Asymptotic properties of a nonlinear αω-dynamo wave: Period, amplitude and latitude dependence

Geophysical and Astrophysical Fluid Dynamics

Volumn 86, Issue 3-4, 1997, Pages 249-285

  Meunier, N ^a   Proctor, M R E ^b   Sokoloff, D D ^a,c,d   Soward, A M ^d   Tobias, S M ^b,e  

^a CNRS   (France)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^c MOSCOW STATE UNIVERSITY   (Russian Federation)

^d UNIVERSITY OF EXETER   (United Kingdom)

^e UNIVERSITY OF COLORADO   (United States)

Author keywords

Solar cycle; Thin shell; quenching

Indexed keywords

EID: 0001191234     PISSN: 03091929     EISSN: None     Source Type: Journal    
DOI: 10.1080/03091929708245464     Document Type: Article

References (36)

1. Baliunas, S. L., Nesme-Ribes, E., Sokoloff, D. and Soon, W., "A dynamo interpretation of stellar activity cycles," Astrophys. J. 460, 848-857 (1996).
2. Baliunas, S. L., Donahue, R. A., Soon, W. H., Horne, J. H., Frazer, J., Woodard-Eklund, L., Bradford, M., Rao, L. M., Wilson, O. C., Zhang, Q., Bennett, W., Briggs, J., Caroll, S. M., Duncan, D. K., Figueroa, D., Lanning, H. H., Mish, T., Mueller, J., Noyes, R. W., Poppe, D., Porter, A. C., Robinson, C. R., Russel, J., Shelton, J. C., Soyumer, T., Vaughan, A. H. and Whitney, J. H., "Chromospheric variations in main-sequence stars. II," Astrophys. J. 438, 269-287 (1995).
3. Bassom, A. P., Kuzanyan, K. M. and Soward, A. M., "A nonlinear dynamo wave riding on a spatially varying background," Proc. R. Soc. Lond. A submitted (1997).
4. Brandenburg, A., "Solar Dynamos: Computational Background," in: Lectures on Solar and Planetary Dynamos, (Ed. M. R. E. Proctor and A. D. Gilbert) pp. 117-159, Cambridge University Press (1994).
5. Bräuer, H., "The nonlinear dynamo problem: Small oscillatory solutions in a strongly simplified model," Astron. Nachr. 300, 43-49 (1979).
6. Dicke, R. H., "The phase variations of the solar cycle," Solar Physics 115, 171-181 (1988).
7. Frick, P., Galyagin, D., Hoyt, D. V., Nesme-Ribes, E., Schatten, K. H., Sokoloff, D. and Zakharov, V., "Wavelet analysis of solar activity recorded by sunspot groups," Astron. Astrophys. in press (1997a).
8. Frick, P., Baliunas, S. L., Galyagin, D., Sokoloff, D. and Soon, W. H., "Wavelet analysis of stellar chromospheric activity variations," Astrophys. J. in press (1997b).
9. Galitsky, V. M. and Sokoloff, D. D., "Dynamo waves in the theory of cosmic magnetism and probability waves in quantum mechanics," Acta Astron. et Geophys. Univ. Comenianae submitted (1997).
10. Heading, J., An Introduction to Phase Integral Methods, Methuen, London (1962).
11. Huerre, P. and Monkewitz, P. A., "Local and global instabilities in spatially developing flows," Annu. Rev. Fluid Mech. 22, 473-537 (1990).
12. Jennings, R. L., "Symmetry breaking in a nonlinear αω-dynamo," Geophys. Astrophys. Fluid Dynam. 57, 147-189 (1991).
13. Jennings, R. L. and Weiss, N. O., "Symmetry breaking in stellar dynamos," Mon. Not. R. astr. Soc. 252, 249-260 (1991).
14. Krause, F. and Rädler, K.-H., Mean-Field Electrodynamics and Dynamo Theory, Pergamon Press, Oxford (1980).
15. Kuzanyan, K. M. and Sokoloff, D. D., "A dynamo wave in an inhomogeneous medium," Geophys. Astrophys. Fluid Dynam. 81, 113-129 (1995).
