Effects of α-effect fluctuations on simple nonlinear dynamo models

Abstract

We investigate the interaction of a fluctuating α-effect with large-scale shear in a simple nonlinear one-dimensional dynamo wave model. We firstly extend the calculations of Proctor [Effects of fluctuation on αΩ dynamo models. Mon. Not. R. Astron. Soc. 2007, 41, L39–L42] to include spatial variation of the fluctuations, and find that there can be a mechanism for magnetic field generation, even when the mean α is zero, provided the spatiotemporal spectrum of the fluctuations has an appropriate form. We investigate mean-field dynamo action when the new term arising from the fluctuations is non-zero, and present results concerning the stability and frequency of the solutions and parity selection in the nonlinear regime. The relation between the asymptotic theory and explicit simulation of a traditional mean-field model with a fluctuating function for the α-effect term is discussed.