Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T16:17:42.600Z Has data issue: false hasContentIssue false

Advances in mean-field dynamo theories

Published online by Cambridge University Press:  18 July 2013

V. V. Pipin*
Affiliation:
Institute of Solar-Terrestrial Physics, Russian Academy of Sciences, Irkutsk, 664033, Russia, email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a short introduction to the subject and review advances in understanding the basic ingredients of the mean-field dynamo theory. The discussion includes the recent analytic and numerical work in developments for the mean electromotive force of the turbulent flows and magnetic field, the nonlinear effects of the magnetic helicity, the non-local generation effects in the dynamo. We give an example of the mean-field solar dynamo model that incorporates the fairly complete expressions for the mean-electromotive force, the subsurface shear layer and the conservation of the total helicity. The model is used to shed light on the issues in the solar dynamo and on the future development of this field of research.

Type
Contributed Papers
Copyright
Copyright © International Astronomical Union 2013 

References

Blackman, E. G., & Field, G. B. 2002, Physical Review Letters, 89, 265007 Google Scholar
Blackman, E. G., & Brandenburg, A. 2003, ApJ, 584, 99 Google Scholar
Bonanno, A., Elstner, D., Rüdiger, G., & Belvedere, G. 2002, A&A, 390, 673 Google Scholar
Brandenburg, A. 2001, ApJ, 550, 824 Google Scholar
Brandenburg, A. 2005, ApJ, 625, 539 Google Scholar
Brandenburg, A. 2006, in Astronomical Society of the Pacific Conference Series, Vol. 354, Solar MHD Theory and Observations: A High Spatial Resolution Perspective, ed. Leibacher, J., Stein, R. F., & Uitenbroek, H., 121–+Google Scholar
Brandenburg, A., & Käpylä, P. J. 2007, New Journal of Physics, 9, 305 Google Scholar
Brandenburg, A., Rädler, K.-H., & Kemel, K. 2012, A&A, 539, A35 Google Scholar
Brandenburg, A., Rädler, K.-H., Rheinhardt, M., & Käpylä, P. J. 2008a, ApJ, 676, 740 Google Scholar
Brandenburg, A., Rädler, K.-H., & Schrinner, M. 2008b, A&A, 482, 739 Google Scholar
Brandenburg, A., & Sokoloff, D. 2002, Geophys. Astrophys. Fluid Dyn., 96, 319 Google Scholar
Brandenburg, A., & Subramanian, K. 2005, Phys. Report, 417, 1 CrossRefGoogle Scholar
Brown, B. P., Browning, M. K., Brun, A. S., Miesch, M. S., & Toomre, J. 2011, in Astronomical Society of the Pacific Conference Series, Vol. 448, 16th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, ed. Johns-Krull, C., Browning, M. K., & West, A. A., 277 Google Scholar
Choudhuri, A. R., Chatterjee, P., & Nandy, D. 2004, ApJL, 615, L57 Google Scholar
Dittrich, P., Molchanov, S. A., Sokolov, D. D., & Ruzmaikin, A. A. 1984, Astronomische Nachrichten, 305, 119 Google Scholar
Fisher, G. H., Longcope, D. W., Linton, M. G., Fan, Y., & Pevtsov, A. A. 1999, in Astronomical Society of the Pacific Conference Series, Vol. 178, Stellar Dynamos: Nonlinearity and Chaotic Flows, ed. Nunez, M. & Ferriz-Mas, A., 35 Google Scholar
Guerrero, G., Chatterjee, P., & Brandenburg, A. 2010, MNRAS, 409, 1619 Google Scholar
Guerrero, G., & de Gouveia Dal Pino, E. M. 2008, A&A, 485, 267 Google Scholar