16. Kuzanyan, K. M. and Sokoloff, D. D., "A dynamo wave in a thin shell," Astron. Rep. 40, 425-430 (1996).
17. Kuzanyan, K. M. and Sokoloff, D. D., "Half-width of a solar dynamo wave in Parker's migratory dynamo," Solar. Phys. in press (1997).
18. 2ω dynamo," Astron. Rep. 40, 415-423 (1996).
19. Moss, D., Tuominen, I. and Brandenburg, A., "Buoyancy-limited thin shell dynamos," Astron. Astrophys. 240, 142-149 (1990).
20. Noyes, R. W., Weiss, N. O. and Vaughan, A. H., "The relationship between stellar rotation rate and activity cycle periods," Astrophys. J. 287, 769-773 (1984).
21. Otmianowska-Mazur, K., Rüdiger, G., Elstner, D. and Ailt, R., "The turbulent EMF as a time series and the 'quality' of dynamo cycles," Geophys. Astrophys Fluid Dynam. 86, 229-247 (1997).
22. Parker, E. N., "Hydromagnetic dynamo models," Astrophys. J. 122, 293-314 (1955).
23. Pier, B. and Huerre, P., "Fully nonlinear global modes in spatially developing media," Physica D 97, 206-222 (1996).
24. Proctor, M. R. E. and Spiegel, E. A., "Waves of solar activity," in: The Sun and Cool Stars: activity, magnetism, dynamos (Ed. I. Tuominen, D. Moss and G. Rüdiger) Lecture notes in physics. Proceedings 380, pp. 117-128, Springer (1991).
25. Roberts, P. H. and Soward, A. M., "Dynamo theory," Annu. Rev. Fluid Mech. 24, 459-512 (1992).
26. Ruzmaikin, A., Shukurov, A., Sokoloff, D. and Starchenko, S., "Maximally-Efficient-Generation-Approach in dynamo theory," Geophys. Astrophys. Fluid Dynam. 52, 125-139 (1990).
27. Sokoloff, D. D., Fioc, M. and Nesme-Ribes, E., "Asymptotic properties of dynamo wave," Magnetohydrodyn. 26, 59-68 (1995a).
28. Sokoloff, D., Nesme-Ribes, E. and Fioc, M., "Asymptotic properties of dynamo waves," in: Physical Processes in Astrophysics, (Ed. I. W. Roxburgh and J.-L. Masnou) Lecture notes in physics. Proceedings 458, pp. 213-217, Springer (1995b).
29. Soward, A. M., "Thin disc αω-dynamo models II. Short length scale modes," Geophys. Astrophys. Fluid Dynam. 64, 201-225 (1992).
30. Soward, A. M. and Jones, C. A., "The linear stability of the flow in the narrow gap between two concentric rotating spheres," Q. J. Mech. appl. Math. 36, 19-42 (1983).
31. Tobias, S. M., "Properties of nonlinear dynamo waves," Geophys. Astrophys. Fluid Dynam. 86, 287-343 (1997).
32. Tobias, S. M., Proctor, M. R. E. and Knobloch, E., "The role of absolute instability in the solar dynamo," Astron. Astrophys. 318, L55-L58 (1997).
33. Tuominen, I., Rüdiger, G. and Brandenburg, A., "Observational constraints for solar-type dynamos," in: Activity in Cool Star Envelopes, (Ed. O. Havnes, B. R. Pettersen, J. H. M. M. Schmitt and J. E. Solheim) pp. 13-20, Kluwer (1988).
34. Weiss, N. O., "Solar and Stellar Dynamos," in: Lectures on Solar and Planetary Dynamos, (Ed. M. R. E. Proctor and A. D. Gilbert) pp. 59-95, Cambridge University Press (1994).
35. Weiss, N. O., Cattaneo, F. and Jones, C. A., "Periodic and aperiodic dynamo waves," Geophys Astrophys. Fluid Dynam. 30, 305-341 (1984).
36. Worledge, D., Knobloch, E., Tobias, S. and Proctor, M. R. E., "Dynamo waves in semi-infinite and finite domains," Proc. R. Soc. Lond. A 453, 119-143 (1997).