In this work a weak-turbulence closure is used to determine the structure of the two-time power spectrum of weak magnetohydrodynamic (MHD) turbulence from the nonlinear equations describing the dynamics. The two-time energy spectrum is a fundamental quantity in turbulence theory from which most statistical properties of a homogeneous turbulent system can be derived. A closely related quantity, obtained via a spatial Fourier transform, is the two-point two-time correlation function describing the space-time correlations arising from the underlying dynamics of the turbulent fluctuations. Both quantities are central in fundamental turbulence theories as well as in the analysis of turbulence experiments and simulations. However, a first-principles derivation of these quantities has remained elusive due to the statistical closure problem, in which dynamical equations for correlations at order $n$ depend on correlations of order $n+1$. The recent launch of the Parker Solar Probe (PSP), which will explore the near-Sun region where the solar wind is born, has renewed the interest in the scientific community to understand the structure, and possible universal properties of space-time correlations. The weak MHD turbulence regime that we consider in this work allows for a natural asymptotic closure of the two-time spectrum, which may be applicable to other weak turbulence regimes found in fluids and plasmas. An integro-differential equation for the scale-dependent temporal correlation function is derived for incompressible Alfvénic fluctuations whose nonlinear dynamics is described by the reduced MHD equations.
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 …
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.
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…
A new sub-grid-scale model is developed for studying influences of the Hall term on macroscopic aspects of magnetohydrodynamic turbulence. Although the Hall term makes numerical simulations extremely expensive by exciting high-wave-number coefficients and makes magnetohydrodynamic equations stiff, studying macroscopic aspects of magnetohydrodynamic turbulence together with the Hall term is meaningful since this term often influences not only sub-ion-scales but also macroscopic scales. A new sub-ion-scale sub-grid-scale model for large eddy simulations of Hall magnetohydrodynamic turbulence is …
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 $\langle {\bf u \cdot \nabla u} \rangle$…
The scaling properties of three-dimensional magnetohydrodynamic turbulence are obtained from direct numerical simulations of decaying turbulence using $512^3$ modes. The results indicate that the turbulence does not follow the Iroshnikov-Kraichnan phenomenology.In the case of hyperresistivity, the structure functions exhibit a clear scaling range yielding absolute values of the scaling exponents $ζ_p$. The scaling exponents agree with a modified She-Leveque model $ζ_p=p/9 + 1 - (1/3)^{p/3}$, corresponding to Kolmogorov scaling but sheet-like geometry of the dissipative structures.
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…
A general framework that incorporates the Iroshnikov-Kraichnan (IK) and Goldreich-Sridhar (GS) phenomenalogies of magnetohydrodynamic (MHD) turbulence is developed. This affords a clarification of the regime of validity of the IK model and hence help resolve some controversies in this problem.
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…
Extended or generalized similarity is a ubiquitous but not well understood feature of turbulence that is realized over a finite range of scales. ULYSSES spacecraft solar polar passes at solar minimum provide \textit{in situ} observations of evolving anisotropic magnetohydrodynamic turbulence in the solar wind under ideal conditions of fast quiet flow. We find a single generalized scaling function characterises this finite range turbulence and is insensitive to plasma conditions. The recent unusually inactive solar minimum -with turbulent fluctuations down by a factor of $\sim 2$ in power- prov…
Experiments and numerical simulations show that the energy spectrum of the magnetohydrodynamic turbulence in the quasi-static limit deviates from Kolmogorov's $k^{-5/3}$ spectrum as the external magnetic field, or equivalently the interaction parameter, is increased. To explain this phenomena, we construct an analytical turbulence model with variable energy flux that arises due to the Lorentz-force induced dissipation. The energy spectra computed using our model for various interaction parameters are in qualitative agreement with earlier experimental and numerical results.
