Abstract
We consider dynamically consistent mean-field dynamos in a spherical shell of incompressible fluid. The generation of magnetic field and differential rotation is parameterized by the α- and Λ-effects, respectively. Extending previous investigations, we include now the cases of moderate and rapid rotation in the sense that the inverse Rossby number can approach or exceed unity: This can lead to disk-shaped Ω-contours, which are in better accordance with recent results of helioseismology than cylindrical Ω-contours. On the other hand, in order to obtain αω-dynamo cycles the Taylor number has to be so large, that eventually cylindrical Ω-contours become unavoidable (cf. Taylor-Proudman theorem). We discuss the different possibilities in a state diagram, where the inverse Rossby number and the relative correlation length are taken as the elementary parameters for mean-field dynamos.
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References
Brandenburg, A. and Tuominen, I.: 1988, Adv. Space Sci. 8(7), 185.
Brandenburg, A., Krause, F., and Tuominen, I.: 1989, in M. Meneguzzi, A. Pouquet, and P. L. Sulem (eds.), Turbulence and Nonlinear Dynamics in MHD Flows, Elsevier Science Publ. B.V. (North-Holland), Amsterdam, p. 35.
Brandenburg, A., Krause, F., Meinel, R., Moss, D., Tuominen, I.: 1989, Astron. Astrophys. 213, 411.
Brandenburg, A., Moss, D., Rüdiger, G., and Tuominen, I.: 1990, Astron. Astrophys. (Paper I), (submitted).
Brown, T. M. and Morrow, C. A.: 1987, Astrophys. J. 314, L21.
Dziembowski, W. A., Goode, P. R., and Libbrecht, K. G.: 1989, Astrophys. J. 337, L53.
Gilman, P. A. and Miller, J.: 1981, Astrophys. J. Suppl. 46, 211.
Gilman, P. A., Morrow, C. A., and DeLuca, E. E.: 1989, Astrophys. J. 338, 528.
Glatzmaier, G. A.: 1985, Astrophys. J. 291, 300.
Kichatinov, L. L.: 1987, Geophys. Astrophys. Fluid Dyn. 38, 273.
Kichatinov, L. L.: 1988, Astron. Nachr. 309, 197.
Kleeorin, N. I. and Ruzmaikin, A. A.: 1982, Magnitnaya gidrodinamika 2, 17.
Krause, F. and Rädler, K.-H.: 1980, Mean-Field Magnetohydrodynamics and Dynamo Theory, Akademie-Verlag, Berlin.
Libbrecht, K. G.: 1988, in E. J. Rolfe (ed.), Seismology of the Sun and Sun-like Stars, ESA SP-286, p. 131.
Nordlund, Å.: 1985, Solar Phys. 100, 209.
Parker, E. N.: 1979, Cosmical Magnetic Fields, Clarendon Press, Oxford.
Roberts, P. H. and Soward, A. M.: 1975, Astron. Nachr. 296, 49.
Rüdiger, G.: 1974, Astron. Nachr. 295, 275.
Rüdiger, G.: 1980, Geophys. Astrophys. Fluid Dyn. 16, 239.
Rüdiger, G.: 1989, Differential rotation and Stellar Convection: Sun and Solar-Type Stars, Gordon and Breach, New York.
Rüdiger, G. and Kichatinov, L. L.: 1990, Astron. Astrophys. (in press).
Tuominen, I. and Rüdiger, G.: 1989, Astron. Astrophys. 217, 217.
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Brandenburg, A., Moss, D., Rüdiger, G. et al. The nonlinear solar dynamo and differential rotation: A Taylor number puzzle?. Sol Phys 128, 243–251 (1990). https://doi.org/10.1007/BF00154160
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DOI: https://doi.org/10.1007/BF00154160