Scaling and intermittency in incoherent \alpha-shear dynamo

TL;DR

This paper analytically investigates mean-field dynamo models with stochastic fect, revealing that while the mean magnetic field does not grow, the mean-squared magnetic field exhibits exponential growth influenced by shear, with non-Gaussian statistics.

Contribution

It provides an analytical framework for understanding incoherent -dynamo behavior with shear, including growth rates and statistical properties of the magnetic field.

Findings

Mean magnetic field does not grow, but mean-squared field grows exponentially.

Growth rate of the mean-squared magnetic field is proportional to shear rate.

Probability density function of the magnetic field is non-Gaussian.

Abstract

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.