Magnetized turbulence is ubiquitous in many astrophysical and terrestrial systems but no complete, uncontested theory even in the simplest form, magnetohydrodynamics (MHD), exists. Many theories and phenomenologies focus on the joint (kinetic and magnetic) energy fluxes and spectra. We highlight the importance of treating kinetic and magnetic energies separately to shed light on MHD turbulence dynamics. We conduct an implicit large eddy simulation of subsonic, super-Alfvénic MHD turbulence and analyze the scale-wise energy transfer over time. Our key finding is that the kinetic energy spectrum develops a scaling of approximately $k^{-4/3}$ in the stationary regime as the kinetic energy cascade is suppressed by magnetic tension. This motivates a reevaluation of existing MHD turbulence theories with respect to a more differentiated modeling of the energy fluxes.
We review the current status of research in MHD turbulence theory and numerical experiments and their applications to astrophysics and solar science. We introduce general tools for studying turbulence, basic turbulence models, MHD equations and their wave modes. Subsequently, we cover the theories and numerics of Alfvenic turbulence, imbalanced turbulence, small-scale dynamos and models and numerics for supersonic MHD turbulence.
We revisit the issue of spectral slope of MHD turbulence in the inertial range and argue that numerics favor Goldreich-Sridhar -5/3 slope rather than -3/2 slope. We also did precision measurements of anisotropy of MHD turbulence and determined the anisotropy constant C_A=0.34 of Alfvenic turbulence. Together with previously measured Kolmogorov constant C_K=4.2, or 3.3 for purely Alfvenic case, it constitutes a full description of MHD cascade in terms of spectral quantities, which is of high practical value for astrophysics.
MHD Turbulence is common in many space physics and astrophysics environments. We first discuss the properties of incompressible MHD turbulence. A well-conductive fluid amplifies initial magnetic fields in a process called small-scale dynamo. Below equipartition scale for kinetic and magnetic energies the spectrum is steep (Kolmogorov -5/3) and is represented by critically balanced strong MHD turbulence. In this paper we report the basic reasoning behind universal nonlinear small-scale dynamo and the inertial range of MHD turbulence. We measured the efficiency of the small-scale dynamo $C_E=0.0…
In this paper we describe the mode-to-mode energy transfers and energy fluxes of MHD turbulence. These energy transfers are very useful for understanding the turbulence dynamics, as well as for applications such as dynamo. We illustrate how the energy fluxes provide valuable insights into the mechanism of growth of the large-scale magnetic energy in dynamo.
Magnetized turbulence is ubiquitous in many astrophysical and terrestrial plasmas but no universal theory exists. Even the detailed energy dynamics in magnetohydrodynamic (MHD) turbulence are still not well understood. We present a suite of subsonic, super-Alfvénic, high plasma-beta MHD turbulence simulations that only vary in their dynamical range, i.e., in their separation between the large-scale forcing and dissipation scales, and their dissipation mechanism (implicit large eddy simulation, ILES, versus and direct numerical simulation, DNS). Using an energy transfer analysis framework we ca…
In hydrodynamic turbulence, the kinetic energy injected at large scales cascades to the inertial range, leading to a constant kinetic energy flux. In contrast, in magnetohydrodynamic (MHD) turbulence, a fraction of kinetic energy is transferred to the magnetic energy. Consequently, for the same kinetic energy injection rate, the kinetic energy flux in MHD turbulence is reduced compared to its hydrodynamic counterpart. This leads to relative weakening of the nonlinear term ($\la | ({\bf u}\cdot \nabla) {\bf u} | \ra$, where ${\bf u}$ is the velocity field) and turbulent drag, but strengthening …
It is shown, using results of recent direct numerical simulations, that spectral properties of distributed chaos in MHD turbulence with zero mean magnetic field are similar to those of hydrodynamic turbulence. An exception is MHD spontaneous breaking of space translational symmetry, when the stretched exponential spectrum $\exp(-k/k_β)^β$ has $β=4/7$.
