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Scaling and intermittency in incoherent α–shear dynamo

Authors

  • Dhrubaditya Mitra,

    Corresponding author
    1. NORDITA, AlbaNova University Centre, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden
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  • Axel Brandenburg

    Corresponding author
    1. NORDITA, AlbaNova University Centre, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden
    2. Department of Astronomy, AlbaNova University Centre, Stockholm University, SE-10691 Stockholm, Sweden
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E-mail: dhruba.mitra@gmail.com (DM); brandenb@nordita.org (AB)

ABSTRACT

We consider mean-field dynamo models with fluctuating α effect, both with and without large-scale shear. The α effect is chosen to be Gaussian white noise with zero mean and a given covariance. In the presence of shear, we show analytically that (in infinitely large domains) the mean-squared magnetic field shows exponential growth. The growth rate of the fastest growing mode is proportional to the shear rate. This result agrees with earlier numerical results of Yousef et al. and the recent analytical treatment by Heinemann, McWilliams & Schekochihin who use a method different from ours. In the absence of shear, an incoherent α2 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.

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