Solar cycle modelling using spatiotemporal decomposition schemes

Journal of Computational Physics

Volumn 223, Issue 1, 2007, Pages 50-66

  St Jean, Cédric ^a   Charbonneau, Paul ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

Decomposition methods; Dynamo; Magnetohydrodynamics; Partial differential equations; Solar cycle

Indexed keywords

INTERACTIVE DEVICES; MAGNETOHYDRODYNAMICS; SOLAR ENERGY;

ADVECTION-DIFFUSION PARTIAL DIFFERENTIAL EQUATIONS; CYCLE MODEL; DECOMPOSITION METHODS; DECOMPOSITION SCHEME; NONLINEAR SOURCE; NOVEL TECHNIQUES; NUMERICAL SOLUTION; SOLAR CYCLE; SOURCE TERMS; SPATIO-TEMPORAL DECOMPOSITION;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 33947126068     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.08.010     Document Type: Article

References (35)

1. Babcock H.W. The topology of the sun's magnetic field and the 22-year cycle. Astrophys. J. 133 (1961) 572
2. Beer J. Long-term indirect indices of solar variability. Space Sci. Rev. 94 (2000) 53
3. Beer J., Tobias S., and Weiss N.O. An active Sun through the Maunder Minimum. Solar Phys. 181 (1998) 237
4. Brooke J.M., Moss D., and Phillips A. Deep minima in stellar dynamos. Astron. Astrophys. 395 (2002) 1013
5. Charbonneau P. Dynamo models of the solar cycle. Living Rev. Solar Phys. 2 (2005). Available from:
6. Charbonneau P., and MacGregor K.B. Solar interface dynamos. II: linear, kinematic models in spherical geometry. Astrophys. J. 486 (1997) 502
7. Charbonneau P., and Dikpati M. Stochastic fluctuations in a Babcock-Leighton model of the solar cycle. Astrophys. J. 543 (2000) 1027
8. Charbonneau P., Blais-Laurier G., and St-Jean-Leblanc C. Intermittency and phase persistence in a Babcock-Leighton model of the solar cycle. Astrophys. J. 616 (2004) L183
9. Charbonneau P., St-Jean-Leblanc C., and Zacharias P. Fluctuations in Babcock-Leighton models of the solar cycle. I: period doubling and transition to chaos. Astrophys. J. 619 (2005) 613
10. Christensen-Dalsgaard J. Helioseismology. Rev. Mod. Phys. 74 (2002) 1073
11. Davidson P.A. An Introduction to Magnetohydrodynamics (2001), Cambridge University Press, New York
12. Dikpati M., and Charbonneau P. A Babcock-Leighton flux transport dynamo with solar-like differential rotation. Astrophys. J. 518 (1999) 508
13. Dikpati M., de Toma G., and Gilman P.A. Predicting the strength of solar cycle 24 using a flux transport dynamo-based tool. Geophys. Res. Lett. 33 (2006) L05102
14. Durney B.R. Solar Phys. 160 (1995) 213
15. Eddy J.A. The Maunder Minimum. Science 192 (1976) 1189
16. Galloway D.J., and Proctor M.R.E. The kinematics of hexagonal magnetoconvection. Geophys. Astrophys. Fluid Dyn. 24 (1983) 109
17. Hathaway D.H., Wilson R.M., and Reichmann E.J. A synthesis of solar cycle prediction techniques. J. Geophys. Res. 104 (1999) 22,375
18. Hoyt D.V., and Schatten K.H. How well was the sun observed during the Maunder Minimum?. Solar Phys. 165 (1996) 181
19. Hoyt D.V., and Schatten K.H. Group sunspot numbers: a new solar activity reconstruction. Solar Phys. 181 (1998) 491
20. Küker M., Arlt R., and Rüdiger R. The Maunder minimum as due to magnetic Λ-quenching. Astron. Astrophys. 343 (1999) 977
21. Leighton R.B. A magneto-kinematic model of the solar cycle. Astrophys. J. 156 (1969) 1
22. Moreno-Insertis F., Schüssler M., and Ferriz-Mas A. Storage of magnetic flux tubes in a convective overshoot region. Astron. Astrophys. 264 (1992) 686
23. Nandy D., and Choudhuri A.R. Toward a mean-field formulation of the Babcock-Leighton type solar dynamo. I: α-coefficient versus Durney's double-ring approach. Astrophys. J. 551 (2001) 576
24. Ossendrijver M.A.J.H. Grand minima in a buoyancy-driven solar dynamo. Astron. Astrophys. 359 (2000) 364
25. Ossendrijver M.A.J.H. The solar dynamo. Astron. Astrophys. Rev. (2003) 287
26. Parker E.N. The formation of sunspots from the solar toroidal field. Astrophys. J. 121 (1955) 491
27. Pipin V.V. The Gleissberg cycle by a nonlinear αΛ dynamo. Astron. Astrophys. 346 (1999) 295
28. Rhines P.R., and Young W.R. How rapidly is a passive scalar mixed within closed streamlines?. J. Fluid Mech. 133 (1983) 133
29. Schmitt D., Schüssler M., and Ferriz-Mas A. Intermittent solar activity by an on-off dynamo. Astron. Astrophys. 311 (1996) L1
30. Schüssler M., Caligari P., Ferriz-Mas A., and Moreno-Insertis F. Instability and eruption of magnetix flux tubes in the solar convection zone. Astron. Astrophys. 281 (1994) L69
31. Stix M. Differential rotation and the solar dynamo. Astron. Astrophys. 47 (1976) 243
32. J.J. Valdés, G. Bonham-Carter, Time dependent neural network models for detecting changes of state in earth and planetary processes, in: Proceedings of the IJCNN'05 International Joint Conference on Neural Networks, July 31-August 4, 2005, Montreal, Canada.
33. Wang Y.-M., Sheeley Jr. N.R., and Nash A.G. A new cycle model including meridional circulation. Astrophys. J. 383 (1991) 431
34. Weiss N.O. The expulsion of magnetic flux by eddies. Proc. Roy. Soc. Lond. A 293 (1966) 310
35. Wood W.L. Practical Time-Stepping Schemes (1990), Oxford University Press, Oxford