Recent numerical and observational studies revealed that spectra of magnetic and velocity fluctuations in MHD turbulence have different scaling indexes. This intriguing feature has been recently explained in the case of weak MHD turbulence, that is, turbulence consisting of weakly interacting Alfven waves. However, astrophysical turbulence is strong in majority of cases. In the present work, we propose a unifying picture that allows one to address weak and strong MHD turbulence on the same footing. We argue that magnetic and kinetic energies are different in both weak and strong MHD turbulence…
A phenomenology of isotropic magnetohydrodynamic turbulence subject to both rotation and applied magnetic field is presented. It is assumed that the triple correlations decay-time is the shortest between the eddy turn-over time and the ones associated to the rotating frequency and Alfvén wave period. For $Pm=1$ it leads to four kinds of piecewise spectra, depending on the four parameters, injection rate of energy, magnetic diffusivity, rotation rate and applied field. With a shell model of MHD turbulence (including rotation and applied magnetic field), spectra for $Pm \le 1$ are presented, tog…
Leveling of MHD turbulence imbalance in shear flows
Abastumani Astrophysical Observatory（阿巴斯图马尼天体物理观测站）；Department of Physics, Faculty of Exact and Natural Sciences, Tbilisi State University（第比利斯国立大学精确与自然科学学院物理系）；Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿-罗斯多夫亥姆霍兹中心）；M. Nodia Institute of Geophysics（M.诺迪亚地球物理研究所）
Magnetised turbulence is ubiquitous in astrophysical systems, where it notoriously spans a broad range of spatial scales. Phenomenological theories of MHD turbulence describe the self-similar dynamics of turbulent fluctuations in the inertial range of scales. Numerical simulations serve to guide and test these theories. However, the computational power that is currently available restricts the simulations to Reynolds numbers that are significantly smaller than those in astrophysical settings. In order to increase computational efficiency and, therefore, probe a larger range of scales, one ofte…
Magnetohydrodynamic (MHD) turbulence is pervasive in astrophysical systems. Recent high-resolution numerical simulations suggest that the energy spectrum of strong incompressible MHD turbulence is $E(k_{\perp})\propto k_{\perp}^{-3/2}$. So far, there has been no phenomenological theory that simultaneously explains this spectrum and satisfies the exact analytic relations for MHD turbulence due to Politano & Pouquet. Indeed, the Politano-Pouquet relations are often invoked to suggest that the spectrum of MHD turbulence instead has the Kolmogorov scaling -5/3. Using geometrical arguments and nume…
Magnetised plasma turbulence pervades the universe and is likely to play an important role in a variety of astrophysical settings. Magnetohydrodynamics (MHD) provides the simplest theoretical framework in which phenomenological models for the turbulent dynamics can be built. Numerical simulations of MHD turbulence are widely used to guide and test the theoretical predictions; however, simulating MHD turbulence and accurately measuring its scaling properties is far from straightforward. Computational power limits the calculations to moderate Reynolds numbers and often simplifying assumptions ar…
A discussion of the advantages and limitations of the concept of critical balance, as employed in turbulence phenomenologies, is presented. The incompressible magnetohydrodynamic (MHD) case is a particular focus. The discussion emphasizes the status of the original Goldreich & Sridhar (1995) critical balance conjecture relative to related theoretical issues and models in an MHD description of plasma turbulence. Issues examined include variance and spectral anisotropy, influence of a mean magnetic field, local and nonlocal effects, and the potential for effects of external driving. Related mode…
We investigate the influence of a uniform magnetic field ${\bf B_0}=B_0 e//$ on energy decay laws in incompressible magnetohydrodynamic (MHD) turbulence. The nonlinear transfer reduction along $B_0$ is included in a model that distinguishes parallel and perpendicular directions, following a phenomenology {\it à la} Kraichnan. We predict a slowing down of the energy decay due to anisotropy in the limit of strong $B_0$, with distinct power laws for energy decay of shear- and pseudo-Alfvén waves. Numerical results from the kinetic equations of Alfvén wave turbulence recover these predictions, and…
