Effects of fluctuation on mean-field α-Ω dynamos

M. R. E. Proctor¹ - K. J. Richardson¹ - P. J. Bushby²

¹ Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK }
² School of Mathematics and Statistics, Newcastle University, Newcastle Upon Tyne, NE1 7RU, UK

Abstract
We analyse the role of a fluctuating α-effect in α-Ω dynamo models. Numerical experiments show that if the alpha-effect is calculated from direct simulation of the governing MHD equations, there are typically large fluctuations compared to the mean, even if the mean is zero. Earlier work has suggested that these fluctuations alone, in concert with the Omega-effect (differential rotation) can lead to dynamo action. Much of this other work has concentrated on reduced versions of the governing equations, but did not address various questions such as the effect of the new mechanism on the speed of dynamo waves and cycle times for models in realistic geometries. Previous developments involving the spatial distribution of the fluctuations were also unnecessarily cumbersome. By means of a simple ansatz we show that there can be a mechanism for magnetic field generation, valid at large scale separation, deriving from the interaction between a mean shear and a fluctuating α-effect. An equivalent term can arise from the 'shear current effect'. The resulting equations, including the new term representing the mean effect of the fluctuations, are investigated in planar and spherical geometries. We show that the new effect can act as a dynamo even in the absence of a mean α-effect, and that the time-scale for dynamo waves is strongly affected by the presence of fluctuations, with the largest values of the fluctuations leading to steady dynamo action. Figs 6, Refs 13.