The problem of the occurrence of an energy cascade for Alfvénic turbulence in solar wind plasmas was hystorically addressed by using phenomenological arguments based to the weakness of nonlinear interactions and the anisotropy of the cascade in wave vectors space. Here, this paradox is reviewed through the formal derivation of a Yaglom relation from anisotropic Magnetohydrodynamic equation. The Yaglom relation involves a third-order moment calculated from velocity and magnetic fields and involving both Elsässer vector fields, and is particularly useful to be used as far as spacecraft observati…
In an earlier paper (Wan et al. 2012), the authors showed that a similarity solution for anisotropic incompressible 3D magnetohydrodynamic (MHD) turbulence, in the presence of a uniform mean magnetic field $\vB_0$, exists if the ratio of parallel to perpendicular (with respect to $\vB_0$) similarity length scales remains constant in time. This conjecture appears to be a rather stringent constraint on the dynamics of decay of the energy-containing eddies in MHD turbulence. However, we show here, using direct numerical simulations, that this hypothesis is indeed satisfied in incompressible MHD t…
We extend the theory for third-order structure functions in homogeneous incompressible magnetohydrodynamic (MHD) turbulence to the case in which a constant velocity shear is present. A generalization is found of the usual relation [Politano and Pouquet, Phys. Rev. E, 57 21 (1998)] between third-order structure functions and the dissipation rate in steady inertial range turbulence, in which the shear plays a crucial role. In particular, the presence of shear leads to a third-order law which is not simply proportional to the relative separation. Possible implications for laboratory and space pla…
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…
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…
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 …
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-…
We simulate forced quasi-static magnetohydrodynamic turbulence and investigate the anisotropy, energy spectrum, and energy flux of the flow, specially for large interaction parameters ($N$). We show that the angular dependence of the energy spectrum is well quantified using Legendre polynomials. For large $N$, the energy spectrum is exponential. Our direct computation of energy flux reveals an inverse cascade of energy at low wavenumbers, similar to that in two-dimensional turbulence. We observe the flow be two-dimensional (2D) for moderate $N$ ($N \sim 20$), and two-dimensional three-componen…
Strong incompressible three-dimensional magnetohydrodynamic turbulence is investigated by means of high resolution direct numerical simulations. The simulations show that the configuration space is characterized by regions of positive and negative cross-helicity, corresponding to highly aligned or anti-aligned velocity and magnetic field fluctuations, even when the average cross-helicity is zero. To elucidate the role of cross-helicity, the spectra and structure of turbulence are obtained in imbalanced regions where cross-helicity is non-zero. When averaged over regions of positive and negativ…
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…
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…
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 …
The evolution of the correlation characteristics in three-dimensional isotropic electron magnetohydrodynamic turbulence is investigated. Universal exact relations between the longitudinal and transverse two-point triple correlations of the components of the fluctuational magnetic fields and the rates of dissipation of the magnetic helicity and energy are obtained in the inertial range.
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…
The plasmoid instability in evolving current sheets has been widely studied due to its effects on the disruption of current sheets, the formation of plasmoids, and the resultant fast magnetic reconnection. In this Letter, we study the role of the plasmoid instability in two-dimensional magnetohydrodynamic (MHD) turbulence by means of high-resolution direct numerical simulations. At sufficiently large magnetic Reynolds number ($R_m=10^6$), the combined effects of dynamic alignment and turbulent intermittency lead to a copious formation of plasmoids in a multitude of intense current sheets. The …
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…
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…
It is shown that in the framework of the weak turbulence theory, the autocorrelation and cascade timescales are always of the same order of magnitude. This means that, contrary to the general belief, any model of turbulence which implies a large number of collisions among wave packets for an efficient energy cascade (such as the Iroshnikov-Kraichnan model) are not compatible with the weak turbulence theory.
