Abstract
We present a one-dimensional αω-dynamo model to study the role of stochastic fluctuations in nonlinear kinematic dynamos. We introduce nonlinearities in the form of α-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 α-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.
Highlights
The solar cycle was discovered by Schwabe in 1843 from observations of the sunspot number as a function of time
We present a one-dimensional !-dynamo model to study the role of stochastic fluctuations in nonlinear kinematic dynamos
We show that the system displays relaxation oscillations that are in good agreement with the oscillations observed in the sunspot number time series
Summary
The solar cycle was discovered by Schwabe in 1843 from observations of the sunspot number as a function of time. We find that the interaction of the deterministic dynamo equations with this stochastic forcing can provide a satisfactory explanation for some of the irregular features observed for the Sun, such as relaxation oscillations in the sunspot time series, variability in the amplitude and period, north-south asymmetries in the butterfly diagrams, and the existence of reverse polarity regions close to the equator. We believe that this treatment of the solar-cycle irregularities could in principle be extended to study long-time trends as well, since our model includes both stochastic and dynamical effects
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