The Eulerian space-time correlation of strong Magnetohydrodynamic (MHD) turbulence in strongly magnetized plasmas is investigated by means of direct numerical simulations of Reduced MHD turbulence and phenomenological modeling. Two new important results follow from the simulations: 1) counter-propagating Alfvénic fluctuations at a each scale decorrelate in time at the same rate in both balanced and imbalanced turbulence; and 2) the scaling with wavenumber of the decorrelation rate is consistent with pure hydrodynamic sweeping of small-scale structures by the fluctuating velocity of the energy-containing scales. An explanation of the simulation results is proposed in the context of a recent phenomenological MHD model introduced by Bourouaine and Perez 2019 (BP19) when restricted to the strong turbulence regime. The model predicts that the two-time power spectrum exhibits an universal, self-similar behavior that is solely determined by the probability distribution function of random velocities in the energy-containing range. Understanding the scale-dependent temporal evolution of the space-time turbulence correlation as well as its associated universal properties is essential in the analysis and interpretation of spacecraft observations, such as the recently launched Parker Solar Probe (PSP).
We derive a Noether current for the Eulerian variational principle of ideal non-barotropic magnetohydrodynamics (MHD). It was shown previously that ideal non-barotropic MHD is mathematically equivalent to a five function field theory with an induced geometrical structure in the case that field lines cover surfaces and this theory can be described using a variational principle. Here we use various symmetries of the flow to derive topological constants of motion through the derived Noether current and discuss their implication for non-barotropic MHD.
Kinetic-range turbulence in magnetized plasmas and, in particular, in the context of solar-wind turbulence has been extensively investigated over the past decades via numerical simulations. Among others, one of the widely adopted reduced plasma model is the so-called hybrid-kinetic model, where the ions are fully kinetic and the electrons are treated as a neutralizing (inertial or massless) fluid. Within the same model, different numerical methods and/or approaches to turbulence development have been employed. In the present work, we present a comparison between two-dimensional hybrid-kinetic …
Magnetic field are transported and tangled by turbulence, even as they lose identity due to nonideal or resistive effects. On balance field lines undergo stretch-twist-fold processes. The curvature field, a scalar that measures the tangling of the magnetic field lines, is studied in detail here, in the context of magnetohydrodynamic turbulence. A central finding is that the magnitudes of the curvature and the magnetic field are anti-correlated. High curvature co-locates with low magnetic field, which gives rise to power-law tails of the probability density function of the curvature field. The …
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 …
Using a three-dimensional compressible magnetohydrodynamic (MHD) simulation, we have reproduced the fast solar wind in a direct and self-consistent manner, based on the wave/turbulence driven scenario. As a natural consequence of Alfvenic perturbations at its base, highly compressional and turbulent fluctuations are generated, leading to heating and acceleration of the solar wind. The analysis of power spectra and structure functions reveals that the turbulence is characterized by its imbalanced (in the sense of outward Alfvenic fluctuations) and anisotropic nature. The density fluctuation ori…
Variational principles for magnetohydrodynamics (MHD) were in\-troduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of non-barotropic stationary magnetohydrodynamics can be derived for certain field topologies. The variational principle is given in terms of three independent functions for stationary non-barotropic flows. This is a smaller number of variables than the eight variables which appear in the standard equations of non-barotropic magnetohydrodynamics which are the mag…
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.
