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Nonlinear mean-field dynamo and prediction of solar activity

Part of: 50 years of Mean Field Electrodynamics

Published online by Cambridge University Press:  14 June 2018

N. Safiullin Open the ORCID record for N. Safiullin [Opens in a new window] ,
N. Kleeorin Open the ORCID record for N. Kleeorin [Opens in a new window] ,
S. Porshnev ,
I. Rogachevskii Open the ORCID record for I. Rogachevskii [Opens in a new window]  and
A. Ruzmaikin
N. Safiullin
Affiliation:
Department of Information Technology and Automation, Ural Federal University, 19 Mira str., 620002 Ekaterinburg, Russia
N. Kleeorin
Affiliation:
Department of Mechanical Engineering, Ben-Gurion University of the Negev, P. O. Box 653, 84105 Beer-Sheva, Israel Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
S. Porshnev
Affiliation:
Department of Information Technology and Automation, Ural Federal University, 19 Mira str., 620002 Ekaterinburg, Russia
I. Rogachevskii*
Affiliation:
Department of Mechanical Engineering, Ben-Gurion University of the Negev, P. O. Box 653, 84105 Beer-Sheva, Israel Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
A. Ruzmaikin
Affiliation:
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
*
†Email address for correspondence: [email protected]
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Abstract

We apply a nonlinear mean-field dynamo model which includes a budget equation for the dynamics of Wolf numbers to predict solar activity. This dynamo model takes into account the algebraic and dynamic nonlinearities of the $\unicode[STIX]{x1D6FC}$ effect, where the equation for the dynamic nonlinearity is derived from the conservation law for the magnetic helicity. The budget equation for the evolution of the Wolf number is based on a formation mechanism of sunspots related to the negative effective magnetic pressure instability. This instability redistributes the magnetic flux produced by the mean-field dynamo. To predict solar activity on the time scale of one month we use a method based on a combination of the numerical solution of the nonlinear mean-field dynamo equations and the artificial neural network. A comparison of the results of the prediction of the solar activity with the observed Wolf numbers demonstrates a good agreement between the forecast and observations.

Keywords

astrophysical plasmasplasma nonlinear phenomenaspace plasma physics
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 3 , June 2018 , 735840306
Copyright
© Cambridge University Press 2018 

