Dhrubaditya Mitra, Axel Brandenburg
We consider mean-field dynamo models with fluctuating \alpha effect, both
with and without shear. The \alpha effect is chosen to be Gaussian white noise
with zero mean and given covariance. We show analytically that the mean
magnetic field does not grow, but, in an infinitely large domain, the
mean-squared magnetic field shows exponential growth of the fastest growing
mode at a rate proportional to the shear rate, which agrees with earlier
numerical results of Yousef et al (2008) and recent analytical treatment by
Heinemann et al (2011) who use a method different from ours. In the absence of
shear, an incoherent \alpha^2 dynamo may also be possible. We further show by
explicit calculation of the growth rate of third and fourth order moments of
the magnetic field that the probability density function of the mean magnetic
field generated by this dynamo is non-Gaussian.
View original:
http://arxiv.org/abs/1107.2419
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