THE EFFECT OF RANDOM ALPHA-FLUCTUATIONS AND THE GLOBAL PROPERTIES OF THE SOLAR MAGNETIC-FIELD

We study the effect of rapid random fluctuations in the dynamo paramet er alpha in a simple axisymmetric mean-field dynamo. The model is 1D; it is shell with latitude-dependent fields. Radial turbulent diffusion is modeled by a prescribed factor exp(ikr)/r in the field potentials. We consider mainly linear models. The fluctuations excite overtones o f the fundamental mode which are otherwise damped. Butterfly diagrams and frequency spectra Sl(v) of the Legendre expansion coefficients Cl( t) of the toroidal mean field [B(theta, t) = SIGMA(l)C(l)(t)P(l)(cos t heta)] are compared with observations of the solar magnetic field. The results are: (1). The model accounts for the observed relative phases of the coefficients C(l)(t) for odd l at the frequency (22 yr)-1 of t he fundamental mode, and potentially also for their relative amplitude s. (2). The spectra S(l)(nu) are broad and featureless for even l, whi le for odd l the frequency (22 yr)-1 of the fundamental mode dominates . They agree qualitatively with the results of Gokhale and coworkers. It is unlikely that the modal structure in the surface field for even l found by Stenflo and colleagues can be produced by mean field models with random alpha-fluctuations. (3). Butterfly diagrams have a solar- type structure for 1 less-than-or-similar-to kR less-than-or-similar-t o 5(R = position of the bottom of the convection zone). The fluctuatio ns generate many phenomena also seen in the solar cycle, such as slow activity modulations due to mode beating, accidental disappearances of the activity, transequatorial activity, and sometimes quite persisten t North-South asymmetries in the butterfly diagram. The character of t he latter depends sensitively on the value of kR. (4). The amplitudes of the eigenmodes are shown to behave as randomly excited coupled osci llators, which allows us to explain the excitation levels of the overt ones, their frequency spectra and the structure of the North-South asy mmetries. (5). In the latitude region where the dynamo operates the lo cal fluctuations in (u . del x u)tau(c) are approximately 60 to 70 tim es larger than the mean value of (u . del x u)tau(c), and the fluctuat ions in alpha are 6 to 7 times larger than the mean value of alpha.