrossRefGoogle Scholar
  4. 4.
    V. I. Il’gisonis, Classical Problems in the Physics of Hot Plasma. Course of Lectures (Mosk. Energet. Inst., Moscow, 2015) [in Russian].Google Scholar
  5. 5.
    C. W. Horton, Jr., Turbulent Transport in Magnetized Plasmas (World Scientific, Singapore, 2017).CrossRefGoogle Scholar
  6. 6.
    A. I. Morozov and L. S. Solov’ev, Vopr. Teor. Plazmy, No. 2, 3 (1963).Google Scholar
  7. 7.
    D. Biskamp, Magnetohydrodynamic Turbulence (Cambridge Univ. Press, Cambridge, 2003).CrossRefGoogle Scholar
  8. 8.
    W.-C. Muller and D. Biskamp, The Evolving Phenomenological View on Magnetohydrodynamic Turbulence, Turbulence and Magnetic Fields in Astrophysics (Springer, Berlin, Heidelberg, 2003).Google Scholar
  9. 9.
    V. P. Pastukhov and N. V. Chudin, JET. Lett. 90, 651 (2009).ADSCrossRefGoogle Scholar
  10. 10.
    V. P. Pastukhov and N. V. Chudin, JET. Lett. 82, 356 (2005).ADSCrossRefGoogle Scholar
  11. 11.
    V. P. Pastukhov and N. V. Chudin, Plasm. Phys. Rep. 27, 907 (2001).ADSCrossRefGoogle Scholar
  12. 12.
    P. W. Terry, Rev. Mod. Phys. 72, 109 (2000).ADSCrossRefGoogle Scholar
  13. 13.
    P. H. Diamond, S.-I. Itoh, K. Itoh, and T. S. Hahm, Plasm. Phys. Control. Fusion 47, R35 (2005).CrossRefGoogle Scholar
  14. 14.
    S. A. Balbus and J. F. Hawley, Rev. Mod. Phys. 70, 1 (1998).ADSCrossRefGoogle Scholar
  15. 15.
    P. J. Armitage, Ann. Rev. Astron. Astrophys. 49, 195 (2011).ADSCrossRefGoogle Scholar
  16. 16.
    Accretion Processes in Astrophysics, Ed. by N. I. Shakura (Fizmatlit, Moscow, 2016) [in Russian].Google Scholar
  17. 17.
    M. S. Miesch, Livin. Rev. Solar Phys. 2, 1 (2005).ADSCrossRefGoogle Scholar
  18. 18.
    S. M. Tobias, P. H. Diamond, and D. W. Hughes, Astrophys. J. 667, 113 (2007).ADSCrossRefGoogle Scholar
  19. 19.
    T. A. Zinyakov and A. S. Petrosyan, JET. Lett. 108, 85 (2018).ADSCrossRefGoogle Scholar
  20. 20.
    J. V. Shebalin, Geophys. Astrophys. Fluid Dyn. 107, 411 (2013).ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    J. V. Shebalin, Discret. Cont. Dyn. Syst. B 5, 153 (2005).MathSciNetCrossRefGoogle Scholar
  22. 22.
    B. Favier, F. S. Godeferd, and C. Cambon, Geophys. Astrophys. Fluid Dyn. 106, 89 (2012).ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 32, 19 (1941).ADSGoogle Scholar
  24. 24.
    R. S. Iroshnikov, Sov. Astron. 7, 566 (1963).ADSMathSciNetGoogle Scholar
  25. 25.
    R. H. Kraichnan, Phys. Fluids 8, 1385 (1965).ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    S. Baklouti, A. Khili, A. Salhi, F. Godeferd, C. Cambon, and T. Lehner, J. Turbulence 20, 263 (2019).ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    H. K. Moffatt, Field Generation in Electrically Conducting Fluids (Cambridge Univ. Press, Cambridge, 1978).Google Scholar
  28. 28.
    E. N. Parker, Cosmical Magnetic Fields: Their Origin and Their Activity (Oxford Univ. Press, Oxford, 1979).Google Scholar
  29. 29.
    O. Pezzi, T. N. Parashar, S. Servidio, F. Valentini, C. L. Vásconez, Y. Yang, F. Malara, W. H. Matthaeus, and P. Veltri, J. Plasma Phys. 83, 905830105 (2017).Google Scholar
  30. 30.
    O. Pezzi, T. N. Parashar, S. Servidio, F. Valentini, C. L. Vásconez, Y. Yang, F. Malara, W. H. Matthaeus, and P. Veltri, Astrophys. J. 834, 166 (2017).ADSCrossRefGoogle Scholar
  31. 31.
    C. S. Ng and A. Bhattacharjee, Astrophys. J. 465, 845 (1996).ADSCrossRefGoogle Scholar
  32. 32.
    G. G. Howes and K. D. Nielson, Phys. Plasmas 20, 072302 (2013).ADSCrossRefGoogle Scholar
  33. 33.
    G. G. Howes, K. D. Nielson, and W. Dorland, Phys. Plasmas 20, 072303 (2013).ADSCrossRefGoogle Scholar
  34. 34.
    G. G. Howes, K. D. Nielson, D. J. Drake, J. W. R. Schroeder, F. Skiff, C. A. Kletzing, and T. A. Carter, Phys. Plasmas 20, 072304 (2013).ADSCrossRefGoogle Scholar
  35. 35.
    D. J. Drake, J. W. R. Schroeder, G. G. Howes, C. A. Kletzing, F. Skiff, T. A. Carter, and D. W. Auerbach, Phys. Plasmas 20, 072901 (2013).ADSCrossRefGoogle Scholar
  36. 36.
    K. Miki and S. Menon, Phys. Plasmas 15, 7 (2008).Google Scholar
  37. 37.
    A. A. Samarskii and A. V. Gulin, Numerical Methods (Nauka, Moscow, 1989) [in Russian].Google Scholar
  38. 38.
    G. I. Taylor and A. E. Green, Proc. R. Soc. London, Ser. A 158 (895), 499 (1937).ADSCrossRefGoogle Scholar
  39. 39.
    M. E. Brachet, Flui. Dyn. Res. 8, 1 (1991).ADSCrossRefGoogle Scholar
  40. 40.
    A. Pouquet, E. Lee, M.-E. Brachet, P. Mininni, and D. Rosenberg, Geophys. Astrophys. Fluid Dyn. 104, 115 (2009).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Space Research InstituteRussian Academy of SciencesMoscowRussia
  2. 2.Moscow Institute of Physics and Technology (National Research University)Dolgoprudnyi, Moscow regionRussia

Personalised recommendations