Statistical anisotropy of magnetohydrodynamic turbulence

Müller, Wolf-Christian; Biskamp, D.; Grappin, R.

doi:10.1103/physreve.67.066302

Cited by 178 publications

(233 citation statements)

References 27 publications

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“…Indeed, while the Yaglom MHD relation (2) involves only differences along the parallel direction, that are in fact the only quantities accessible from single satellite measurements, phenomenological arguments involve the full spatial dependence of vector fields that cannot be directly measured yet. This means that our result is compatible with both Kolmogorov and Iroshnikov-Kraichnan type cascade [4,2], and does not help in discriminating between these phenomenologies [26,27].In conclusion, we observed, for the first time in the solar wind, the only natural plasma directly accessible, evidence of Yaglom MHD scaling law indicating the existence of a local energy cascade in hydromagnetic turbulence. The scaling holds in a number of relatively long periods of about 10 days, and also provides the first estimation of the pseudo-energy dissipation rate.…”

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confidence: 43%

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confidence: 47%

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Observation of Inertial Energy Cascade in Interplanetary Space Plasma

Sorriso‐Valvo¹,

et al. 2007

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We show in this article direct evidence for the presence of an inertial energy cascade, the most characteristic signature of hydromagnetic turbulence (MHD), in the solar wind as observed by the Ulysses spacecraft. After a brief rederivation of the equivalent of Yaglom's law for MHD turbulence, we show that a linear relation is indeed observed for the scaling of mixed third order structure functions involving Elsässer variables. This experimental result, confirming the prescription stemming from a theorem for MHD turbulence, firmly establishes the turbulent character of low-frequency velocity and magnetic field fluctuations in the solar wind plasma.Space flights have shown that the interplanetary medium is permeated by a supersonic, highly turbulent plasma flowing out from the solar corona, the so called solar wind [1,2]. The turbulent character of the flow, at frequencies below the ion gyrofrequency f ci ≃ 1Hz, has been invoked since the first Mariner mission [3]. In fact, velocity and magnetic fluctuations power spectra are close to the Kolmogorov's -5/3 law [2,6]. However, even if fields fluctuations are usually considered within the framework of magnetohydrodynamic (MHD) turbulence [2], a firm established proof of the existence of an energy cascade, namely the main characteristic of turbulence, remains a conjecture so far [4]. This apparent lack could be fulfilled through the evidence for the existence of the only exact and nontrivial result of turbulence [6], that is a relation between the third order moment of the longitudinal increments of the fields and the separation [5]. This observation would firmly put low frequency solar wind fluctuations within the framework of MHD turbulence. The importance of such question stands beyond the understanding of the basic physics of solar wind turbulence. For example, it is well known that turbulence is one of the main obstacles to the confinement of plasmas in the fusion devices [7,8]. The understanding of interplanetary turbulence and its effects on energetic particle transport is of great importance also for Space Weather research [9], which is a relevant issue for spacecrafts and communication satellites operations, and for the security of human beings. Finally, more theoretical problems are concerned, such as the puzzle of solar coronal heating due to the turbulent flux toward small scales [10].Incompressible MHD equations are more complicated than the standard neutral fluid mechanics equations because the velocity of the charged fluid is coupled with the magnetic field generated by the motion of the fluid itself. However, written in terms of the Elsässer variables defined as z ± = v ± (4πρ) −1/2 b (v and b are the velocity and magnetic field respectively and ρ the mass density), they have the same structure as the Navier-Stokes equations [4]where P is the total hydromagnetic pressure, while ν is the viscosity and κ the magnetic diffusivity. In particular, the nonlinear term appears as z ∓ · ∇z ± , suggesting the form of a transport process, in which Alfvé...

