Magnetohydrodynamic Turbulence Research Articles

Anisotropic Energy Transfer and Conversion in Magnetized Compressible Turbulence

We present a spatial filtering (or coarse-graining) analysis on 3D magnetized magnetohydrodynamic (MHD) turbulence simulations. The filtered compressible MHD formulae show transfer of kinetic and magnetic energies from large to small scales, as well as energy conversion between kinetic, magnetic, and thermal energies. The anisotropic filtering enables separate analyses of the energy flows perpendicular and parallel to the global mean magnetic field. Anisotropy in energy cascade is demonstrated by the larger perpendicular energy cascade rate and also the larger perpendicular wavenumbers associated with the peak energy transfer rate. We also find that the “inertial range” along the parallel (perpendicular) direction in the anisotropic energy cascade formulation is no longer strictly dissipation-free, because it includes the dissipation in the perpendicular (parallel) direction. A change in the driving force (kinetic only versus kinetic and magnetic) affects the energy conversion between kinetic and magnetic energies. While the compressibility of the driving force changes the partition of different channels of energy transfer and conversion, and also increases the total energy transfer rate, the global energy flow remains unaffected by compressibility qualitatively. Our analysis can be applied to multispacecraft observations of turbulence in the solar wind or a planetary magnetosphere.

Outlook on Magnetohydrodynamical Turbulence and Its Astrophysical Implications

Magnetohydrodynamical (MHD) turbulence is ubiquitous in magnetized astrophysical plasmas, and it radically changes a great variety of astrophysical processes. In this review, we introduce the concept of MHD turbulence and explain the origin of its scaling. We consider the implications of MHD turbulence for various problems: dynamo in different types of stars, flare activity, solar and stellar wind from different stars, the propagation of cosmic rays, and star formation. We also discuss how the properties of MHD turbulence provide a new means of tracing magnetic fields in interstellar and intracluster media.

Influence of streamwise and spanwise wall magnet arrays on near-wall MHD turbulence

ABSTRACT The effect of a permanent, localised and non-uniform magnetic field on the near-wall turbulence in a fully developed channel flow is analysed through direct numerical simulations. The magnetic field distribution is obtained by an arrangement of magnets placed on the upper and lower channel walls, producing preferentially either a streamwise (i.e. in the main flow direction) or a spanwise magnetic field component. The wall shear stress is drastically reduced under the effect of the streamwise arrangement of the wall magnets wherein both streamwise and wall-normal magnetic fields are involved. The magnetic braking effect leads to an important increase of the body force. Paradoxically enough, the small-scale turbulent activity is significantly increased above the low buffer layer in this case. On the opposite, imposing a magnetic field with a predominant spanwise component reduces tremendously the population of the turbulent shear stress producing eddies by directly affecting the regeneration of the buffer layer quasi-streamwise vortices. The flow is quasi-relaminarised between the magnets in the low-buffer and viscous sublayers. The wall shear increases in a predictable and deterministic way over the magnets, wherein the wall normal magnetic field component induces electric current loops.

Turbulence, Intermittency, and Cross-Scale Energy Transfer in an Interplanetary Coronal Mass Ejection

Solar wind measurements carried out by NASA’s Wind spacecraft before, during, and after the passing of an interplanetary coronal mass ejection (ICME), detected on 12 – 14 September 2014, have been used in order to examine several properties of magnetohydrodynamic (MHD) turbulence. Spectral indices and flatness scaling exponents of magnetic field, velocity, and proton density measurements were obtained, and provided a standard description of the characteristics of turbulence within different sub-regions of the ICME and its surroundings. This analysis was followed by the validation of the third-order moment scaling law for isotropic, incompressible MHD turbulence in the same sub-regions, which confirmed the fully developed nature of turbulence in the ICME plasma. The energy transfer rate was also estimated in each ICME sub-region and in the surrounding solar wind. An exceptionally high value was found within the ICME sheath, accompanied by enhanced intermittency, possibly related to the powerful energy injection associated with the arrival of the ICME.