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…
It has recently been proposed (Loureiro & Boldyrev 2017; Mallet et al. 2017) that the inertial interval in magnetohydrodynamic (MHD) turbulence is terminated at small scales not by a Kolmogorov-like dissipation region, but rather by a new sub-inertial interval mediated by tearing instability. However, many astrophysical plasmas are nearly collisionless so that the MHD approximation is not applicable to turbulence at small scales. In this Letter, we propose the extension of the theory of reconnection-mediated turbulence to plasmas which are so weakly collisional that the reconnection occurring …
In situ spacecraft data on the solar wind show events identified as magnetic reconnection with outflows and apparent "`$X$-lines" $10^{3-4}$ times ion scales. To understand the role of turbulence at these scales, we make a case study of an inertial-range reconnection event in a magnetohydrodynamic (MHD) simulation. We observe stochastic wandering of field-lines in space, breakdown of standard magnetic flux-freezing due to Richardson dispersion, and a broadened reconnection zone containing many current sheets. The coarse-grain magnetic geometry is like large-scale reconnection in the solar wind…
Energy dissipation in magnetohydrodynamic (MHD) turbulence is known to be highly intermittent in space, being concentrated in sheet-like coherent structures. Much less is known about intermittency in time, another fundamental aspect of turbulence which has great importance for observations of solar flares and other space/astrophysical phenomena. In this Letter, we investigate the temporal intermittency of energy dissipation in numerical simulations of MHD turbulence. We consider four-dimensional spatiotemporal structures, "flare events", responsible for a large fraction of the energy dissipati…
In this review, we describe turbulent drag reduction in a variety of flows using a universal framework of energy flux. In a turbulent flow with dilute polymers and magnetic field, the kinetic energy injected at large scales cascades to the velocity field at intermediate scales, as well as to the polymers and magnetic field at all scales. Consequently, the kinetic energy flux, $ Π_u(k) $, is suppressed in comparison to the pure hydrodynamic turbulence. We argue that the suppression of $Π_u(k)$ is an important factor in the reduction of the inertial force $\langle {\bf u \cdot \nabla u} \rangle$…
We derive a first exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence. For a gyrotropic pressure tensor, we study the double-adiabatic case and show the presence of new flux and source terms in the exact law, reminiscent of the plasma instability conditions due to pressure anisotropy. The Hall term is shown to bring ion-scale corrections to the exact law without affecting explicitly the pressure terms. In the pressure isotropy limit we recover all known results obtained for isothermal and polytropic closures. The incompressible limit of the gyrotropic system leads to…
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…
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…
We study incompressible imbalanced magnetohydrodynamic turbulence in the presence of background velocity shears. Using scaling arguments, we show that the turbulent cascade is significantly accelerated when the background velocity shear is stronger than the velocity shears in the subdominant Alfv% én waves at the injection scale. The spectral transport is then controlled by the background shear rather than the turbulent shears and the Tchen spectrum with spectral index $-1$ is formed. This spectrum extends from the injection scale to the scale of the spectral break where the subdominant wave s…
Magnetohydrodynamical (MHD) turbulence is ubiquitous in magnetized astrophysical plasmas, and it radically changes a great variety of astrophysical processes. In this review, we give the concept of MHD turbulence and explain the origin of its scaling. We consider the implications of MHD turbulence to various problems: dynamo in different types of stars, flare activity, solar and stellar wind from different stars, propagation of cosmic rays, and star formation. We also discuss how the properties of MHD turbulence provide a new way of tracing magnetic fields in interstellar and intracluster medi…
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…
We conduct a three-dimensional magnetohydrodynamic (MHD) simulation of the parametric decay instability of Alfvén waves and resultant compressible MHD turbulence, which is likely to develop in the solar wind acceleration region. Because of the presence of the mean magnetic field, the nonlinear stage is characterized by filament-like structuring and anisotropic cascading. By calculating the timescales of phase mixing and the evolution of Alfvén wave turbulence, we have found that the early nonlinear stage is dominated by phase mixing, while the later phase is dominated by imbalanced Alfvén wave…
Energy dissipation is highly intermittent in turbulent plasmas, being localized in coherent structures such as current sheets. The statistical analysis of spatial dissipative structures is an effective approach to studying turbulence. In this paper, we generalize this methodology to investigate four-dimensional spatiotemporal structures, i.e., dissipative processes representing sets of interacting coherent structures, which correspond to flares in astrophysical systems. We develop methods for identifying and characterizing these processes, and then perform a statistical analysis of dissipative…
Intermittency is investigated using decaying direct numerical simulations of incompressible weak magnetohydrodynamic turbulence with a strong uniform magnetic field ${\bf b_0}$ and zero cross-helicity. At leading order, this regime is achieved via three-wave resonant interactions with the scattering of two of these waves on the third/slow mode for which $k_{\parallel} = 0$. When the interactions with the slow mode are artificially reduced the system exhibits an energy spectrum with $k_{\perp}^{-3/2}$, whereas the expected exact solution with $k_{\perp}^{-2}$ is recovered with the full nonlinea…