Guerrero, G., & de Gouveia Dal Pino, E. M. 2009, in Revista Mexicana de Astronomia y Astrofisica Conference Series , Vol. 36, Revista Mexicana de Astronomia y Astrofisica Conference Series, 252 Google Scholar
Harvey, K. 2000, Solar Active Regions: Ephemeral, ed. Murdin, P. Google Scholar
Hubbard, A., & Brandenburg, A. 2012, ApJ, 748, 51 Google Scholar
Käpylä, P. J., & Brandenburg, A. 2007, Astronomische Nachrichten, 328, 1006 CrossRefGoogle Scholar
Käpylä, P. J., Korpi, M. J., & Brandenburg, A. 2008, A&A, 491, 353 Google Scholar
Käpylä, P. J., Korpi, M. J., & Brandenburg, A. 2009, A&A, 500, 633 Google Scholar
Kichatinov, L. L. 2003, Erdelyi, R. et al. (eds.), Turbulence, Waves and Instabilities in the Solar Plasma, Kluwer, 81 CrossRefGoogle Scholar
Kichatinov, L. L., Pipin, V., & Rüdiger, G. 1994, Astron. Nachr., 315, 157 CrossRefGoogle Scholar
Kitchatinov, L. L. 2002, A&A, 394, 1135 Google Scholar
Kitchatinov, L. L., & Olemskoy, S. V. 2011, Astronomy Letters, 37, 286 CrossRefGoogle Scholar
Kleeorin, N., Mond, M., & Rogachevskii, I. 1996, A&A, 307, 293 Google Scholar
Kleeorin, N., Moss, D., Rogachevskii, I., & Sokoloff, D. 2000, A&A, 361, L5 Google Scholar
Kleeorin, N., & Rogachevskii, I. 1999, Phys. Rev. E, 59, 6724 Google Scholar
Kleeorin, N., & Rogachevskii, I. 2003, Phys. Rev. E, 67, 026321 Google Scholar
Krause, F., & Rädler, K.-H. 1980, Mean-Field Magnetohydrodynamics and Dynamo Theory (Berlin: Akademie-Verlag), 271 Google Scholar
Kuzanyan, K. M., Pipin, V. V., & Seehafer, N. 2006, Sol. Phys., 233, 185 Google Scholar
Livermore, P. W., Hughes, D. W., & Tobias, S. M. 2010, Physics of Fluids, 22, 037101 Google Scholar
Makarov, V. I., & Makarova, V. V. 1996, Sol.Phys., 163, 267 Google Scholar
Makarov, V. I., Tlatov, A. G., & Callebaut, D. K. 2004, in IAU Symposium, Vol. 223, Multi-Wavelength Investigations of Solar Activity, ed. Stepanov, A. V., Benevolenskaya, E. E., & Kosovichev, A. G., 4956 Google Scholar
Mitra, D., Candelaresi, S., Chatterjee, P., Tavakol, R., & Brandenburg, A. 2010, Astronomische Nachrichten, 331, 130 Google Scholar
Mitra, D., Moss, D., Tavakol, R., & Brandenburg, A. 2011, A&A 526 A138+ Google Scholar
Moffatt, H. K. 1978, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge, England: Cambridge University Press)Google Scholar
Monin, A. S., & Yaglom, A. M. 1975, Statistical fluid mechanics: Mechanics of turbulence. Volume 2 /revised and enlarged edition/ (MIT)Google Scholar
Morin, J., Dormy, E., Schrinner, M., & Donati, J.-F. 2011, Mon. Not. Roy. Soc., 418, L133 Google Scholar
Ossendrijver, M., Stix, M., & Brandenburg, A. 2001, A&A, 376, 713 Google Scholar
Ossendrijver, M., Stix, M., Brandenburg, A., & Rüdiger, G. 2002, A&A, 394, 735 Google Scholar
Parker, E. 1955, Astrophys. J., 122, 293 Google Scholar
Parker, E. N. 1979, Cosmical magnetic fields: Their origin and their activity (Oxford: Clarendon Press)Google Scholar
Parnell, C. E., DeForest, C. E., Hagenaar, H. J., Johnston, B. A., Lamb, D. A., & Welsch, B. T. 2009, ApJ, 698, 75 CrossRefGoogle Scholar