Simulating Rayleigh-Taylor induced magnetohydrodynamic turbulence in prominences

Aims.Solar prominences are large-scale condensations suspended against gravity within the solar atmosphere. The Rayleigh-Taylor (RT) instability is proposed to be one of the fundamental processes that lead to the generation of dynamics at many spatial and temporal scales within these long-lived, cool, and dense structures, which are located in the solar corona. We aim to study such turbulent processes using high-resolution, direct numerical simulations of solar prominences.Methods.We ran 2.5D ideal magnetohydrodynamic (MHD) simulations with the open-sourceMPI-AMRVACcode far into the nonlinear evolution of an RT instability perturbed at the prominence-corona interface. Our simulation achieves a resolution down to ∼23 km on a 2D (x, y) domain of size 30 Mm × 30 Mm. We followed the instability transitioning from a multimode linear perturbation to its nonlinear, fully turbulent state. Over the succeeding ∼25 min period, we performed a statistical analysis of the prominence at a cadence of ∼0.858 s.Results.We find that the dominant guiding component,Bz, induces coherent structure formation predominantly in the vertical velocity component,Vy, consistent with observations, indicating an anisotropic turbulence state within our prominence. We find power-law scalings in the inertial range for the velocity, magnetic, and temperature fields. The presence of intermittency is evident from the probability density functions of the field fluctuations, which depart from Gaussianity as we consider smaller and smaller scales. In exact agreement, the higher-order structure functions quantify the multi-fractality, as do different scale characteristics and the behavior between the longitudinal and transverse directions. Thus, the statistics remain consistent with conclusions from previous observational studies, enabling us to directly relate the RT instability to the turbulent characteristics found within quiescent prominences.

Analytic characterization of sub-Alfvénic turbulence energetics

Magnetohydrodynamic (MHD) turbulence is a cross-field process relevant to many systems. A prerequisite for understanding these systems is to constrain the role of MHD turbulence, and in particular, the energy exchange between kinetic and magnetic forms. The energetics of strongly magnetized and compressible turbulence has so far resisted attempts to understand them. Numerical simulations reveal that kinetic energy can be orders of magnitude higher than fluctuating magnetic energy. We solved this lack-of-balance puzzle by calculating the energetics of compressible and sub-Alfvénic turbulence based on the dynamics of coherent cylindrical fluid parcels. Using the MHD Lagrangian, we proved analytically that the bulk of the magnetic energy transferred to kinetic energy is the energy that is stored in the coupling between the ordered and fluctuating magnetic field. The analytical relations are in strikingly good agreement with numerical data, up to second-order terms.

Transition to Equilibrium and Coherent Structure in Ideal MHD Turbulence

Transition of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence to near-equilibrium from non-equilibrium initial conditions is examined through new long-time numerical simulations on a 1283 periodic grid. Here, we neglect dissipation because we are primarily concerned with behavior at the largest scale which has been shown to be essentially the same for ideal and real (forced and dissipative) MHD turbulence. A Fourier spectral transform method is used to numerically integrate the dynamical equations forward in time and results from six computer runs are presented with various combinations of imposed rotation and mean magnetic field. There are five separate cases of ideal, homogeneous, incompressible, MHD turbulence: Case I, with no rotation or mean field; Case II, where only rotation is imposed; Case III, which has only a mean magnetic field; Case IV, where rotation vector and mean magnetic field direction are aligned; and Case V, which has nonaligned rotation vector and mean field directions. Dynamic coefficients are predicted by statistical mechanics to be zero-mean random variables, but largest-scale coherent magnetic structures emerge in all cases during transition; this implies dynamo action is inherent in ideal MHD turbulence. These coherent structures are expected to occur in Cases I, II and IV, but not in Cases III and V; future studies will determine whether they persist.

MHD instability dynamics and turbulence enhancement towards the plasma disruption at the HL-2A tokamak

The evolutions of MHD instability behaviors and enhancement of both electrostatic and electromagnetic turbulence towards the plasma disruption have been clearly observed in the HL-2A plasmas. Two types of plasma disruptive discharges have been investigated for similar equilibrium parameters: one with a distinct stage of a small central temperature collapse (sim 5–10%) around 1 millisecond before the thermal quench (TQ), while the other without. For both types, the TQ phase is preceded by a rotating 2/1 tearing mode, and it is the development of the cold bubble from the inner region of the 2/1 island O-point along with its inward convection that causes the massive energy loss. In addition, the micro-scale turbulence, including magnetic fluctuations and density fluctuations, increases before the small collapse, and more significantly towards the TQ. Also, temperature fluctuations measured by electron cyclotron emission imaging enhances dramatically at the reconnection site and expand into the island when approaching the small collapse and TQ, and the expansion is more significant close to the TQ. The observed turbulence enhancement near the X-point cannot be fully interpreted by the linear stability analysis by GENE. Evidences suggest that nonlinear effects, such as the reduction of local E_rtimes B shear and turbulence spreading, may play an important role in governing turbulence enhancement and expansion. These results imply that the turbulence and its interaction with the island facilitate the stochasticity of the magnetic flux and formation of the cold bubble, and hence, the plasma disruption.