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References

Belvedere, G., Kuzanyan, K. M. & Sokoloff, D. 2000 A two-dimensional asymptotic solution for a dynamo wave in the light of the solar internal rotation. Mon. Not. R. Astron. Soc. 315 (4), 778–790.CrossRefGoogle Scholar
Blackman, E. G. & Field, G. B. 2000 Constraints on the magnitude of $\unicode[STIX]{x1D6FC}$ in dynamo theory. Astrophys. J. 534 (2), 984.CrossRefGoogle Scholar
Brandenburg, A., Gressel, O., Jabbari, S., Kleeorin, N. & Rogachevskii, I. 2014 Mean-field and direct numerical simulations of magnetic flux concentrations from vertical field. Astron. Astrophys. 562, A53.CrossRefGoogle Scholar
Brandenburg, A., Kemel, K., Kleeorin, N., Mitra, Dh. & Rogachevskii, I. 2011 Detection of negative effective magnetic pressure instability in turbulence simulations. Astrophys. J. Lett. 740 (2), L50.CrossRefGoogle Scholar
Brandenburg, A., Kemel, K., Kleeorin, N. & Rogachevskii, I. 2012 The negative effective magnetic pressure in stratified forced turbulence. Astrophys. J. 749 (2), 179.CrossRefGoogle Scholar
Brandenburg, A., Kleeorin, N. & Rogachevskii, I. 2010 Large-scale magnetic flux concentrations from turbulent stresses. Astron. Nachr. 331 (1), 5–13.CrossRefGoogle Scholar
Brandenburg, A., Kleeorin, N. & Rogachevskii, I. 2013 Self-assembly of shallow magnetic spots through strongly stratified turbulence. Astrophys. J. Lett. 776 (2), L23.CrossRefGoogle Scholar
Brandenburg, A., Rogachevskii, I. & Kleeorin, N. 2016 Magnetic concentrations in stratified turbulence: the negative effective magnetic pressure instability. New J. Phys. 18 (12), 125011.CrossRefGoogle Scholar
Brandenburg, A. & Subramanian, K. 2005 Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417 (1), 1–209.CrossRefGoogle Scholar
Bushby, P. J. & Tobias, S. M. 2007 On predicting the solar cycle using mean-field models. Astrophys. J. 661 (2), 1289.CrossRefGoogle Scholar
Choudhuri, A. R., Chatterjee, P. & Jiang, J. 2007 Predicting solar cycle 24 with a solar dynamo model. Phys. Rev. Lett. 98 (13), 131103.CrossRefGoogle ScholarPubMed
Conway, A. J. 1998 Time series, neural networks and the future of the sun. New Astron. Rev. 42 (5), 343–394.CrossRefGoogle Scholar
De Jager, C. & Duhau, S. 2009 Forecasting the parameters of sunspot cycle 24 and beyond. J. Atmos. Sol.-Terr. Phys. 71 (2), 239–245.CrossRefGoogle Scholar
Dikpati, M., De Toma, G. & Gilman, P. A. 2006 Predicting the strength of solar cycle 24 using a flux-transport dynamo-based tool. Geophys. Res. Lett. 33 (5), L05102.CrossRefGoogle Scholar
Fessant, F., Pierret, C. & Lantos, P. 1996 Comparison of neural network and McNish and Lincoln methods for the prediction of the smoothed sunspot index. Solar Phys. 168 (2), 423–433.CrossRefGoogle Scholar
Field, G. B., Blackman, E. G. & Chou, H. 1999 Nonlinear $\unicode[STIX]{x1D6FC}$ -effect in dynamo theory. Astrophys. J. 513 (2), 638.CrossRefGoogle Scholar
Gibson, E. G. 1973 The Quiet Sun. NASA.Google Scholar
Gruzinov, A. V. & Diamond, P. H. 1994 Self-consistent theory of mean-field electrodynamics. Phys. Rev. Lett. 72 (11), 1651–1654.CrossRefGoogle ScholarPubMed
Hagan, M., Demuth, H. & Beale, M. 2016 Neural Network Design. Amazon.Google Scholar
Jabbari, S., Brandenburg, A., Mitra, D., Kleeorin, N. & Rogachevskii, I. 2016 Turbulent reconnection of magnetic bipoles in stratified turbulence. Mon. Not. R. Astron. Soc. 459 (4), 4046–4056.CrossRefGoogle Scholar
Kane, R. P. 2007 Solar cycle predictions based on solar activity at different solar latitudes. Solar Phys. 246 (2), 471–485.CrossRefGoogle Scholar
