Helicity fluctuations in mean field theory: an explanation for the variability of the solar cycle?

Abstract

We consider the effect of fluctuations δα(t) in the mean helicity α 0 (both assumed independent of position) on a plane dynamo wave. The time scale in, of the fluctuations is much shorter than the diffusion time 1/β 0 k 2 (β 0 k 2 τ c 1; β 0 = turbulent diffusion coefficient; k = wave number). We distinguish weak and strong random forcing, according to whether (δα r.m.s. /α 0 )√β 0 k 2 τ c is small or large with respect to 1, and we present a detailed analysis of the weak forcing case. Simple equations are derived for the phases and the logarithmic amplitudes of the poloidal and toroidal mean field, in which the forcing terms appear as additive noise