High-Resolution Simulations of Nonhelical MHD Turbulence

  • N. E. L. Haugen
  • A. Brandenburg
  • W. Dobler


According to the kinematic theory of nonhelical dynamo action, the magnetic energy spectrum increases with wavenumber and peaks at the resistive cutoff wavenumber. It has previously been argued that even in the dynamical case, the magnetic energy peaks at the resistive scale. Using high resolution simulations (up to 10243 meshpoints) with no large-scale imposed field, we show that the magnetic energy peaks at a wavenumber that is independent of the magnetic Reynolds number and about five times larger than the forcing wavenumber. Throughout the inertial range, the spectral magnetic energy exceeds the kinetic energy by a factor of two to three. Both spectra are approximately parallel. The total energy spectrum seems to be close to k−3/2, but there is a strong bottleneck effect and we suggest that the asymptotic spectrum is instead k −5/3. This is supported by the value of the second-order structure function exponent that is found to be ζ 2 = 0.70, suggesting a k −1.70 spectrum. The third-order structure function scaling exponent is very close to unity,—in agreement with Goldreich—Sridhar theory.

Adding an imposed field tends to suppress the small-scale magnetic field. We find that at large scales the magnetic energy spectrum then follows a k−1 slope. When the strength of the imposed field is of the same order as the dynamo generated field, we find almost equipartition between the magnetic and kinetic energy spectra.


interstellar medium turbulence 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Batchelor, G.K.: 1950, Proc. Roy. Soc. Lone. A201, 405.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  2. Brandenburg, A.: 2001, ApT 550, 824.Google Scholar
  3. Brandenburg, A., Jennings, R.L., Nordlund, A., Rieutord, M., Stein, R.F. and Tuominen, I.: 1996, J. Fluid Mech. 306, 325.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  4. Cho, J. and Vishniac, E.: 2000, ApJ 539, 273.ADSCrossRefGoogle Scholar
  5. Dobler, W., Haugen, N.E.L., Yousef, T.A. and Brandenburg, A.: (2003), Phys. Rev. E 68, 026304.Google Scholar
  6. Falkovich, G.: 1994, Phys. Fluids 6, 1411.ADSCrossRefzbMATHGoogle Scholar
  7. Goldreich, P. and Sridhar, S.: 1995, Api 438, 763.ADSGoogle Scholar
  8. Haugen, N.E.L., Brandenburg, A. and Dobler, W.: (2003), Api 597, L141.ADSGoogle Scholar
  9. Iroshnikov, R.S.: (1963), Sol’. Astron. 7, 566.ADSMathSciNetGoogle Scholar
  10. Kazantsev, A.P.: (1968), Sov. Phys. JETP 26, 1031.ADSGoogle Scholar
  11. Kida, S., Yanase, S. and Mizushima, J.: 1991, Phys. Fluids A3, 457.ADSCrossRefGoogle Scholar
  12. Kleeorin, N. and Rogachevskii, I.: (1994), Phys. Rev. 50, 2716.ADSGoogle Scholar
  13. Kraichnan, R.H.: 1965, Phys. Fluids 8, 1385.ADSCrossRefMathSciNetGoogle Scholar
  14. Maron, J. and Blackman, E.G.: (2002), Api 566, L41.ADSGoogle Scholar
  15. Matthaeus, W.H. and Goldstein, M.L.: (1986), Phys. Rev. Lett. 57, 495.ADSCrossRefGoogle Scholar
  16. Meneguzzi, M., Frisch, U. and Pouquet, A.: (1981), Phys. Rev. Lett. 47, 1060.ADSCrossRefGoogle Scholar
  17. Ruzmaikin, A.A. and Shukurov, A.M.: (1982), Astrophys. Spa. Sci. 82, 397.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • N. E. L. Haugen
    • 1
  • A. Brandenburg
    • 2
  • W. Dobler
    • 3
  1. 1.Department of PhysicsThe Norwegian University of Science and TechnologyTrondheimNorway
  2. 2.NORDITACopenhagen ØDenmark
  3. 3.Kiepenheuer-Institut für SonnenphysikFreiburgGermany

Personalised recommendations