Helios 2 observations of solar wind turbulence decay in the inner heliosphere

Aims. A linear scaling of the mixed third-order moment of the magnetohydrodynamic (MHD) fluctuations is used to estimate the energy transfer rate of the turbulent cascade in the expanding solar wind. Methods. In 1976, the Helios 2 spacecraft measured three samples of fast solar wind originating from the same coronal hole, at different distances from the Sun. Along with the adjacent slow solar wind streams, these intervals represent a unique database for studying the radial evolution of turbulence in samples of undisturbed solar wind. A set of direct numerical simulations of the MHD equations performed with the Lattice-Boltzmann code FLAME was also used for interpretation. Results. We show that the turbulence energy transfer rate decays approximately as a power law of the distance and that both the amplitude and decay law correspond to the observed radial temperature profile in the fast wind case. Results from MHD numerical simulations of decaying MHD turbulence show a similar trend for the total dissipation, suggesting an interpretation of the observed dynamics in terms of decaying turbulence and that multi-spacecraft studies of the solar wind radial evolution may help clarify the nature of the evolution of the turbulent fluctuations in the ecliptic solar wind.

Relative alignment between magnetic fields and molecular gas structure in molecular clouds

ABSTRACT We compare the structure of synthetic dust polarization with synthetic molecular line emission from radiative transfer calculations using a three-dimensional, turbulent collapsing-cloud magnetohydrodynamics simulation. The histogram of relative orientation (HRO) technique and the projected Rayleigh statistic (PRS) are considered. In our trans-Alfvénic (more strongly magnetized) simulation, there is a transition to perpendicular alignment at densities above ∼4 × 103 cm−3. This transition is recovered in most of our synthetic observations of optically thin molecular tracers; however, for 12CO it does not occur and the PRS remains in parallel alignment across the whole observer space. We calculate the physical depth of the optical depth τ = 1 surface and find that for 12CO it is largely located in front of the cloud mid-plane, suggesting that 12CO is too optically thick and instead mainly probes low-volume density gas. In our super-Alfvénic simulation, the magnetic field becomes significantly more tangled, and all observed tracers tend towards no preference for perpendicular or parallel alignment. An observable difference in alignment between optically thin and optically thick tracers may indicate the presence of a dynamically important magnetic field, though there is some degeneracy with viewing angle. We convolve our data with a Gaussian beam and compare it with HRO results of the Vela C molecular cloud. We find good agreement between these results and our sub-Alfvénic simulations when viewed with the magnetic field in the plane of the sky (especially when sensitivity limitations are considered), though the observations are also consistent with an intermediately inclined magnetic field.

Statistical Study of Release Time and Its Energy Dependence of In Situ Energetic Electrons in Impulsive Solar Flares

AbstractUsing the fraction velocity dispersion analysis method, it has been shown recently that in two impulsive solar energetic electron (SEE) events, the release times of near‐relativistic electrons at the Sun for outward‐propagating electrons are energy dependent and are delayed compared to those of the downward‐propagating electrons. In this work, we perform a statistical study of the release time and its energy dependence of near‐relativistic electrons in impulsive SEE events. We use in situ observations from the WIND spacecraft and remote hard X‐ray observations from the RHESSI and/or Fermi spacecraft. The difference in the release times between outward electrons and downward electrons for 29 events is obtained. In all events, the release of the outward‐propagating electrons is delayed from those precipitating downward. In 26 of the 29 events, the release times of outward‐propagating electrons also show clear energy dependence. In 15 of these 26 events, in situ electron data from more than five energy channels were available. The delay time as a function of energy for nine of these can be fitted by a form proposed by G. Li et al. (2021, https://doi.org/10.1029/2021GL095138). The implication of this energy‐dependent release on the Magnetohydrodynamics turbulence property at the electron acceleration site is discussed.

