Speaker
D. Mitra
(NORDITA)
Description
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.