The ideal invariants present in the formalism of magnetohydrodynamics (MHD), i.e. global quantities that are conserved in the absence of sources and dissipative effects, play an important role in various theoretical and numerical studies of MHD turbulence. The fluxes of these ideal invariants represent separate channels that transfer the information across different scales in a turbulent system. Once a statistically stationary state of turbulence is reached, the amount of any ideal invariant quantity introduced in the system by a forcing mechanism equals the amount of the same quantity removed…
Magnetohydrodynamics (MHD) provides the simplest description of magnetic plasma turbulence in a variety of astrophysical and laboratory systems. MHD turbulence with nonzero cross helicity is often called imbalanced, as it implies that the energies of Alfvén fluctuations propagating parallel and anti-parallel the background field are not equal. Recent analytical and numerical studies have revealed that at every scale, MHD turbulence consists of regions of positive and negative cross helicity, indicating that such turbulence is inherently locally imbalanced. In this paper, results from high reso…
The question is addressed to what extent incompressible magnetohydrodynamics (MHD) can describe random magnetic and velocity fluctuations measured in the solar wind. It is demonstrated that distributions of spectral indices for the velocity, magnetic field, and total energy obtained from high resolution numerical simulations are qualitatively and quantitatively similar to solar wind observations at 1 AU. Both simulations and observations show that in the inertial range the magnetic field spectrum E_b is steeper than the velocity spectrum E_v with E_b >~ E_v and that the residual energy E_R = E…
The objective of this work is to understand how the characteristics of relativistic MHD turbulence may differ from those of nonrelativistic MHD turbulence. We accomplish this by studying the ideal invariants in the relativistic case and comparing them to what we know of nonrelativistic turbulence. Although much work has been done to understand the dynamics of nonrelativistic systems (mostly for ideal incompressible fluids), there is minimal literature explicitly describing the dynamics of relativistic MHD turbulence using numerical simulations. Many researchers simply assume that relativistic …
The transport of waves and turbulence beyond the photosphere is central to the coronal heating problem. Turbulence in the quiet solar corona has been modeled on the basis of the nearly incompressible magnetohydrodynamic (NI MHD) theory to describe the transport of low-frequency turbulence in open magnetic field regions. It describes the evolution of the coupled majority quasi-2D and minority slab component, driven by the magnetic carpet and advected by a subsonic, sub-Alfvenic flow from the lower corona. In this paper, we couple the NI MHD turbulence transport model with an MHD model of the so…
Astrophysical plasmas are turbulent and magnetized. The interaction between cosmic rays (CRs) and magnetohydrodynamic (MHD) turbulence is a fundamental astrophysical process. Based on the current understanding of MHD turbulence, we revisit the trapping of CRs by magnetic mirrors in the context of MHD turbulence. In compressible MHD turbulence, isotropic fast modes dominate both trapping and gyroresonant scattering of CRs. The presence of trapping significantly suppresses the pitch-angle scattering and the spatial diffusion of CRs along the magnetic field. The resulting parallel diffusion coeff…
A variety of studies of magnetised plasma turbulence invoke theories for the advection of a passive scalar by turbulent fluctuations. Examples include modelling the electron density fluctuations in the interstellar medium, understanding the chemical composition of galaxy clusters and the intergalactic medium, and testing the prevailing phenomenological theories of magnetohydrodynamic turbulence. While passive scalar turbulence has been extensively studied in the hydrodynamic case, its counterpart in MHD turbulence is significantly less well understood. Herein we conduct a series of high-resolu…
The purpose of this work is to investigate the spectral properties of the developed isotropic (non-Alfven) MHD turbulence stationary excited by an external force, which injects the cross helicity into the flow simultaneously with the energy. It is shown that the cross helicity blocks the spectral energy transfer in MHD turbulence and results in energy accumulation in the system. This accumulation proceeds until the vortex intensification compensates the decreasing efficiency of nonlinear interactions. The formula for estimating the average turbulence energy is obtained for the set ratio betwee…
