Study of stochastic fluctuations in a shell dynamo

We present a one-dimensional alphaomega-dynamo model to study the role of stochastic fluctuations in nonlinear kinematic dynamos. We introduce nonlinearities in the form of alpha-quenching and consider the effect of a meridional flow. Solutions are seen to settle down to a nonlinear periodic mode with a given amplitude. We show that the system displays relaxation oscillations that are in good agreement with the oscillations observed in the sunspot number time series. Irregularities are generated by adding a random forcing term to the alpha-coefficient to simulate the spatial and temporal complexity of the turbulent motions in the dynamo region. These fluctuations induce amplitude and cycle period variability, fluctuations in the dividing line between polarities around the equator, emergence of regions of reverse polarity, and north-south asymmetries. These results are in good agreement with observations and can be explained as the interaction of the deterministic solution with overtones excited by noise.