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confidence: 47%

Observation of Inertial Energy Cascade in Interplanetary Space Plasma

Sorriso‐Valvo¹,

et al. 2007

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“…It is a well known fact that in magnetohydrodynamic turbulence turbulent eddies are anisotropic with respect to a mean magnetic field. [43][44][45][46][47][48] As the fluid elements travel on average preferentially along the magnetic lines of force the relative dispersion is significantly reduced in the fieldperpendicular direction. Motions across field lines trigger quasi-oscillatory flow patterns which are supposed to drive the energy cascade 44 but apparently do not lead to an effective separation of the particle pairs.…”

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confidence: 99%

Statistics of passive tracers in three-dimensional magnetohydrodynamic turbulence

et al. 2007

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A priori analysis of subgrid mass diffusion vectors in high pressure turbulent hydrogen/oxygen reacting shear layer flames Phys. Fluids 24, 075114 (2012) Hybrid simulations of metal particle nucleation: A priori and a posteriori analyses of the effects of unresolved scalar interactions on nanoparticle nucleation Phys. Fluids 24, 075110 (2012) Mitigation of preferential concentration of small inertial particles in stationary isotropic turbulence using electrical and gravitational body forces Phys. Magnetohydrodynamic ͑MHD͒ turbulence is studied from the Lagrangian viewpoint by following fluid particle tracers in high resolution direct numerical simulations. Results regarding turbulent diffusion and dispersion as well as Lagrangian structure functions are presented. Whereas turbulent single-particle diffusion exhibits essentially the same behavior in Navier-Stokes and MHD turbulence, two-particle relative dispersion in the MHD case differs significantly from the Navier-Stokes behavior. This observation is linked to the local anisotropy of MHD turbulence which is clearly reflected by quantities measured in a Lagrangian frame of reference. In the MHD case the Lagrangian structure functions display a lower level of intermittency as compared to the Navier-Stokes case contrasting Eulerian results. This is not only true for short time increments ͓H. Homann, R. Grauer, A. Busse, and W.-C. Müller, J. Plasma Phys. 73, 821 ͑2007͔͒ but also holds for increments up to the order of the integral time scale. The apparent discrepancy can be explained by the difference in the characteristic shapes of fluid particle trajectories in the vicinity of most singular dissipative structures.

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“…Its theory has attracted a sizable literature (Iroshnikov 1963;Kraichnan 1965;Shebalin et al 1983;Goldreich & Sridhar 1995, 1997Ng & Bhattacharjee 1996;Cho & Vishniac 2000;Biskamp & Müller 2000;Maron & Goldreich 2001;Cho et al 2002;Galtier et al 2000Galtier et al , 2002Müller et al 2003;Galtier et al 2005;Boldyrev 2005;Müller & Grappin 2005;Beresnyak & Lazarian 2006). The simplest of cases concerns the small-scale dynamics of the excitations of an incompressible fluid with a mean magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Imbalanced Strong MHD Turbulence

Lithwick

Goldreich

Sridhar

2007

ApJ

161

215

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We present a phenomenological model of imbalanced MHD turbulence in an incompressible magnetofluid. The steady state cascades, of waves traveling in opposite directions along the mean magnetic field, carry unequal energy fluxes to small length scales, where they decay as a result of viscous and resistive dissipation. The inertial range scalings are well understood when both cascades are weak. We study the case in which both cascades are, in a sense, strong. The inertial range of this imbalanced cascade has the following properties: (1) The ratio of the rms Elsässer amplitudes is independent of scale and is equal to the ratio of the corresponding energy fluxes. (2) In common with the balanced strong cascade, the energy spectra of both Elsässer waves are of the anisotropic Kolmogorov form, with their parallel correlation lengths equal to each other on all scales, and proportional to the two-thirds power of the transverse correlation length. (3) The equality of cascade time and wave period (critical balance) that characterizes the strong balanced cascade does not apply to the Elsässer field with the larger amplitude. Instead, the more general criterion that always applies to both Elsässer fields is that the cascade time is equal to the correlation time of the straining imposed by oppositely directed waves. (4) In the limit of equal energy fluxes, the turbulence corresponds to the balanced strong cascade. Our results are particularly relevant for turbulence in the solar wind. Spacecraft measurements have established that in the inertial range of solar wind turbulence, waves traveling away from the Sun have higher amplitudes than those traveling toward it. Result 1 allows us to infer the turbulent flux ratios from the amplitude ratios, thus providing insight into the origin of the turbulence.

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Statistical anisotropy of magnetohydrodynamic turbulence

Cited by 178 publications

References 27 publications

Observation of Inertial Energy Cascade in Interplanetary Space Plasma

Observation of Inertial Energy Cascade in Interplanetary Space Plasma

Statistics of passive tracers in three-dimensional magnetohydrodynamic turbulence

Imbalanced Strong MHD Turbulence

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