We report on a comparison of high-resolution numerical simulations of Lagrangian particles advected by incompressible turbulent hydro- and magnetohydrodynamic (MHD) flows. Numerical simulations were performed with up to $1024^3$ collocation points and 10 million particles in the Navier-Stokes case and $512^3$ collocation points and 1 million particles in the MHD case. In the hydrodynamics case our findings compare with recent experiments from Mordant et al. [1] and Xu et al. [2]. They differ from the simulations of Biferale et al. [3] due to differences of the ranges choosen for evaluating the…
We present a model for compressible sub-Alfvenic isothermal magnetohydrodynamic (MHD) turbulence in low-beta plasmas and numerically test it. We separate MHD fluctuations into 3 distinct families - Alfven, slow, and fast modes. We find that, production of slow and fast modes by Alfvenic turbulence is suppressed. As a result, Alfven modes in compressible regime exhibit scalings and anisotropy similar to those in incompressible regime. Slow modes passively mimic Alfven modes. However, fast modes show isotropy and a scaling similar to acoustic turbulence.
We study the damping from neutral-ion collisions of both incompressible and compressible magnetohydrodynamic (MHD) turbulence in partially ionized medium. We start from the linear analysis of MHD waves applying both single-fluid and two-fluid treatments. The damping rates derived from the linear analysis are then used in determining the damping scales of MHD turbulence. The physical connection between the damping scale of MHD turbulence and cutoff boundary of linear MHD waves is investigated. Our analytical results are shown to be applicable in a variety of partially ionized interstellar mediu…
Incompressible MHD turbulence is investigated under the presence of a uniform magnetic field $\bb0$. Such a situation is described in the correlation space by a divergence relation which expresses the statistical conservation of the Elsässer energy flux through the inertial range. The ansatz is made that the development of anisotropy, observed when $B_0$ is strong enough, implies a foliation of space correlation. A direct consequence is the possibility to derive a vectorial law for third-order Elsässer moments which is parametrized by the intensity of anisotropy. We use the so-called critical …
The scale locality of energy fluxes for magnetohydrodynamics (MHD) is investigated numerically for stationary states of turbulence. Two types of forces are used to drive turbulence, a kinetic force that acts only on the velocity field and a kinetic-inductive forcing mechanism, which acts on the velocity and magnetic fields alike. The analysis is performed in spectral space, which is decomposed into a series of shells following a power law for the boundaries. The triadic transfers occurring among these shells are computed and the fluxes and locality functions are recovered by partial summation …
We propose a phenomenological theory of incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale magnetic field, which establishes a link between the known anisotropic models of strong and weak MHD turbulence We argue that the Iroshnikov-Kraichnan isotropic cascade develops naturally within the plane perpendicular to the mean field, while oblique-parallel cascades with weaker amplitudes can develop, triggered by the perpendicular cascade, with a reduced flux resulting from a quasi-resonance condition. The resulting energy spectrum $E(k_\parallel,k_\bot)$ has the sa…
We investigate the transfer of energy from large scales to small scales in fully developed forced three-dimensional MHD-turbulence by analyzing the results of direct numerical simulations in the absence of an externally imposed uniform magnetic field. Our results show that the transfer of kinetic energy from the large scales to kinetic energy at smaller scales, and the transfer of magnetic energy from the large scales to magnetic energy at smaller scales, are local, as is also found in the case of neutral fluids, and in a way that is compatible with Kolmogorov (1941) theory of turbulence. Howe…
