Fluctuation dynamo and turbulent induction at small Prandtl number

Journal Article · Fri Oct 15 04:00:00 EDT 2010 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.82.046314· OSTI ID:21464549

Eyink, Gregory L ^[1]

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1. Department of Applied Mathematics and Statistics and Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218 (United States)

We study the Lagrangian mechanism of the fluctuation dynamo at zero Prandtl number and infinite magnetic Reynolds number, in the Kazantsev-Kraichnan model of white-noise advection. With a rough velocity field corresponding to a turbulent inertial range, flux freezing holds only in a stochastic sense. We show that field lines arriving to the same point which were initially separated by many resistive lengths are important to the dynamo. Magnetic vectors of the seed field that point parallel to the initial separation vector arrive anticorrelated and produce an 'antidynamo' effect. We also study the problem of 'magnetic induction' of a spatially uniform seed field. We find no essential distinction between this process and fluctuation dynamo, both producing the same growth rates and small-scale magnetic correlations. In the regime of very rough velocity fields where fluctuation dynamo fails, we obtain the induced magnetic energy spectra. We use these results to evaluate theories proposed for magnetic spectra in laboratory experiments of turbulent induction.

• OSTI ID: 21464549
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print) Journal Issue: 4 Vol. 82; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ADVECTION
CORRELATIONS
DIMENSIONLESS NUMBERS
ENERGY SPECTRA
FLUCTUATIONS
FREEZING
FUNCTIONS
INDUCTION
LAGRANGIAN FUNCTION
MAGNETIC REYNOLDS NUMBER
MASS TRANSFER
NOISE
PHASE TRANSFORMATIONS
PRANDTL NUMBER
REYNOLDS NUMBER
SPECTRA
STOCHASTIC PROCESSES
TENSORS
TURBULENCE
VARIATIONS
VECTORS
VELOCITY