Käpylä, P. J., Brandenburg, A., Kleeorin, N., Käpylä, M. J. & Rogachevskii, I. 2016 Magnetic flux concentrations from turbulent stratified convection. Astron. Astrophys. 588, A150.CrossRefGoogle Scholar
Käpylä, P. J., Brandenburg, A., Kleeorin, N., Mantere, M. J. & Rogachevskii, I. 2012 Negative effective magnetic pressure in turbulent convection. Mon. Not. R. Astron. Soc. 422 (3), 2465–2473.CrossRefGoogle Scholar
Kemel, K., Brandenburg, A., Kleeorin, N., Mitra, Dh. & Rogachevskii, I. 2012 Spontaneous formation of magnetic flux concentrations in stratified turbulence. Solar Phys. 280 (2), 321–333.CrossRefGoogle Scholar
Kemel, K., Brandenburg, A., Kleeorin, N., Mitra, Dh. & Rogachevskii, I. 2013 Active region formation through the negative effective magnetic pressure instability. Solar Phys. 287 (1–2), 293–313.CrossRefGoogle Scholar
Kitiashvili, I. N. & Kosovichev, A. G. 2011 Modeling and prediction of solar cycles using data assimilation methods. In The Pulsations of the Sun and the Stars, pp. 121–137. Springer.CrossRefGoogle Scholar
Kleeorin, N., Kuzanyan, K., Moss, D., Rogachevskii, I., Sokoloff, D. & Zhang, H. 2003 Magnetic helicity evolution during the solar activity cycle: observations and dynamo theory. Astron. Astrophys. 409 (3), 1097–1105.CrossRefGoogle Scholar
Kleeorin, N., Mond, M. & Rogachevskii, I. 1993 Magnetohydrodynamic instabilities in developed small-scale turbulence. Phys. Fluids B 5 (11), 4128–4134.CrossRefGoogle Scholar
Kleeorin, N., Mond, M. & Rogachevskii, I. 1996 Magnetohydrodynamic turbulence in the solar convective zone as a source of oscillations and sunspots formation. Astron. Astrophys. 307, 293–309.Google Scholar
Kleeorin, N., Moss, D., Rogachevskii, I. & Sokoloff, D. 2000 Helicity balance and steady-state strength of the dynamo generated galactic magnetic field. Astron. Astrophys. 361, L5–L8.Google Scholar
Kleeorin, N. & Rogachevskii, I. 1994 Effective ampère force in developed magnetohydrodynamic turbulence. Phys. Rev. E 50 (4), 2716.Google ScholarPubMed
Kleeorin, N. & Rogachevskii, I. 1999 Magnetic helicity tensor for an anisotropic turbulence. Phys. Rev. E 59 (6), 6724–6729.Google ScholarPubMed
Kleeorin, N., Rogachevskii, I. & Ruzmaikin, A. 1989 Negative magnetic pressure as a trigger of large-scale magnetic instability in the solar convective zone. Sov. Astron. Lett 15, 274–277.Google Scholar
Kleeorin, N., Rogachevskii, I. & Ruzmaikin, A. 1990 Magnetic force reversal and instability in a plasma with advanced magnetohydrodynamic turbulence. Sov. Phys. JETP 70, 878–883.Google Scholar
Kleeorin, N., Rogachevskii, I. & Ruzmaikin, A. 1995 Magnitude of the dynamo-generated magnetic field in solar-type convective zones. Astron. Astrophys. 297, 159–167.Google Scholar
Kleeorin, N. & Ruzmaikin, A. 1982 Dynamics of the average turbulent helicity in a magnetic field. Magnetohydrodynamics 18, 116.Google Scholar
Kleeorin, Y., Safiullin, N., Kleeorin, N., Porshnev, S., Rogachevskii, I. & Sokoloff, D. 2016 The dynamics of wolf numbers based on nonlinear dynamos with magnetic helicity: comparisons with observations. Mon. Not. R. Astron. Soc. 460 (4), 3960–3967.CrossRefGoogle Scholar
Krause, F. & Rädler, K. H. 1980 Mean-Field Magnetohydrodynamics and Dynamo Theory. Pergamon.Google Scholar
Losada, I. R., Brandenburg, A., Kleeorin, N., Mitra, Dh. & Rogachevskii, I. 2012 Rotational effects on the negative magnetic pressure instability. Astron. Astrophys. 548, A49.CrossRefGoogle Scholar
Mitra, D., Brandenburg, A., Kleeorin, N. & Rogachevskii, I.r 2014 Intense bipolar structures from stratified helical dynamos. Mon. Not. R. Astron. Soc. 445 (1), 761–769.CrossRefGoogle Scholar
