MULTIPLICATIVE NOISE IN GEODYNAMO MODELS

P. Hoyng, SRON National Institute for Space Research, Utrecht.


The small scale velocity field of a dynamo acts as noise in the time evolution of the large-scale magnetic field. This noise is said to be multiplicative because of the $v\times B$ term in the induction equation: a given $\delta v$ produces a larger $\delta B$ when $B$ is large. The effect of multiplicative noise in geodynamo models is that the variability of the fundamental mode is large while reversals are nevertheless rare (and fast) events. We outline a technique that allows us to infer the statistical properties of the fundamental dipole mode theoretically. Reversals are rare because they require three independent processes to occur by chance within an overtone decay time: a surge of one or more overtone amplitudes, a collapse of the dipole amplitude, and overtones pushing the dipole to the other basin of attraction. Surprisingly, ADM time series of the geodynamo (Sint 2000) and from numerical dynamo models suggest that the noise is quasi-additive, at least at finite magnetic field amplitudes.