We unite the one-flow-dominated-state (OFDS) argument of \citet{MeyrandGaltierPRL12} with the one-chiral-sector-dominated-state (OCSCS) one \citep[][]{hydrochirality} to form a nonlinear extended-magnetohydrodynamics (XMHD) theory for the solar wind turbulence (SWT), \textbf{ranging from the MHD- to subproton-, and even to subelectron-scale regimes} \citep[modifying the theory of][]{AbdelhamidLingamMahajanAPJ16}. Degenerate chiral states in \citet{MiloshevichLingamMorrisonNJP17}'s XMHD absolute equilibria are exposed with helical representation, to offer the basis of replacing the linear wave …
A comparison of turbulent diffusion and pair-dispersion in homogeneous, macroscopically isotropic Navier-Stokes (NS) and nonhelical magnetohydrodynamic (MHD) turbulence based on high-resolution direct numerical simulations is presented. Significant differences between MHD and NS systems are observed in the pair-dispersion properties, in particular a strong reduction of the separation velocity in MHD turbulence as compared to the NS case. It is shown that in MHD turbulence the average pair-dispersion is slowed down for $τ_\mathrm{d}\lesssim t\lesssim 10 τ_\mathrm{d}$, $τ_\mathrm{d}$ being the K…
The free decay of MHD turbulence at large Reynolds numbers is studied numerically using a shell model. We study the statistical properties based on representative sample of realisations (128 realisations for each type of initial conditions) over the period of $10^5$ large-scale turnover times. The performed simulations show that the force-free non-helical MHD turbulence can demonstrate two different scenarios of evolution in spite of similar initial conditions. Within the first scenario, the cross-helicity accumulation is so fast that the energy cascade vanishes before significant magnetic ene…
In the period of 1948-1955, Chandrasekhar wrote four papers on magnetohydrodynamic (MHD) turbulence, which are the first set of papers in the area. The field moved on following these pioneering efforts. In this paper, I will briefly describe important works of MHD turbulence, starting from those by Chandrasekhar.
As the fundamental physical process with many astrophysical implications, the diffusion of cosmic rays (CRs) is determined by their interaction with magnetohydrodynamic (MHD) turbulence. We consider the magnetic mirroring effect arising from MHD turbulence on the diffusion of CRs. Due to the intrinsic superdiffusion of turbulent magnetic fields, CRs with large pitch angles that undergo mirror reflection, i.e., bouncing CRs, are not trapped between magnetic mirrors, but move diffusively along the turbulent magnetic field, leading to a new type of parallel diffusion, i.e., mirror diffusion. This…
We present the results of three-dimensional (3D) ideal magnetohydrodynamics (MHD) simulations on the dynamics of a perpendicularly inhomogeneous plasma disturbed by propagating Alfvénic waves. Simpler versions of this scenario have been extensively studied as the phenomenon of phase mixing. We show that, by generalizing the textbook version of phase mixing, interesting phenomena are obtained, such as turbulence-like behavior and complex current-sheet structure, a novelty in longitudinally homogeneous plasma excited by unidirectionally propagating waves. This constitutes an important finding fo…
Pitch-angle scattering rates for cosmic-ray particles in magnetohydrodynamic (MHD) simulations with imbalanced turbulence are calculated for fully evolving electromagnetic turbulence. We compare with theoretical predictions derived from the quasilinear theory of cosmic-ray diffusion for an idealized slab spectrum and demonstrate how cross helicity affects the shape of the pitch-angle diffusion coefficient. Additional simulations in evolving magnetic fields or static field configurations provide evidence that the scattering anisotropy in imbalanced turbulence is not primarily due to coherence w…
Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics based on the wavelet coefficients. We then show how to extract coherent structures out of fully developed turbulent flows using wavelet-based denoising. Finally some multiscale numerical simulation schemes using wavelets are described. Several examples for analyzing, compressing and computing one, two and three dimensional turbulent MHD or plasma flows are pres…
As a fundamental astrophysical process, the scattering of particles by turbulent magnetic fields has its physical foundation laid by the magnetohydrodynamic (MHD) turbulence theory. In the framework of the modern theory of MHD turbulence, we derive a generalized broadened resonance function by taking into account both the magnetic fluctuations and nonlinear decorrelation of turbulent magnetic fields arising in MHD turbulence, and we specify the energy range of particles for the dominance of different broadening mechanisms. The broadened resonance allows for scattering of particles beyond the e…
