STOCHASTIC EXCITATION OF GLOBAL MAGNETIC-FIELDS BY FLUCTUATIONS IN THE MEAN HELICITY

The mean field B in the dynamo equation can be interpreted as a longit ude-averaged field, and this implies that there are fluctuations in th e mean parameters characterizing the turbulent flow. In this paper we study the effect of fluctuations in the mean helicity numerically and analytically in a very simple spherical alpha2-dynamo: there is no dif ferential rotation and the non-fluctuating parts of alpha and beta do not depend on position (we call this the alpha2-sphere dynamo). The dy namo equation then contains a term del x sigmaalpha((t) B, which descr ibes the effect of the fluctuations in the mean helicity. We show that this type of random forcing implies that the dynamo has to operate (s lightly) subcritically, and that in addition many eigenmodes are excit ed, rather than only the fundamental mode. The advantage of this simpl e alpha2-dynamo model is that we can support the numerical results wit h analytical estimates, for instance, for the value of the dynamo numb er at which the dynamo operates, the relative excitation levels of the modes, and their spectra. This is achieved with the help of an expans ion technique: B is expanded in terms of a complete, orthogonal set of eigenfunctions. We have taken the mean helicity fluctuations to be po sition-independent for simplicity. This, however, renders the dynamo m odel so simple that only dipole fields are excited and magnetic field reversals are absent. We also briefly study the effect of non-linearit ies, in particular of alpha-effect quenching. Non-linearities provide a reference level to the fundamental mode, but do not affect the relat ive excitation levels of the modes.