Stochastic and nonlinear fluctuations in a mean field dynamo.

Details Stochastic and nonlinear fluctuations in a mean field dynamo. Stochastic and nonlinear fluctuations in a mean field dynamo.

Sep 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996a%26a...313..959o&link_type=abstract

Astronomy and Astrophysics, v.313, p.959-970

Astronomy and Astrophysics

Astrophysics

31

Sun: Magnetic Fields, Sunspots, Convection, Turbulence, Mhd

Scientific paper

We study the effect of rapid stochastic fluctuations in the kinetic helicity in a plane parallel mean field dynamo model for the Sun. The α-parameter has a fluctuating component δα=α-α_0_, which is modelled as a random forcing term. The fluctuations give rise to variations in the amplitude and phase of the dynamo wave, such that shorter cycles have higher amplitudes, as is observed in the solar cycle. By making a second order expansion close to the unperturbed marginally stable dynamo wave we are able to go beyond the weak forcing limit studied by Hoyng. We show that with increasing strength of the forcing the effective dynamo frequency decreases. We introduce a simple non-linearity to model α-quenching and derive a set of linear equations for the mean field, valid in the weak forcing case. With α-quenching, phase and amplitude fluctuations are bounded, but still correlated. The strength of the α-quenching is measured by a parameter q=-(T_e_/α_0_)(dα/dT)|_T_e__, where T_e_ is the equilibrium value of the toroidal field. We make a comparison with sunspot data, and conclude that these are well explained by the model if δα/α_0_=~2.2 and q=~0.7. Finally we briefly consider the alternative possibility of fluctuations caused by nonlinear dynamics, without external forcing (δα=0). We show that the resulting phase-amplitude diagram does not agree with observations. Although this is no proof that the phase-amplitude correlation cannot be reproduced by nonlinear chaos, we conclude that stochastic noise provides a more natural explanation.

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