Pevtsov, A. A., & Longcope, D. W. 2007, in Astronomical Society of the Pacific Conference Series, Vol. 369, New Solar Physics with Solar-B Mission, ed. Shibata, K., Nagata, S., & Sakurai, T., 99 Google Scholar
Pipin, V. V. 2008, Geophysical and Astrophysical Fluid Dynamics, 102, 21 Google Scholar
Pipin, V. V., & Kosovichev, A. G. 2011a, ApJ, 738, 104 CrossRefGoogle Scholar
Pipin, V. V., & Kosovichev, A. G. 2011b, ApJ, 741, 1 CrossRefGoogle Scholar
Pipin, V. V., & Kosovichev, A. G. 2011c, ApJL, 727, L45 Google Scholar
Pipin, V. V., & Seehafer, N. 2009, A&A, 493, 819 Google Scholar
Pipin, V. V., & Sokoloff, D. D. 2011, Physica Scripta, 84, 065903 Google Scholar
Pouquet, A., Frisch, U., & Léorat, J. 1975, J. Fluid Mech., 68, 769 Google Scholar
Racine, É., Charbonneau, P., Ghizaru, M., Bouchat, A., & Smolarkiewicz, P. K. 2011, ApJ, 735, 46 CrossRefGoogle Scholar
Rädler, K., Kleeorin, N., & Rogachevskii, I. 2003, Geophysical and Astrophysical Fluid Dynamics, 97, 249 Google Scholar
Rädler, K.-H. 1969, Monats. Dt. Akad. Wiss., 11, 194 Google Scholar
Rädler, K.-H., Kleeorin, N., & Rogachevskii, I. 2003, Geophys. Astrophys. Fluid Dyn., 97, 249 CrossRefGoogle Scholar
Rädler, K.-H., & Rheinhardt, M. 2007, Geophysical and Astrophysical Fluid Dynamics, 101, 117 Google Scholar
Rempel, M. 2006, ApJ, 647, 662 Google Scholar
Rheinhardt, M., & Brandenburg, A. 2010, A&A, 520, A28 Google Scholar
Rheinhardt, M., & Brandenburg, A. 2012, Astronomische Nachrichten, 333, 71 CrossRefGoogle Scholar
Rogachevskii, I., & Kleeorin, N. 2003, Phys. Rev. E, 68, 1 Google Scholar
Rogachevskii, I., Kleeorin, N., Käpylä, P. J., & Brandenburg, A. 2011, Phys. Rev. E, 84, 056314 Google Scholar
Rüdiger, G., & Hollerbach, R. 2004, The Magnetic Universe (Wiley-Vch Verlag)Google Scholar
Rüdiger, G., & Kitchatinov, L. L. 2000, Astronomische Nachrichten, 321, 75 Google Scholar
Ruediger, G., & Brandenburg, A. 1995, A&A, 296, 557 Google Scholar
Schrinner, M. 2011, A&A, 533, A108 Google Scholar
Schrinner, M., Petitdemange, L., & Dormy, E. 2012, ApJ, 752, 121 CrossRefGoogle Scholar
Schrinner, M., Rädler, K.-H., Schmitt, D., Rheinhardt, M., & Christensen, U. 2005, Astronomische Nachrichten, 326, 245 Google Scholar
Seehafer, N. 1990, Sol.Phys., 125, 219 CrossRefGoogle Scholar
Sokoloff, D., Bao, S. D., Kleeorin, N., Kuzanyan, K., Moss, D., Rogachevskii, I., Tomin, D., & Zhang, H. 2006, Astron. Nachr., 327, 876 Google Scholar
Stenflo, J. O., & Kosovichev, A. G. 2012, ApJ, 745, 129 Google Scholar
Stix, M. 1976, Astron. Astrophys., 47, 243 Google Scholar
Stix, M. 2002, The sun: an introduction, 2nd edn. (Berlin: Springer), 521 Google Scholar
Subramanian, K., & Brandenburg, A. 2004, Phys. Rev. Lett., 93, 205001 Google Scholar
Tobias, S. M., Dagon, K., & Marston, J. B. 2011, ApJ, 727, 127 CrossRefGoogle Scholar
Vishniac, E. T., & Cho, J. 2001, Astrophys. J., 550, 752 Google Scholar
Zel'dovich, Y. B., Ruzmaikin, A. A., Molchanov, S. A., & Sokolov, D. D. 1984, Journal of Fluid Mechanics, 144, 1 Google Scholar
Zhang, H., Moss, D., Kleeorin, N., Kuzanyan, K., Rogachevskii, I., Sokoloff, D., Gao, Y., & Xu, H. 2012, ApJ, 751, 47 Google Scholar
Zhang, H., Sakurai, T., Pevtsov, A., Gao, Y., Xu, H., Sokoloff, D. D., & Kuzanyan, K. 2010, Mon. Not. Roy. Soc., 402, L30 Google Scholar