The present work investigates the acceleration of test particles in balanced and imbalanced Alfvénic turbulence, relevant to the solar-wind problem. These turbulent states, obtained numerically by prescribing the injection rates for the ideal invariants, are evolved dynamically with the particles. While the energy spectrum for balanced and imbalanced states is known, the impact made on particle heating is a matter of debate, with different considerations giving different results. By performing direct numerical simulations, resonant and non-resonant particle accelerations are automatically cons…
Motivated by recent analytic predictions, we report numerical evidence showing that in driven incompressible magnetohydrodynamic turbulence the magnetic- and velocity-field fluctuations locally tend to align the directions of their polarizations. This dynamic alignment is stronger at smaller scales with the angular mismatch between the polarizations decreasing with the scale λapproximately as θ_λ~ λ^{1/4}. This can naturally lead to a weakening of the nonlinear interactions and provide an explanation for the energy spectrum E(k) ~ k^{-3/2} that is observed in numerical experiments of strongly …
A higher-order multiscale analysis of spatial anisotropy in inertial range magnetohydrodynamic turbulence is presented using measurements from the STEREO spacecraft in fast ambient solar wind. We show for the first time that, when measuring parallel to the local magnetic field direction, the full statistical signature of the magnetic and Elsässer field fluctuations is that of a non-Gaussian globally scale-invariant process. This is distinct from the classic multi-exponent statistics observed when the local magnetic field is perpendicular to the flow direction. These observations are interprete…
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…
We present a quantitative estimate of the anisotropic power and scaling of magnetic field fluctuations in inertial range magnetohydrodynamic turbulence, using a novel wavelet technique applied to spacecraft measurements in the solar wind. We show for the first time that, when the local magnetic field direction is parallel to the flow, the spacecraft-frame spectrum has a spectral index near 2. This can be interpreted as the signature of a population of fluctuations in field-parallel wavenumbers with a $k_{\parallel}^{-2}$ spectrum but is also consistent with the presence of a "critical balance"…
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…
We derive the exact law for three-dimensional (3D) homogeneous compressible isothermal Hall magnetohydrodynamics (CHMHD) turbulence, without the assumption of isotropy. The Hall current is shown to introduce new flux and sources terms that act at the small scales (comparable or smaller than the ion skin depth) to significantly impact the turbulence dynamics. The new law provides an accurate means to estimate for the first time the energy cascade rate over a broad range of scales covering the MHD inertial range and the sub-ion dispersive range in 3D numerical simulations and {\it in situ} space…
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 …
We explore the effect of the magnetic Prandtl number Pm on energy and dissipation in fully resolved direct numerical simulations of steady-state, mechanically forced homogeneous magnetohydrodynamic turbulence in the range Pm = 1/32 to 32. We compare the spectra and show that if the simulations are not fully resolved, the steepness of the scaling of the kinetic-to-magnetic dissipation ratio with Pm is overestimated. We also present results of decaying turbulence with helical and nonhelical magnetic fields, where we find nonhelical reverse spectral transfer for Pm < 1. The results of this system…
Weak turbulence of magnetohydrodynamic (MHD) waves in strongly magnetized plasma is studied when the thermal pressure is less than the magnetic field pressure. In this situation the main nonlinear mechanism is the resonance scattering of fast magneto-acoustic and Alfvenic waves on slow magneto-acoustic waves. As a result, the former waves serve as the high-frequency waves with respect to the latter ones so that the total number of HF waves - an adiabatic invariant - conserves additionally. In the weak turbulence regime this invariant is shown to generate the Kolmogorov type spectrum with a con…
We perform direct numerical simulations of magnetohydrodynamic (MHD) turbulence with kinetic energy and cross helicity injections at large scales. We observe that the cross helicity changes sign as we go from large and intermediate scales to small scales. In addition, the magnetic reconnections are strongest at the regions where the cross helicity changes sign and becomes smallest in magnitude. Thus, our simulations provide an important window to explore the regions of magnetic reconnections in nonlinear MHD.
