Fluctuation dynamo and turbulent induction at small Prandtl number

Journal Article · Fri Oct 15 00:00:00 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), Vol. 82, Issue 4; Other Information: DOI: 10.1103/PhysRevE.82.046314; (c) 2010 The American Physical Society; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

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