When magnetohydrodynamic turbulence evolves in the presence of a large-scale mean magnetic field, an anisotropy develops relative to that preferred direction. The well-known tendency is to develop stronger gradients perpendicular to the magnetic field, relative to the direction along the field. This anisotropy of the spectrum is deeply connected with anisotropy of estimated timescales for dynamical processes, and requires reconsideration of basic issues such as scale locality and spectral transfer. Here analysis of high-resolution three-dimensional simulations of unforced magnetohydrodynamic t…
Magnetohydrodynamic turbulence and magnetic reconnection are ubiquitous in astrophysical environments. In most situations, these processes do not occur in isolation, but interact with each other. This renders a comprehensive theory of these processes highly challenging. Here, we propose a theory of magnetohydrodynamic turbulence driven at large scale that self-consistently accounts for the mutual interplay with magnetic reconnection occurring at smaller scales. Magnetic reconnection produces plasmoids that grow from turbulence-generated noise and eventually disrupt the sheet-like structures in…
We compare non-locality of interactions between different scales in hydrodynamic (HD) turbulence and magnetohydrodynamic (MHD) turbulence in a strongly magnetized medium. We use 3-dimensional incompressible direct numerical simulations to evaluate non-locality of interactions. Our results show that non-locality in MHD turbulence is much more pronounced than that in HD turbulence. Roughly speaking, non-local interactions count for more than 10\% of total interactions in our MHD simulation on a grid of $512^3$ points. However, there is no evidence that non-local interactions are important in our…
We present a systematic study of the influence of different forcing types on the statistical properties of supersonic, isothermal turbulence in both the Lagrangian and Eulerian frameworks. We analyse a series of high-resolution, hydrodynamical grid simulations with Lagrangian tracer particles and examine the effects of solenoidal (divergence-free) and compressive (curl-free) forcing on structure functions, their scaling exponents, and the probability density functions of the gas density and velocity increments. Compressively driven simulations show a significantly larger density contrast, a mo…
Single point spacecraft observations of the turbulent solar wind flow exhibit a characteristic nonaxisymmetric anisotropy that depends sensitively on the perpendicular power spectral exponent. For the first time we use this nonaxisymmetric anisotropy as a function of wave vector direction to test models of magnetohydrodynamic (MHD) turbulence. Using Ulysses magnetic field observations in the fast, quiet polar solar wind we find that the Goldreich-Sridhar model of MHD turbulence is not consistent with the observed anisotropy, whereas the observations are well reproduced by the "Slab + 2D" model…
The first estimation of the energy cascade rate ${|ε_C|}$ of magnetosheath turbulence is obtained using the CLUSTER and THEMIS spacecraft data and an exact law of compressible isothermal magnetohydrodynamics turbulence. ${|ε_C|}$ is found to be of the order of ${10{^{-13}} J.m^{3}.s^{-1}}$, at least two orders of magnitude larger than its value in the solar wind (order of ${10{^{-16}} J.m^{3}.s^{-1}}$ in the fast wind). Two types of turbulence are evidenced and shown to be dominated either by incompressible Alfvénic or magnetosonic-like fluctuations. Density fluctuations are shown to amplify t…
This article reviews recent studies of scale interactions in magnetohydrodynamic turbulence. The present day increase of computing power, which allows for the exploration of different configurations of turbulence in conducting flows, and the development of shell-to-shell transfer functions, has led to detailed studies of interactions between the velocity and the magnetic field and between scales. In particular, processes such as induction and dynamo action, the damping of velocity fluctuations by the Lorentz force, or the development of anisotropies, can be characterized at different scales. I…
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…
Recently a model for noisy reduced magnetohydrodynamic turbulence was proposed. The latter model was already used to study the random walk of magnetic field lines. In the current article we use the same model to investigate the diffusion of energetic particles across the mean magnetic field. To compute the perpendicular diffusion coefficient two analytical theories are used, namely the Non- Linear Guiding Center (NLGC) theory and the Unified Non-Linear Transport (UNLT) theory. It is shown that the two theories provide different results for the perpendicular diffusion coefficient. We also perfo…
In this Letter, we report compressible mode effects on relativistic magnetohydrodynamic (RMHD) turbulence in Poynting-dominated plasmas using 3-dimensional numerical simulations. We decomposed fluctuations in the turbulence into 3 MHD modes (fast, slow, and Alfvén) following the procedure mode decomposition in (Cho & Lazarian 2002), and analyzed their energy spectra and structure functions separately. We also analyzed the ratio of compressible mode to Alfvén mode energy with respect to its Mach number. We found the ratio of compressible mode increases not only with the Alfvén Mach number but w…
This article presents a calculation of the mean electromotive force arising from general small-scale magnetohydrodynamical turbulence, within the framework of the second-order correlation approximation. With the goal of improving understanding of the accretion disk dynamo, effects arising through small-scale magnetic fluctuations, velocity gradients, density and turbulence stratification, and rotation, are included. The primary result, which supplements numerical findings, is that an off-diagonal turbulent resistivity due to magnetic fluctuations can produce large-scale dynamo action -- the ma…
