Stochastic flux freezing and magnetic dynamo

Journal Article · Sun May 15 04:00:00 EDT 2011 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.83.056405· OSTI ID:21560293

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)

Magnetic flux conservation in turbulent plasmas at high magnetic Reynolds numbers is argued neither to hold in the conventional sense nor to be entirely broken, but instead to be valid in a statistical sense associated to the ''spontaneous stochasticity'' of Lagrangian particle trajectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. Empirical evidence is presented for spontaneous stochasticity, including numerical results. A Lagrangian path-integral approach is then exploited to establish stochastic flux freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux conservation must remain stochastic at infinite magnetic Reynolds number. An important application of these results is the kinematic, fluctuation dynamo in nonhelical, incompressible turbulence at magnetic Prandtl number (Pr{sub m}) equal to unity. Numerical results on the Lagrangian dynamo mechanisms by a stochastic particle method demonstrate a strong similarity between the Pr{sub m}=1 and 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. Finally, some consequences for nonlinear magnetohydrodynamic turbulence, dynamo, and reconnection are briefly considered.

• OSTI ID: 21560293
• 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: 5 Vol. 83; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
DIFFUSION
DIMENSIONLESS NUMBERS
EQUATIONS
FLUCTUATIONS
FLUID MECHANICS
FUNCTIONS
HYDRODYNAMICS
LAGRANGIAN FUNCTION
LAPLACIAN
MAGNETIC FLUX
MAGNETIC REYNOLDS NUMBER
MAGNETOHYDRODYNAMICS
MATHEMATICAL OPERATORS
MECHANICS
NONLINEAR PROBLEMS
PARTICLES
PLASMA
PRANDTL NUMBER
REYNOLDS NUMBER
RICHARDSON EQUATION
STOCHASTIC PROCESSES
TRAJECTORIES
TURBULENCE
VARIATIONS