The Anisotropy of Magnetohydrodynamic Alfvenic Turbulence

Cho, Jungyeon; Vishniac, Ethan T.

doi:10.1086/309213

Cited by 600 publications

(737 citation statements)

References 10 publications

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“…First, there is the issue of local anisotropy (e.g. Cho & Vishniac 2000;Milano et al 2001), where it is argued that despite the global isotropy, various subregions have a well-defined (large-scale) local mean field which induces anisotropy in the small scales of the subregion. If the local anisotropy is present, it is in a randomly oriented coordinate system and is properly considered to be a higher-order quantity (that is, a property of higher-order moments).…”

mentioning

confidence: 99%

von Kármán self-preservation hypothesis for magnetohydrodynamic turbulence and its consequences for universality

et al. 2012

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AbstractWe argue that the hypothesis of preservation of shape of dimensionless second- and third-order correlations during decay of incompressible homogeneous magnetohydrodynamic (MHD) turbulence requires, in general, at least two independent similarity length scales. These are associated with the two Elsässer energies. The existence of similarity solutions for the decay of turbulence with varying cross-helicity implies that these length scales cannot remain in proportion, opening the possibility for a wide variety of decay behaviour, in contrast to the simpler classic hydrodynamics case. Although the evolution equations for the second-order correlations lack explicit dependence on either the mean magnetic field or the magnetic helicity, there is inherent implicit dependence on these (and other) quantities through the third-order correlations. The self-similar inertial range, a subclass of the general similarity case, inherits this complexity so that a single universal energy spectral law cannot be anticipated, even though the same pair of third-order laws holds for arbitrary cross-helicity and magnetic helicity. The straightforward notion of universality associated with Kolmogorov theory in hydrodynamics therefore requires careful generalization and reformulation in MHD.

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confidence: 99%

von Kármán self-preservation hypothesis for magnetohydrodynamic turbulence and its consequences for universality

et al. 2012

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“…Evidence in support of equation (1) has been found in direct numerical simulations of MHD turbulence (Maron 2000, Cho & Vishniac 2000. In this spectrum, there is only power at small scales when k º k 2 3 l 1 3 .…”

Section: Goldreich-sridhar Spectrummentioning

confidence: 53%

The Importance of Anisotropic Interstellar Turbulence and Molecular-Cloud Magnetic Mirrors for Galactic Cosmic-Ray Propagation

Chandran

2001

Space Sciences Series of ISSI

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Recent studies suggest that when magnetohydrodynamic (MHD) turbulence is excited by stirring a plasma at large scales, the cascade of energy from large to small scales is anisotropic, in the sense that small-scale fluctuations satisfy the inequality k k , where k and k are, respectively, the components of a fluctuation's wave vector and to the background magnetic field. Such anisotropic fluctuations are very inefficient at scattering cosmic rays. Results based on the quasilinear approximation for scattering of cosmic rays by anisotropic MHD turbulence are presented and explained. The important role played by molecular-cloud magnetic mirrors in confining and isotropizing cosmic rays when scattering is weak is also discussed.

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“…On the other hand, Cho & Vishniac (2000) find almost perfect equipartition for all scales. The difference is small, Figure 6.…”

Section: Imposed Magnetic Fieldmentioning

confidence: 91%

“…Cho & Vishniac (2000). The obvious question is therefore, is it really true that the cases of dynamo-generated and imposed fields are indeed drastically different?…”

Section: Introductionmentioning

confidence: 99%

High-Resolution Simulations of Nonhelical MHD Turbulence

Haugen

Brandenburg

Dobler

2004

Magnetic Fields and Star Formation

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Abstract. According to the kinematic theory of nonhelical dynamo action the magnetic energy spectrum increases with wavenumber and peaks at the resistive cutoff wavenumber. It has previously been argued that even in the dynamical case the magnetic energy peaks at the resistive scale. Using high resolution simulations (up to 1024 3 meshpoints) with no large scale imposed field we show that the magnetic energy peaks at a wavenumber that is independent of the magnetic Reynolds number and about 5 times larger than the forcing wavenumber. Throughout the inertial range the spectral magnetic energy exceeds the kinetic energy by a factor of 2 to 3. Both spectra are approximately parallel. The total energy spectrum seems to be close to k −3/2 , but there is a strong bottleneck effect and it is suggested that the asymptotic spectrum is instead k −5/3 . This is supported by the value of the second order structure function exponent that is found to be ζ2 = 0.70, suggesting a k −1.70 spectrum. The third order structure function scaling exponent is very close to unity, in agreement with Goldreich-Sridhar theory.Adding an imposed field tends to suppress the small scale magnetic field. We find that at large scales the magnetic power spectrum follows then a k −1 slope. When the strength of the imposed field is of the same order as the dynamo generated field, we find almost equipartition between the magnetic and kinetic power spectra.

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The Anisotropy of Magnetohydrodynamic Alfvenic Turbulence

Cited by 600 publications

References 10 publications

von Kármán self-preservation hypothesis for magnetohydrodynamic turbulence and its consequences for universality

von Kármán self-preservation hypothesis for magnetohydrodynamic turbulence and its consequences for universality

The Importance of Anisotropic Interstellar Turbulence and Molecular-Cloud Magnetic Mirrors for Galactic Cosmic-Ray Propagation

High-Resolution Simulations of Nonhelical MHD Turbulence

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