Evolution of localized magnetic field perturbations and the nature of turbulent dynamo

Abstract

Kinematic dynamo in incompressible isotropic turbulent flows with high magnetic Prandtl number is considered. The approach interpreting an arbitrary magnetic field distribution as a superposition of localized perturbations (blobs) is proposed. We derive a relation between stochastic properties of a blob and a stochastically homogenous distribution of magnetic field advected by the same stochastic flow. This relation allows to investigate the evolution of a localized blob at late stage when its size exceeds the viscous scale. It is shown that in 3-dimansional flows, the average magnetic field of the blob increases exponentially in the inertial range of turbulence, as opposed to the late-Batchelor stage when it decreases. Our approach reveals the mechanism of dynamo generation in the inertial range both for blobs and homogenous contributions. It explains the absence of dynamo in the two-dimensional case and its efficiency in three dimensions. We propose the way to observe the mechanism in numerical simulations.

10 pages, 1 figure

References in corpus (4)

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• Dynamo effect in the Kraichnan magnetohydrodynamic turbulence
• Two-dimensional magnetohydrodynamic turbulence with large and small energy-injection length scales
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Cited by in corpus (5)

• Long-term properties of finite-correlation time isotropic stochastic systems
• Non-Gaussian generalization of the Kazantsev-Kraichnan model
• Suppression of small-scale dynamo in time irreversible turbulence
• Small-scale turbulent dynamo for low-Prandtl number fluid: comparison of the theory with results of numerical simulations
• Virtual states and exponential decay in small-scale dynamo