Moffatt, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.Google Scholar
Obridko, V. N. & Shelting, B. D. 2008 On prediction of the strength of the 11-year solar cycle no. 24. Solar Phys. 248 (1), 191–202.CrossRefGoogle Scholar
Ossendrijver, M. 2003 The solar dynamo. Astron. Astrophys. Rev. 11 (4), 287–367.CrossRefGoogle Scholar
Parker, E. 1979 Cosmical Magnetic Fields. Oxford University Press.Google Scholar
Parker, E. N. 1966 The dynamical state of the interstellar gas and field. Astrophys. J. 145, 811.CrossRefGoogle Scholar
Pesnell, W. D. 2012 Solar cycle predictions (invited review). Solar Phys. 281 (1), 507–532.Google Scholar
Pouquet, A., Frisch, U. & Léorat, J. 1976 Strong MHD helical turbulence and the nonlinear dynamo effect. J. Fluid Mech. 77 (2), 321–354.CrossRefGoogle Scholar
Priest, E. R. 1982 Solar Magnetohydrodynamics. Reidel.CrossRefGoogle Scholar
Roberts, P. H. & Stix, M. 1971 The Turbulent Dynamo. NCAR.Google Scholar
Rogachevskii, I. & Kleeorin, N. 2000 Electromotive force for an anisotropic turbulence: intermediate nonlinearity. Phys. Rev. E 61, 5202–5210.Google ScholarPubMed
Rogachevskii, I. & Kleeorin, N. 2001 Nonlinear turbulent magnetic diffusion and mean-field dynamo. Phys. Rev. E 64, 056307.Google ScholarPubMed
Rogachevskii, I. & Kleeorin, N. 2004 Nonlinear theory of a ‘shear-current’ effect and mean-field magnetic dynamos. Phys. Rev. E 70 (4), 046310.Google ScholarPubMed
Rogachevskii, I. & Kleeorin, N. 2007 Magnetic fluctuations and formation of large-scale inhomogeneous magnetic structures in a turbulent convection. Phys. Rev. E 76 (5), 056307.Google Scholar
Rüdiger, G., Kitchatinov, L. L. & Hollerbach, R. 2013 Magnetic Processes in Astrophysics: Theory, Simulations, Experiments. Wiley-VCH.CrossRefGoogle Scholar
Spruit, H. C. 1974 A model of the solar convection zone. Solar Phys. 34 (2), 277–290.CrossRefGoogle Scholar
Steenbeck, M., Krause, F. & Rädler, K. H. 1966 Berechnung der mittleren lorentfeldstrke v bfür ein elektrisch leitendendes medium in turbulenter, durch coriolis-kräfte beeinfluter bewegung. Z. Naturforsch. 21a, 369–376.CrossRefGoogle Scholar
Stix, M. 2012 The Sun: An Introduction. Springer Science & Business Media.Google Scholar
Tlatov, A. G. 2009 The minimum activity epoch as a precursor of the solar activity. Solar Phys. 260 (2), 465–477.CrossRefGoogle Scholar
Tlatov, A. G. 2015 The change of the solar cyclicity mode. Adv. Space Res. 55 (3), 851–856.CrossRefGoogle Scholar
Usoskin, I. G. 2017 A history of solar activity over millennia. Living Rev. Solar Phys. 14 (1), 3.CrossRefGoogle Scholar
Warnecke, J., Losada, I. R., Brandenburg, A., Kleeorin, N. & Rogachevskii, I. 2013 Bipolar magnetic structures driven by stratified turbulence with a coronal envelope. Astrophys. J. Lett. 777 (2), L37.CrossRefGoogle Scholar
Warnecke, J., Losada, I. R., Brandenburg, A., Kleeorin, N. & Rogachevskii, I. 2016 Bipolar region formation in stratified two-layer turbulence. Astron. Astrophys. 589, A125.CrossRefGoogle Scholar
Zeldovich, Y. B., Ruzmaikin, A. A. & Sokoloff, D. D. 1983 Magnetic Fields in Astrophysics. Gordon and Breach.Google Scholar
Zhang, H., Moss, D., Kleeorin, N., Kuzanyan, K., Rogachevskii, I., Sokoloff, D., Gao, Y. & Xu, H. 2012 Current helicity of active regions as a tracer of large-scale solar magnetic helicity. Astrophys. J. 751 (1), 47.CrossRefGoogle Scholar
Zhang, H., Sokoloff, D., Rogachevskii, I., Moss, D., Lamburt, V., Kuzanyan, K. & Kleeorin, N. 2006 The radial distribution of magnetic helicity in the solar convective zone: observations and dynamo theory. Mon. Not. R. Astron. Soc. 365 (1), 276–286.CrossRefGoogle Scholar