Abstract
Isotropic homogeneous hydromagnetic turbulence is studied using numerical simulations at resolutions of up to 10243 meshpoints. It is argued that, in contrast to the kinematic regime, the nonlinear regime is characterized by a spectral magnetic power that is decreasing with increasing wavenumber, regardless of whether or not the turbulence has helicity. This means that the root-mean-square field strength converges to a limiting value at large magnetic Reynolds numbers. The total (magnetic and kinetic) energy spectrum tends to be somewhat shallower than k −5/3, in agreement with the findings of other groups. In the presence of helicity, an inverse cascade develops, provided the scale separation between the size of the computational box and the scale of the energy carrying eddies exceeds a ratio of at least two. Finally, the constraints imposed by magnetic helicity conservation on mean-field theory are reviewed and new results of simulations are presented.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Arlt, R. and Brandenburg, A.: 2001. Astron. Astrophys. 380, 359.
Balbus, S. A. and Hawley, J. F.: 1991. ApJ 376, 214.
Beck, R., Brandenburg, A., Moss, D., Shukurov, A. and Sokoloff, D.: 1996. ARA&A 34, 155.
Biskamp, D.: 1993. Europhys. Lett. 21, 563.
Biskamp, D. and Bremer, U.: 1994. PRL 72, 3819.
Biskamp, D.: 1995. Chaos, Solitons & Fractals 5, 1779.
Biskamp, D. and Müller, W.-C.: 2000. Phys. Plasmas 7, 4889.
Biskamp, D., Schwarz, E. and Celani, A.: 1998. PRL 81, 4855.
Bhattacharjee, A. and Yuan, Y.: 1995. ApJ 449, 739.
Blackman, E. G. and Brandenburg, A.: 2002. ApJ 579, 359.
Blackman, E. G. and Field, G. F.: 2000. ApJ 534, 984.
Blackman, E. G. and Field, G. B.: 2002. PRL 89, 265007.
Brandenburg, A.: 2001. ApJ 550, 824. (B01)
Brandenburg, A. and Sarson, G. R.: 2002. PRL 88, 055003–1.
Brandenburg, A., Bigazzi, A. and Subramanian, K.: 2001. Monthly Notices Roy. Astron. Soc. 325, 685.
Brandenburg, A., Dobler, W. and Subramanian, K.: 2002. Astr. Nachr. 323, 99. (Also available as astro-ph/0111567.)
Brandenburg, A., Nordlund, Å., Stein, R. F. and Torkelsson, U.: 1995. ApJ 446, 741.
Cho, J. and Vishniac, E.: 2000a. ApJ 539, 273.
Cho, J. and Vishniac, E.: 2000b. ApJ 538, 217.
Cho, J., Lazarian, A. and Vishniac, E.: 2002a. ApJ 564, 291.
Cho, J., Lazarian, A. and Vishniac, E.: 2002b. ApJ 566, L49.
Dobler, W., Haugen, N. E. L., Yousef, T. A., and Brandenburg, A.: 2003. Phys. Rev. E, submitted (astro-ph/0303324).
Field, G. B., Blackman, E. G. and Chou, H.: 1999. ApJ 513, 638.
Field, G. B. and Blackman, E. G.: 2002. ApJ 572, 685.
Frisch, U.: 1995. Turbulence. The legacy of A. N. Kolmogorov Cambridge UP.
Fuchs, H., Rädler, K.-H. and Rheinhardt, M.: 1999. Astr. Nachr. 320, 129.
Glatzmaier, G. A. and Roberts, P. H.: 1995. Nature 377, 203.
Goldreich, P. and Sridhar, S.: 1995. ApJ 438, 763.
Goldreich, P. and Sridhar, S.: 1997. ApJ 485, 680.
Gruzinov, A. V. and Diamond, P.H.: 1994. PRL 72, 1651.
Haugen, N. E. L., Brandenburg, A., and Dobler, W.: 2003. Phys. Rev. Lett., submitted (astro-ph/0303372).
Iroshnikov, R. S.: 1963. Sov. Astron. 7, 566.
Kazantsev, A. P.: 1968. Sov. Phys. JETP 26, 1031.
Kerr, R. M.: 1985. JFM 153, 31.
Kida, S., Yanase, S. and Mizushima, J.: 1991. Phys. Fluids A 3, 457.
Kleeorin, N. I. and Ruzmaikin, A. A.: 1982. Magnetohydrodynamics, 18, 116.
Kleeorin, N. I, Rogachevskii, I. and Ruzmaikin, A.: 1995. Astron. Astrophys. 297, 159.
Kleeorin, N. I, Moss, D., Rogachevskii, I. and Sokoloff, D.: 2000. Astron. Astrophys. 361, L5.
Kleeorin, N. I, Moss, D., Rogachevskii, I. and Sokoloff, D.: 2002. Astron. Astrophys. 387, 453.
Kraichnan, R. H.: 1965. Phys. Fluids 8, 1385.
Krause, F. and Rädler, K.-H.: 1980. Mean-Field Magnetohydrodynamics and Dynamo Theory Pergamon Press, Oxford.
Kulsrud, R. M. and Anderson, S. W.: 1992. ApJ 396, 606.
Maron, J. and Cowley, S. 2001 (astro-ph/011008)
Maron, J. and Goldreich, P.: 2001. ApJ 554, 1175.
Matthaeus, W. H. and Goldstein, M. L.: 1982. JGR 87, 6011.
Moffatt, H. K.: 1978. Magnetic Field Generation in Electrically Conducting Fluids Cambridge UP.
Oughton S., Matthaeus W. H., and Ghosh, S.: 1998. Phys. Plasmas 5, 4235.
Porter, D. H., Pouquet A. and Woodward, P. R.: 1992. PRL 68, 3156.
Porter, D. H., Woodward, P. R. and Pouquet A.: 1998. Phys. Fluids 10, 237.
Pouquet, A., Frisch, U. and Léorat, J.: 1976. JFM 77, 321.
Rädler, K.-H.: 1969. Geod. Geophys. Veröff., Reihe II, 13, 131.
She, Z.-S., Jackson, E. and Orszag, S. A.: 1990. Nature 344, 226.
Subramanian, K.: 2002. Bull. Astr. Soc. India, in press, (astro-ph/0204450).
Vainshtein, S. I. and Cattaneo, F.: 1992. ApJ 393, 165.
Vainshtein, S. I. and Rosner, R.: 1991. ApJ 376, 199.
Vincent, A. and Meneguzzi, M.: 1991. JFM 225, 1.
Vishniac, E. T. and Cho, J.: 2001. ApJ 550, 752.
Widrow, L. M.: 2002. Rev. Mod. Phys., 74., 775.
Zheligovsky, V. A., Podvigina, O. M. and Frisch, U.: 2001. Geophys. Astrophys. Fluid Dyn. 95, 227. (Also available as nlin. CD/0012005.)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Brandenburg, A., Haugen, N.E.L., Dobler, W. (2003). MHD Simulations of Small and Large Scale Dynamos. In: Erdélyi, R., Petrovay, K., Roberts, B., Aschwanden, M. (eds) Turbulence, Waves and Instabilities in the Solar Plasma. NATO Science Series II: Mathematics, Physics and Chemistry, vol 124. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1063-4_3
Download citation
DOI: https://doi.org/10.1007/978-94-007-1063-4_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-1659-2
Online ISBN: 978-94-007-1063-4
eBook Packages: Springer Book Archive