P. Hoyng et Jhgm. Vangeffen, STOCHASTIC EXCITATION OF GLOBAL MAGNETIC-FIELDS BY FLUCTUATIONS IN THE MEAN HELICITY, Geophysical and astrophysical fluid dynamics, 68(1-4), 1993, pp. 203-236
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.