Spectral and Imaging Diagnostics of Spatially Extended Turbulent Electron Acceleration and Transport in Solar Flares

Solar flares are efficient particle accelerators with a large fraction of released magnetic energy (10%–50%) converted into energetic particles such as hard X-ray producing electrons. This energy transfer process is not well constrained, with competing theories regarding the acceleration mechanism(s), including MHD turbulence. We perform a detailed parameter study examining how various properties of the acceleration region, including its spatial extent and the spatial distribution of turbulence, affect the observed electron properties, such as those routinely determined from X-ray imaging and spectroscopy. Here, a time-independent Fokker–Planck equation is used to describe the acceleration and transport of flare electrons through a coronal plasma of finite temperature. Motivated by recent nonthermal line broadening observations that suggested extended regions of turbulence in coronal loops, an extended turbulent acceleration region is incorporated into the model. We produce outputs for the density-weighted electron flux, a quantity directly related to observed X-rays, modeled in energy and space from the corona to chromosphere. We find that by combining several spectral and imaging diagnostics (such as spectral index differences or ratios, energy or spatial-dependent flux ratios, and electron depths into the chromosphere) the acceleration properties, including the timescale and velocity dependence, can be constrained alongside the spatial properties. Our diagnostics provide a foundation for constraining the properties of acceleration in an individual flare from X-ray imaging spectroscopy alone, and can be applied to past, current, and future observations including those from RHESSI and Solar Orbiter.

A statistical study of the compressible energy cascade rate in solar wind turbulence: Parker solar probe observations

We investigated incompressible and compressible magnetohydrodynamic (MHD) energy cascade rates in the solar wind at different heliocentric distances. We used in situ magnetic field and plasma observations provided by the Parker Solar Probe mission and exact relations in fully developed turbulence. To estimate the compressible cascade rate, we applied two recent exact relations for compressible isothermal and polytropic MHD turbulence, respectively. Our observational results show a clear increase in the absolute value of the compressible and incompressible cascade rates as we get closer to the Sun. Moreover, we obtained an increase in both isothermal and polytropic cascade rates with respect to the incompressible case as compressibility increases in the plasma. Further discussion about the relation between the compressibility and the heliocentric distance is carried out. Furthermore, we compared both exact relations as compressibility increases in the solar wind, and although we note a slight trend to observe larger cascades using a polytropic closure, we obtained essentially the same cascade rate in the range of compressibility observed. Finally, we investigated the signed incompressible and compressible energy cascade rates and its connection with the real cascade rate.

Impact of Submerged Entry Nozzle (SEN) Immersion Depth on Meniscus Flow in Continuous Casting Mold under Electromagnetic Brake (EMBr)

Complex multi-phase phenomena, including turbulent flow, solidification, and magnetohydrodynamics (MHD) forces, occur during the continuous casting (CC) under the applied electromagnetic brake (EMBr). The results of the small-scale experiment of the liquid metal model for continuous casting (mini-LIMMCAST) at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR), investigating MHD flow with a deep immersion depth of 100 mm, are supplemented by newly presented numerical studies with the shallow position of the submerged entry nozzle (SEN) at 50 mm below the meniscus. Herein, the focus is on the MHD effects at the meniscus level considering (i) a fully insulating domain boundary, (ii) a perfectly conductive mold, or (iii) the presence of the solid shell. The volume-of-fluid (VOF) approach is utilized to model a Galinstan flow, including free surface behavior. A multiphase solver is developed using conservative MHD formulations in the framework of the open-source computational fluid dynamics (CFD) package OpenFOAM®. The wall-adapting local eddy-viscosity (WALE) subgrid-scale (SGS) model is employed to model the turbulent effects on the free surface flow. We found that, for the deep immersion depth, the meniscus remains calm under the EMBr for the conductive and semi-conductive domain. For the insulated mold disregarding the SEN position, the self-inducing MHD vortices, aligned with the magnetic field, cause strong waving of the meniscus and air bubble entrapment for shallow immersion depth. Secondary MHD structures can form close to the meniscus under specific conditions. The influence of the EMBr and immersion depth on the flow energy characteristics is analyzed using power spectral density (PSD).

Anomalous scaling in kinematic magnetohydrodynamic turbulence: Two-loop anomalous dimensions of leading composite operators.

