A Unified Approach to Mean Field Electrodynamics

An effect of sheared large-scale motions on a mean electromotive force in a nonrotating turbulent flow of a conducting fluid is studied. It is demonstrated that in a homogeneous divergence-free turbulent flow the α-effect does not exist, however a mean magnetic field can be generated even in a nonrotating turbulence with an imposed mean velocity shear due to a new "shear-current" effect. A mean velocity shear results in an anisotropy of turbulent magnetic diffusion. A contribution to the electromotive force related with the symmetric parts of the gradient tensor of the mean magnetic field (the κ-effect) is found in a nonrotating turbulent flows with a mean shear. The κ-effect and turbulent magnetic diffusion reduce the growth rate of the mean magnetic field. It is shown that a mean magnetic field can be generated when the exponent of the energy spectrum of the background turbulence (without the mean velocity shear) is less than 2. The "shear-current" effect was studied using two different methods: the τ -approximation (the Orszag third-order closure procedure) and the stochastic calculus (the path integral representation of the solution of the induction equation, Feynman-Kac formula and Cameron-Martin-Girsanov theorem). Astrophysical applications of the obtained results are discussed.

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“…(see, e.g., [29,30]), where R and K correspond to the large scales, and r and k to the small scales, i.e., R = (…”

Section: Effect Of a Mean Velocity Shear On A Turbulencementioning

confidence: 99%

Electromotive force and large-scale magnetic dynamo in a turbulent flow with a mean shear

2003

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“…We use here the two-scale approach (see, e.g., [13,14]). Indeed, let us consider, for example, a correlation func-…”

Section: Appendix B: the Derivation Of Eq (13)mentioning

confidence: 99%

Magnetic helicity tensor for an anisotropic turbulence

1999

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The evolution of the magnetic helicity tensor for a nonzero mean magnetic field and for large magnetic Reynolds numbers in an anisotropic turbulence is studied. It is shown that the isotropic and anisotropic parts of the magnetic helicity tensor have different characteristic times of evolution. The time of variation of the isotropic part of the magnetic helicity tensor is much larger than the correlation time of the turbulent velocity field. The anisotropic part of the magnetic helicity tensor changes for the correlation time of the turbulent velocity field. The mean turbulent flux of the magnetic helicity is calculated as well. It is shown that even a small anisotropy of turbulence strongly modifies the flux of the magnetic helicity. It is demonstrated that the tensor of the magnetic part of the α-effect for weakly inhomogeneous turbulence is determined only by the isotropic part of the magnetic helicity tensor.

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“…Work by Roberts & Soward (1975) and Rüdiger et al (1986Rüdiger et al ( , 2012) using a quasi-linear approach suggests that the total magnetic tension force (which includes the effects of fluctuations) is reduced in the presence of a mean magnetic field and might formally even change sign for larger magnetic Reynolds numbers, but this would then be beyond the validity of their approximation. Using the spectral τ approach, Kleeorin et al (1989Kleeorin et al ( , 1990) do indeed find this reversal of the sign of the total magnetic tension force.…”

Section: Introductionmentioning

confidence: 99%

Properties of the negative effective magnetic pressure instability

et al. 2012

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As was demonstrated in earlier studies, turbulence can result in a negative contribution to the effective mean magnetic pressure, which, in turn, can cause a large-scale instability. In this study, hydromagnetic mean-field modelling is performed for an isothermally stratified layer in the presence of a horizontal magnetic field. The negative effective magnetic pressure instability (NEMPI) is comprehensively investigated. It is shown that, if the effect of turbulence on the mean magnetic tension force vanishes, which is consistent with results from direct numerical simulations of forced turbulence, the fastest growing eigenmodes of NEMPI are two-dimensional. The growth rate is found to depend on a parameter β characterizing the turbulent contribution of the effective mean magnetic pressure for moderately strong mean magnetic fields. A fit formula is proposed that gives the growth rate as a function of turbulent kinematic viscosity, turbulent magnetic diffusivity, the density scale height, and the parameter β . The strength of the imposed magnetic field does not explicitly enter provided the location of the vertical boundaries are chosen such that the maximum of the eigenmode of NEMPI fits into the domain. The formation of sunspots and solar active regions is discussed as possible applications of NEMPI.

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A Unified Approach to Mean Field Electrodynamics

Cited by 144 publications

References 25 publications

Electromotive force and large-scale magnetic dynamo in a turbulent flow with a mean shear

Electromotive force and large-scale magnetic dynamo in a turbulent flow with a mean shear

Magnetic helicity tensor for an anisotropic turbulence

Properties of the negative effective magnetic pressure instability

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