Magnetohydrodynamics (MHD) is invoked to address turbulent fluctuations in a variety of astrophysical systems. MHD turbulence in nature is often anisotropic and imbalanced, in that Alfvenic fluctuations moving in opposite directions along the background magnetic field carry unequal energies. This work formulates specific requirements for effective numerical simulations of strong imbalanced MHD turbulence with a guide field B0 High-resolution simulations are then performed and they suggest that the spectra of the counter-propagating Alfven modes do not differ from the balanced case, while their…
This paper examines the behavior of the dimensionless dissipation rate $C_{\varepsilon}$ for stationary and nonstationary magnetohydrodynamic (MHD) turbulence in presence of external forces. By combining with previous studies for freely decaying MHD turbulence, we obtain here both the most general model equation for $C_{\varepsilon}$ applicable to homogeneous MHD turbulence and a comprehensive numerical study of the Reynolds number dependence of the dimensionless total energy dissipation rate at unity magnetic Prandtl number. We carry out a series of medium to high resolution direct numerical …
The field theoretic renormalization group and operator product expansion are applied to the Kazantsev--Kraichnan kinematic model for the magnetohydrodynamic turbulence. The anomalous scaling emerges as a consequence of the existence of certain composite fields ("operators") with negative dimensions. The anomalous exponents for the correlation functions of arbitrary order are calculated in the two-loop approximation (second order of the renormalization-group expansion), including the anisotropic sectors. The anomalous scaling and the hierarchy of anisotropic contributions become stronger due to…
A subcritical transition to turbulence in magnetized Keplerian shear flows is investigated using a statistical approach. Three-dimensional numerical simulations of the shearing box equations with zero net magnetic flux are employed to determine the transition from decaying to sustained turbulence as a function of the magnetic Reynolds number Rm. The results reveal no clear transition to sustained turbulence as the average lifetime of the transients grows as an exponential function of Rm, in accordance with a type-II supertransient law.
Compressible isothermal magnetohydrodynamic turbulence is analyzed under the assumption of statistical homogeneity and in the asymptotic limit of large kinetic and magnetic Reynolds numbers. Following Kolmogorov we derive an exact relation for some two-point correlation functions which generalizes the expression recently found for hydrodynamics. We show that the magnetic field brings new source and flux terms into the dynamics which may act on the inertial range similarly as a source or a sink for the mean energy transfer rate. The introduction of a uniform magnetic field simplifies significan…
It is proposed that critical balance - a scale-by-scale balance between the linear propagation and nonlinear interaction time scales - can be used as a universal scaling conjecture for determining the spectra of strong turbulence in anisotropic wave systems. Magnetohydrodynamic (MHD), rotating and stratified turbulence are considered under this assumption and, in particular, a novel and experimentally testable energy cascade scenario and a set of scalings of the spectra are proposed for low-Rossby-number rotating turbulence. It is argued that in neutral fluids, the critically balanced anisotro…
We investigate the scale-locality of cascades of conserved invariants at high kinetic and magnetic Reynolds numbers in the ``inertial-inductive range'' of magnetohydrodynamic (MHD) turbulence, where velocity and magnetic field increments exhibit suitable power-law scaling. We prove that fluxes of total energy and cross-helicity--or, equivalently, fluxes of Elsässer energies--are dominated by the contributions of local triads. Corresponding spectral transfers are also scale-local when defined using octave wavenumber bands. Flux and transfer of magnetic helicity may be dominated by non-local tri…
Intermittent large-scale high-shear flows are found to occur frequently and spontaneously in direct numerical simulations of statistically stationary turbulent Boussinesq magnetohydrodynamic (MHD) convection. The energetic steady-state of the system is sustained by convective driving of the velocity field and small-scale dynamo action. The intermittent emergence of flow structures with strong velocity and magnetic shearing generates magnetic energy at an elevated rate over time-scales longer than the characteristic time of the large-scale convective motion. The resilience of magnetic energy am…
Non-ideal magnetohydrodynamics (MHD) is the dominant process. We investigate the effect of magnetic fields (ideal and non-ideal) and turbulence (sub- and transsonic) on the formation of circumstellar discs that form nearly simultaneously with the formation of the protostar. This is done by modelling the gravitational collapse of a 1~M$_\odot$ gas cloud that is threaded with a magnetic field and imposed with both rotational and turbulent velocities. We investigate magnetic fields that are parallel/anti-parallel and perpendicular to the rotation axis, two rotation rates and four Mach numbers. Di…
We show that a shell-model version of the three-dimensional Hall-magnetohydrodynamic (3D Hall-MHD) equations provides a natural theoretical model for investigating the multiscaling behaviors of velocity and magnetic structure functions. We carry out extensive numerical studies of this shell model, obtain the scaling exponents for its structure functions, in both the low-$k$ and high-$k$ power-law ranges of 3D Hall-MHD, and find that the extended-self-similarity (ESS) procedure is helpful in extracting the multiscaling nature of structure functions in the high-$k$ regime, which otherwise appear…