In quasi-static MHD, experiments and numerical simulations reveal that the energy spectrum is steeper than Kolmogorov's $k^{-5/3}$ spectrum. To explain this observation, we construct turbulence models based on variable energy flux, which is caused by the Joule dissipation. In the first model, which is applicable to small interaction parameters, the energy spectrum is a power law, but with a spectral exponent steeper than -5/3. In the other limit of large interaction parameters, the second model predicts an exponential energy spectrum and flux. The model predictions are in good agreement with t…
It has been proposed recently by Loureiro & Boldyrev [Phys. Rev. Lett. 118, 245101 (2017)] and Mallet et al. [Mon. Not. R. Astron. Soc. 468, 4862 (2017)] that strongly anisotropic current sheets formed in the inertial range of magnetohydrodynamic turbulence become affected by the tearing instability at scales smaller than a critical scale $λ_\mathrm{c}$, and larger than the dissipation scale of turbulence. If true, this process can modify the nature of energy cascade at smaller scales, leading to a new, tearing-mediated regime of magnetohydrodynamic (MHD) turbulence. In this work we present a …
A weak wave turbulence theory is developed for two-dimensional (2D) magnetohydrodynamics (MHD). We derive and analyze the kinetic equation describing the three-wave interactions of pseudo-Alfvén waves. Our analysis is greatly helped by the fortunate fact that in 2D the wave-kinetic equation is integrable. In contrast with the 3D case, in 2D the wave interactions are nonlocal. Another distinct feature is that strong derivatives of spectra tend to appear in the region of small parallel (i.e. along the uniform magnetic field direction) wavenumbers leading to a breakdown of the weak turbulence des…
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…
Direct numerical simulations of decaying and forced magnetohydrodynamic (MHD) turbulence without and with mean magnetic field are analyzed by higher-order two-point statistics. The turbulence exhibits statistical anisotropy with respect to the direction of the local magnetic field even in the case of global isotropy. A mean magnetic field reduces the parallel-field dynamics while in the perpendicular direction a gradual transition towards two-dimensional MHD turbulence is observed with $k^{-3/2}$ inertial-range scaling of the perpendicular energy spectrum. An intermittency model based on the L…
A signed measure analysis of two-dimensional intermittent magnetohydrodynamic turbulence is presented. This kind of analysis is performed to characterize the scaling behavior of the sign-oscillating flow structures, and their geometrical properties. In particular, it is observed that cancellations between positive and negative contributions of the field inside structures, are inhibited for scales smaller than the Taylor microscale, and stop near the dissipative scale. Moreover, from a simple geometrical argument, the relationship between the cancellation exponent and the typical fractal dimens…
Space and astrophysical plasmas are frequently found in the regime of differential rotation, where the presence of a magnetic field can result in the magnetorotational instability, directly responsible for important phenomena such as turbulent angular momentum transport in accretion disks. In the absence of an imposed magnetic field, a nonlinear dynamo is necessary for this transport mechanism to take place. In protoplanetary disks there are regions with high density and very low temperatures, which are two necessary conditions for the Hall effect to operate, affecting the development of the d…
In this review we summarise the current status of the quasi-static magnetohydrodynamic turbulence. The energy spectrum is steeper than Kolmogorov's $k^{-5/3}$ spectrum due to the decrease of the kinetic energy flux with wavenumber $k$ as a result of Joule dissipation. The spectral index decreases with the increase of interaction parameter. The flow is quasi two-dimensional with strong ${\bf U}_\perp$ at small $k$ and weak $U_\parallel$ at large $k$, where ${\bf U}_\perp$ and $U_\parallel$ are the perpendicular and parallel components of velocity relative to the external magnetic field. For sma…
In magnetohydrodynamic (MHD) turbulence, the large-scale magnetic field sets a preferred local direction for the small-scale dynamics, altering the statistics of turbulence from the isotropic case. This happens even in the absence of a total magnetic flux, since MHD turbulence forms randomly oriented large-scale domains of strong magnetic field. It is therefore customary to study small-scale magnetic plasma turbulence by assuming a strong background magnetic field relative to the turbulent fluctuations. This is done, for example, in reduced models of plasmas, such as reduced MHD, reduced-dimen…
Turbulence is ubiquitous in plasmas, leading to rich dynamics characterized by irregularity, irreversibility, energy fluctuations across many scales, and energy transfer across many scales. Another fundamental and generic feature of turbulence, although sometimes overlooked, is the inhomogeneous dissipation of energy in space and in time. This is a consequence of intermittency, the scale-dependent inhomogeneity of dynamics caused by fluctuations in the turbulent cascade. Intermittency causes turbulent plasmas to self-organize into coherent dissipative structures, which may govern heating, diff…
We present numerical simulations and explore scalings and anisotropy of compressible magnetohydrodynamic (MHD) turbulence. Our study covers both gas pressure dominated (high beta) and magnetically dominated (low beta) plasmas at different Mach numbers. In addition, we present results for superAlfvenic turbulence and discuss in what way it is similar to the subAlfvenic turbulence. We describe a technique of separating different magnetohydrodynamic (MHD) modes (slow, fast and Alfven) and apply it to our simulations. We show that, for both high and low beta cases, Alfven and slow modes reveal the…
