Scaling Properties of Three-Dimensional Magnetohydrodynamic Turbulence

Müller, Wolf-Christian; Biskamp, D.

doi:10.1103/physrevlett.84.475

Cited by 271 publications

(267 citation statements)

References 24 publications

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“…Intermittency in the context of MHD turbulence has been studied numerically (see e.g. Müller and Biskamp, 2000also Merrifield et al, 2006 with reference to models such as that of She and Leveque (She and Leveque, 1994; see also Politano and Pouquet, 1995). Dimensional analysis, as we shall see next, provides an overall framework from which we can obtain intermittency free exponents that are independent of this phenomenology.…”

Section: Scaling Exponents Mhd Turbulence Models and Similarity Analmentioning

confidence: 99%

Solar cycle dependence of scaling in solar wind fluctuations

Chapman

Hnat

Kiyani

2008

Nonlin. Processes Geophys.

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Abstract. In this review we collate recent results for the statistical scaling properties of fluctuations in the solar wind with a view to synthesizing two descriptions: that of evolving MHD turbulence and that of a scaling signature of coronal origin that passively propagates with the solar wind. The scenario that emerges is that of coexistent signatures which map onto the well known "two component" picture of solar wind magnetic fluctuations. This highlights the need to consider quantities which track Alfvénic fluctuations, and energy and momentum flux densities to obtain a complete description of solar wind fluctuations.

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Section: Scaling Exponents Mhd Turbulence Models and Similarity Analmentioning

confidence: 99%

Solar cycle dependence of scaling in solar wind fluctuations

Chapman

Hnat

Kiyani

2008

Nonlin. Processes Geophys.

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“…We base the modeling on the well-established von Kármán-Taylor 2,3 approach for energy decay phenomenology in hydrodynamics, that is, on the pair of equations du 2 / dt ϳ −u 2 / sp and dᐉ / dt ϳ ᐉ / sp , with the spectral transfer time sp identified with the global hydrodynamic nonlinear ͑or "eddy turnover"͒ time nl = ᐉ / u. Analogous equations for MHD 12,25,26,6 have been written as direct extensions of this isotropic homogeneous hydrodynamic case, and these have been found to account well for decaying MHD turbulence simulations. 6,27,28 Here, we will adopt a straightforward generalization to account for two evolving MHD components.…”

Section: A Modeling Nonlinear Termsmentioning

confidence: 99%

A two-component phenomenology for homogeneous magnetohydrodynamic turbulence

2006

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A one-point closure model for energy decay in three-dimensional magnetohydrodynamic ͑MHD͒ turbulence is developed. The model allows for influence of a large-scale magnetic field that may be of strength sufficient to induce Alfvén wave propagation effects, and takes into account components of turbulence in which either the wave-like character is negligible or is dominant. This two-component model evolves energy and characteristic length scales, and may be useful as a simple description of homogeneous MHD turbulent decay. In concert with spatial transport models, it can form the basis for approximate treatment of low-frequency plasma turbulence in a variety of solar, space, and astrophysical contexts.

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“…Numerical simulations and experiments show that multipoint velocity correlation functions are intermittent, i.e., they develop a power-law behavior with non-dimensional (anomalous) scaling exponents [1][2][3]. The question of the origins of intermittency in turbulence and its relation inter alia to small structures is also of central importance in the areas of non-equilibrium statistical physics, fluid dynamics, astrophysics, and geophysics [4][5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Intermittency in fractal Fourier hydrodynamics: Lessons from the Burgers equation

et al. 2016

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We present theoretical and numerical results for the one-dimensional stochastically forced Burgers equation decimated on a fractal Fourier set of dimension D.We investigate the robustness of the energy transfer mechanism and of the small-scale statistical fluctuations by changing D. We find that a very small percentage of mode-reduction (D 1) is enough to destroy most of the characteristics of the original non-decimated equation. In particular, we observe a suppression of intermittent fluctuations for D < 1 and a quasi-singular transition from the fully intermittent (D = 1) to the non-intermittent case for D 1. Our results indicate that the existence of strong localized structures (shocks) in the one-dimensional Burgers equation is the result of highly entangled correlations amongst all Fourier modes.

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Scaling Properties of Three-Dimensional Magnetohydrodynamic Turbulence

Cited by 271 publications

References 24 publications

Solar cycle dependence of scaling in solar wind fluctuations

Solar cycle dependence of scaling in solar wind fluctuations

A two-component phenomenology for homogeneous magnetohydrodynamic turbulence

Intermittency in fractal Fourier hydrodynamics: Lessons from the Burgers equation

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