A wave turbulence theory is developed for inertial electron magnetohydrodynamics (IEMHD) in the presence of a relatively strong and uniform external magnetic field $\boldsymbol{B_0} = B_0 \hat{\boldsymbol{e}}_\|$. This regime is relevant for scales smaller than the electron inertial length $d_e$. We derive the kinetic equations that describe the three-wave interactions between inertial whistler or kinetic Alfvén waves. We show that for both invariants, energy and momentum, the transfer is anisotropic (axisymmetric) with a direct cascade mainly in the direction perpendicular ($\perp$) to $\boldsymbol{B_0}$. The exact stationary solutions (Kolmogorov-Zakharov spectra) are obtained for which we prove the locality. We also found the Kolmogorov constant $C_K \simeq 8.474$. In the simplest case, the study reveals an energy spectrum in $k_\perp^{-5/2} k_\|^{-1/2}$ and a momentum spectrum enslaved to the energy dynamics in $k_\perp^{-3/2} k_\|^{-1/2}$. These solutions correspond to a magnetic energy spectrum $\sim k_\perp^{-9/2}$, which is steeper than the EMHD prediction made for scales larger than $d_e$. We conclude with a discussion on the application of the theory to space plasmas.
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 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…
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.
A version of extended magnetohydrodynamics (MHD) that incorporates electron inertia is obtained by constructing an action principle. Unlike MHD which freezes in magnetic flux, the present theory freezes in an alternative flux related to the electron canonical momentum. The associated Hamiltonian formulation is derived and reduced models that have previously been used to describe collisionless reconnection are obtained.
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…
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 …
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…
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…
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.
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…
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.
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.
Recent observational and analytical studies suggested that a new regime of kinetic turbulence may exist in plasma environments with low electron beta (Chen and Boldyrev, 2017). Such a regime, termed inertial kinetic-Alfvén turbulence, is relevant for the solar corona, Earth's magnetosheath, and other astrophysical systems where the electron and ion plasma beta parameters satisfy the condition $β_e\ll β_i\lesssim 1$. In this paper we present kinetic numerical simulations that confirm existence of the iKAW regime. Specifically, the simulations demonstrate a transition at scales below electron in…
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…
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"…
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…
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 $\langle {\bf u \cdot \nabla u} \rangle$…
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 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…
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…
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…
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.
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…
Magnetohydrodynamic (MHD) turbulence in the solar wind is observed to show the spectral behavior of classical Kolmogorov fluid turbulence over an inertial subrange and departures from this at short wavelengths, where energy should be dissipated. Here we present the first measurements of the electric field fluctuation spectrum over the inertial and dissipative wavenumber ranges in a $β\gtrsim 1$ plasma. The $k^{-5/3}$ inertial subrange is observed and agrees strikingly with the magnetic fluctuation spectrum; the wave phase speed in this regime is shown to be consistent with the Alfvén speed. At…
The exact law for fully developed homogeneous compressible magnetohydrodynamics (CMHD) turbulence is derived. For an isothermal plasma, without the assumption of isotropy, the exact law is expressed as a function of the plasma velocity field, the compressible Alfvén velocity and the scalar density, instead of the Elsässer variables used in previous works. The theoretical results show four different types of terms that are involved in the nonlinear cascade of the total energy in the inertial range. Each category is examined in detail, in particular those that can be written either as source or …
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…
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 …
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.
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…
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…
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.
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…
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…
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…
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…
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.
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…
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…
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…
There is mounting evidence in solar wind observations and in numerical simulations that kinetic and magnetic energies are not in equipartition in magnetohydrodynamic turbulence. The origin of their mismatch, the residual energy E_r=E_v-E_b, is not well understood. In the present work this effect is studied analytically in the regime of weak magnetohydrodynamic turbulence. We find that residual energy is spontaneously generated by turbulent dynamics, and it has a negative sign, in good agreement with the observations. We obtain that the residual energy condenses around k_||=0 with its k_||-spec…
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…
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…
We develop a framework for studying the statistical properties of current sheets in numerical simulations of 3D magnetohydrodynamic (MHD) turbulence. We describe an algorithm that identifies current sheets in a simulation snapshot and then determines their geometrical properties (including length, width, and thickness) and intensities (peak current density and total energy dissipation rate). We then apply this procedure to simulations of reduced MHD turbulence and perform a statistical analysis on the obtained population of current sheets. We evaluate the role of reconnection by separately stu…
Based on the Langevin equation of Brownian motion, we present a simple model that emulates a typical mode in incompressible magnetohydrodynamic turbulence, providing a demonstration of several key properties. The model equation is consistent with von Kármán decay law and Kolmogorov's symmetries. We primarily focus on the behavior of inertial range modes although we also attempt to include some properties of the large scale modes. Dissipation scales are not considered. Results from the model are compared with results from published Direct Numerical Simulations.
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 …
When magnetic energy density is much larger than that of matter, as in pulsar/black hole magnetospheres, the medium becomes force-free and we need relativity to describe it. As in non-relativistic magnetohydrodynamics (MHD), Alfvénic MHD turbulence in the relativistic limit can be described by interactions of counter-traveling wave packets. In this paper we numerically study strong imbalanced MHD turbulence in such environments. Here, imbalanced turbulence means the waves traveling in one direction (dominant waves) have higher amplitudes than the opposite-traveling waves (sub-dominant waves). …
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-…
The three-dimensional (3D) Hall magnetohydrodynamics (HMHD) equations are often used to study turbulence in the solar wind. Some earlier studies have investigated the statistical properties of 3D HMHD turbulence by using simple shell models or pseudospectral direct numerical simulations (DNSs) of the 3D HMHD equations; these DNSs have been restricted to modest spatial resolutions and have covered a limited parameter range. To explore the dependence of 3D HMHD turbulence on the Reynolds number $Re$ and the ion-inertial scale $d_{i}$, we have carried out detailed pseudospectral DNSs of the 3D HM…
Recent numerical and observational studies contain conflicting reports on the spectrum of magnetohydrodynamic turbulence. In an attempt to clarify the issue we investigate anisotropic incompressible magnetohydrodynamic turbulence with a strong guide field $B_0$. We perform numerical simulations of the reduced MHD equations in a special setting that allows us to elucidate the transition between weak and strong turbulent regimes. Denote $k_{\|}$, $k_\perp$ characteristic field-parallel and field-perpendicular wavenumbers of the fluctuations, and $b_λ$ the fluctuating field at the scale $λ\sim 1/…
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…
A model-independent first-principle first-order investigation of the shape of turbulent density-power spectra in the ion-inertial range of the solar wind at 1 AU is presented. De-magnetised ions in the ion-inertial range of quasi-neutral plasmas respond to Kolmogorov (K) or Iroshnikov-Kraichnan (IK) inertial-range velocity turbulence power spectra via the spectrum of the velocity-turbulence-related random-mean-square induction-electric field. Maintenance of electrical quasi-neutrality by the ions causes deformations in the power spectral density of the turbulent density fluctuations. Kolmogoro…
