Fourier space intermittency of the small-scale turbulent dynamo

Abstract

The small-scale turbulent dynamo in the high Prandtl number regime is described in terms of the one-point Fourier space correlators. The second order correlator of this kind is the energy spectrum and it has been previously studied in detail. We examine the higher order k-space correlators which contain important information about the phases of the magnetic wavepackets and about the dominant structures of the magnetic turbulence which cause intermittency. In particular, the fourth-order correlators contain information about the mean-square phase difference between any two components of the magnetic field in a plane transverse to the wavevector. This can be viewed as a measure of the magnetic field's polarization. Examining this new quantity, the magnetic field is shown to become plane polarized in the Kazantsev-Kraichnan model at large time, corresponding to a strong deviation from Gaussianity. We derive a closed equation for the generating function of the Fourier correlators and find the large-time asymptotic solutions of these correlators at all orders. The time scaling of these solutions implies the magnetic field has log-normal statistics, whereas the wavenumber scaling indicates that the field is dominated by intermittent fluctuations at high k.

26 pages, 2 figures. Submitted to PRE

References in corpus (4)

• Particles and fields in fluid turbulence
• Spectra and Growth Rates of Fluctuating Magnetic Fields in the Kinematic Dynamo Theory with Large Magnetic Prandtl Numbers
• The small-scale structure of magnetohydrodynamic turbulence with large magnetic Prandtl numbers
• Structure of Small-Scale Magnetic Fields in the Kinematic Dynamo Theory

Cited by in corpus (3)

• Astrophysical magnetic fields and nonlinear dynamo theory
• Simulations of small-scale turbulent dynamo
• A model for rapid stochastic distortions of small-scale turbulence