The transport of heavy, neutral or charged, point-like particles by incompressible, resistive magnetohydrodynamic (MHD) turbulence is investigated by means of high-resolution numerical simulations. The spatial distribution of such impurities is observed to display strong deviations from homogeneity, both at dissipative and inertial range scales. Neutral particles tend to cluster in the vicinity of coherent vortex sheets due to their viscous drag with the flow, leading to the simultaneous presence of very concentrated and almost empty regions. The signature of clustering is different for charge…
A review of some of the issues that have arisen over the years concerning the energy distribution among scales for magnetohydrodynamics (MHD) turbulence is given here. A variety of tools are employed to that effect, and a central role is played by taking into consideration the ideal (non-dissipative) invariants, namely the total energy, the magnetic helicity and the cross-correlations between the velocity and the magnetic field (concentrating on the three-dimensional case). These concepts, based mostly on theory, models and direct numerical simulations, are briefly put in the context of observ…
Magnetohydrodynamic (MHD) turbulence in the majority of natural systems, including the interstellar medium, the solar corona, and the solar wind, has Reynolds numbers far exceeding the Reynolds numbers achievable in numerical experiments. Much attention is therefore drawn to the universal scaling properties of small-scale fluctuations, which can be reliably measured in the simulations and then extrapolated to astrophysical scales. However, in contrast with hydrodynamic turbulence, where the universal structure of the inertial and dissipation intervals is described by the Kolmogorov self-simila…
Anisotropy of MHD turbulence has been studied extensively for many years, most prominently by measurements in the solar wind and high resolution simulations. The spectrum parallel to the local magnetic field was observed to be steeper than perpendicular spectrum, typically $k^{-2}$, consistent with the widely accepted Goldreich-Sridhar (1995) model. In this Letter I looked deeper into the nature of the relation between parallel and perpendicular spectra and argue that this $k^{-2}$ scaling has the same origin as the $ω^{-2}$ scaling of Lagrangian frequency spectrum in strong hydrodynamic turbu…
Astrophysical fluids are turbulent, magnetized and frequently partially ionized. As an example of astrophysical turbulence, the interstellar turbulence extends over a remarkably large range of spatial scales and participates in key astrophysical processes happening in different ranges of scales. A significant progress has been achieved in the understanding of the magnetohydrodynamic (MHD) turbulence since the turn of the century, and this enables us to better describe turbulence in magnetized and partially ionized plasmas. In fact, the modern revolutionized picture of the MHD turbulence physic…
Turbulence is the most common state of astrophysical flows. In typical astrophysical fluids, turbulence is accompanied by strong magnetic fields, which has a large impact on the dynamics of the turbulent cascade. Recently, there has been a significant breakthrough on the theory of magnetohydrodynamic (MHD) turbulence. For the first time we have a scaling model that is supported by both observations and numerical simulations. We review recent progress in studies of both incompressible and compressible turbulence. We compare Iroshnikov-Kraichnan and Goldreich-Sridhar models, and discuss scalings…
Turbulence is the most common state of astrophysical flows. In typical astrophysical fluids, turbulence is accompanied by strong magnetic fields, which has a large impact on the dynamics of the turbulent cascade. Recently, there has been a significant breakthrough on the theory of magnetohydrodynamic (MHD) turbulence. For the first time we have a scaling model that is supported by both observations and numerical simulations. We review recent progress in studies of both incompressible and compressible turbulence. We compare Iroshnikov-Kraichnan and Goldreich-Sridhar models, and discuss scalings…
