Astronomy and Astrophysics – Astrophysics
Scientific paper
Sep 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994a%26a...289..265h&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 289, no. 1, p. 265-278
Astronomy and Astrophysics
Astrophysics
33
Dynamo Theory, Magnetic Variations, Magnetohydrodynamics, Power Spectra, Solar Activity, Solar Magnetic Field, Diffusion, Spherical Harmonics, Stellar Convection, Stellar Models, Turbulence
Scientific paper
We study the effect of rapid random fluctuations in the dynamo parameter alpha in a simple axisymmetric mean-field dynamo. The model is 1D; it is a shell with latitude-dependent fields. Radial turbulent diffusion is modeled by a prescribed factor ikr r in the field potentials. We consider mainly linear models. The fluctuations excite overtones of the fundamental mode which are otherwise damped. Butterfly diagrams and frequency spectra Sl(nu) of the Legendre expansion coefficients cl(t) of the toroidal mean field (B(theta, t) = Sigmalcl(t)Pl(cos(theta))) are compared with observations of the solar magnetic field. The results are: (1). The model accounts for the observed relative phases of the coefficients cl(t) for odd l at the frequency per 22 yr of the fundamental mode, and potentially also for their relative amplitudes. (2). The spectra Sl(nu) are broad and featureless for even l, while for odd l the frequency per 22 yr of the fundamental mode dominates. (3). Butterfly diagrams have a solar-type structure for 1 less than or approximately = kR less than or approximately = 5 (R = position of the bottom of the convection zone). (4). The amplitudes of the eigenmodes are shown to behave as randomly excited coupled oscillators. (5). In the latitude region where the dynamo operates the local fluctuations in (u dot del-V x u)tauc are approximately 60 to 70 times larger than the mean value of (u dot del-V x u)tauc, and the fluctuations in alpha are 6 to 7 times larger than the mean value of alpha.
Hoyng Peter
Schmitt Denis
Teuben J. W. L.
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