The solar wind is a magnetized and turbulent plasma. Its turbulence is often dominated by Alfvénic fluctuations and often deemed as nearly incompressible far away from the Sun, as shown by in-situ measurements near 1AU. However, for solar wind closer to the Sun, the plasma $β$ decreases (often lower than unity) while the turbulent Mach number $M_t$ increases (can approach unity, e.g., transonic fluctuations). These conditions could produce significantly more compressible effects, characterized by enhanced density fluctuations, as seen by several space missions. In this paper, a series of 3D MH…
Alfvénic component of MHD turbulence damps Alfvénic waves. The consequences of this effect are important for many processes, from cosmic ray (CR) propagation to launching outflows and winds in galaxies and other magnetized systems. We discuss the differences in the damping of the streaming instability by turbulence and the damping of a plane parallel wave. The former takes place in the system of reference aligned with the local direction of magnetic field along which CRs stream. The latter is in the reference frame of the mean magnetic field and traditionally considered in plasma studies. We a…
Measurements of intensity and polarization of diffuse Galactic synchrotron emission as well as starlight polarization reveal power law spectra of fluctuations. We show that these fluctuations can arise from magnetohydrodynamic (MHD) turbulence in the Galactic disk and halo. To do so we take into account the converging geometry of lines of sight for the observations when the observer is within the turbulent volume. Assuming that the intensity of turbulence changes along the line of sight, we get a reasonable fit to the observed synchrotron data. As for the spectra of polarized starlight we get …
This chapter reviews the recent progress made mainly during the last two decades on wave turbulence in magnetized plasmas (MHD, Hall MHD and electron MHD) in the incompressible and compressible cases. The emphasis is made on homogeneous and anisotropic turbulence which usually provides the best theoretical framework to investigate space and laboratory plasmas. The interplanetary medium and the solar atmosphere are presented as two examples of media where anisotropic wave turbulence is relevant. The most important results of wave turbulence are reported and discussed in the context of space and…
The transition from weak to strong turbulence when passing from large to small scales in magnetohydrodynamic (MHD) turbulence with guide field is a cornerstone of anisotropic turbulence theory. We present the first check of this transition, using the Shell-RMHD which combines a shell model of perpendicular nonlinear coupling and linear propagation along the guide field. This model allows us to reach Reynolds numbers around $10^6$. We obtain surprisingly good agreement with the theoretical predictions, with a reduced perpendicular energy spectrum scaling as $k^{-2}$ at large scales and as $k^{-…
The aim of this study is to analyze the feedback process between the magnetic turbulence and the pressure gradients in LHD inward-shifted configurations as well as its role in the transition between the soft-hard MHD regimes for instabilities driven by the mode $1/2$ in the middle plasma. In the present paper we summarize the results of two simulations with different Lundquist numbers, $S = 2.5 \times 10^5$ and $10^6$, assuming a plasma in the slow reconnection regime. The results for the high Lundquist number simulation shows that the magnetic turbulence and the pressure gradient in the middl…
A weakly dispersive sub-range (WDR) of kinetic Alfvén turbulence is distinguished and investigated for the first time in the context of MHD/kinetic turbulence transition. We found perpendicular wavenumber spectra ~ k^{-3} and ~ k^{-4} formed in WDR by strong and weak turbulence of kinetic Alfvén waves (KAWs), respectively. These steep WDR spectra connect shallower spectra in the MHD and strongly dispersive KAW sub-ranges, which results in a specific double-kink (2-k) pattern often seen in observed turbulent spectra. The first kink occurs where MHD turbulence transforms into weakly dispersive K…
This review puts the developments of the last few years in the context of the canonical time line (Kolmogorov to Iroshnikov-Kraichnan to Goldreich-Sridhar to Boldyrev). It is argued that Beresnyak's objection that Boldyrev's alignment theory violates the RMHD rescaling symmetry can be reconciled with alignment if the latter is understood as an intermittency effect. Boldyrev's scalings, recovered in this interpretation, are thus an example of a physical theory of intermittency in a turbulent system. Emergence of aligned structures brings in reconnection physics, so the theory of MHD turbulence …