Using the field theoretic formulation of the kinematic magnetohydrodynamic turbulence, the explicit expressions for the anomalous dimensions of leading composite operators, which govern the inertial-range scaling properties of correlation functions of the weak magnetic field passively advected by the electrically conductive turbulent environment driven by the Navier-Stokes velocity field, are derived and analyzed in the second order of the corresponding perturbation expansion (in the two-loop approximation). Their properties are compared to the properties of the same anomalous dimensions obtained in the framework of the Kazantsev-Kraichnan model of the kinematic magnetohydrodynamics with the Gaussian statistics of the turbulent velocity field as well as to the analogous anomalous dimensions of the leading composite operators in the problem of the passive scalar advection by the Gaussian (the Kraichnan model) and non-Gaussian (driven by the Navier-Stokes equation) turbulent velocity field. It is shown that, regardless of the Gaussian or non-Gaussian statistics of the turbulent velocity field, the two-loop corrections to the leading anomalous dimensions are much more important in the case of the problem of the passive advection of the vector (magnetic) field than in the case of the problem of the passive advection of scalar fields. At the same time, it is also shown that, in phenomenologically the most interesting case with three spatial dimensions, higher velocity correlations of the turbulent environment given by the Navier-Stokes velocity field play a rather limited role in the anomalous scaling of passive scalar as well as passive vector quantities, i.e., that the two-loop corrections to the corresponding leading anomalous dimensions are rather close to those obtained in the framework of the Gaussian models, especially as for the problem of scalar field advection. On the other hand, the role of the non-Gaussian statistics of the turbulent velocity field becomes dominant for higher spatial dimensions in the case of the kinematic magnetohydrodynamic turbulence but remains negligible in the problem of the passive scalar advection.

How the existence of unstable neutral media restricts the aspect ratio of cold neutral media?

ABSTRACT The ubiquity of very thin and lengthy cold neutral medium (CNM) has been reported by multiple authors in the H i community. Yet, the reason of how the CNM can be so long and lengthy is still in debate. In this paper, we recognize a new type of instability due to the attractive nature of the pressure force in the unstable phase. We provide a new estimation of the average CNM filament aspect ratio with the consideration of force balances at the phase boundary, which is roughly 5–20 in common CNM environment. We show that most of the cold filaments are less filamentary than what usually predicted via MHD turbulence theory or inferred from observations: The average length of CNM filament is roughly 1/2 of that in isothermal MHD turbulence with similar turbulence conditions. This suggests that the ‘cold filaments’ that are identified in observations might not be in pressure equilibrium or generated via other mechanisms.

Generation of momentum transport in weakly turbulent β-plane magnetohydrodynamics.

Magnetohydrodynamic turbulence on a β plane with an in-plane mean field, a system which serves as a simple model for the solar tachocline, is investigated analytically and computationally. We first derive two useful analytic constraints: We express the mean turbulent cross-helicity in terms of the mean turbulent magnetic energy, and then show that (for weak turbulence) the time-averaged momentum transport in the system can be expressed in terms of the cross-helicity spectrum. We then complete a closure of the system using weak turbulence theory, appropriately extended to a system with multiple interacting eigenmodes. We use this closure to perturbatively solve for the spectra at lowest order in the Rossby parameter β and thereby show that the momentum transport in the system is O(β^{2}), thus quantifying the transition away from Alfvénized turbulence. Finally, we verify our theoretical results by performing direct numerical simulations of the system over a broad range of β.

Coronal Loop Heating by Nearly Incompressible Magnetohydrodynamic and Reduced Magnetohydrodynamic Turbulence Models

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-Alfvénic flow from the lower corona. In this paper, we couple the NI MHD turbulence transport model with an MHD model of the solar corona to study the heating problem in a coronal loop. In a realistic benchmark coronal loop problem, we find that a loop can be heated to ∼1.5 million K by transport and dissipation of MHD turbulence described by the NI MHD model. We also find that the majority 2D component is as important as the minority slab component in the heating of the coronal loop. We compare our coupled MHD/NI MHD model results with a reduced MHD (RMHD) model. An important distinction between these models is that RMHD solves for small-scale velocity and magnetic field fluctuations and obtains the actual viscous/resistive dissipation associated with their evolution whereas NI MHD evolves scalar moments of the fluctuating velocity and magnetic fields and approximates dissipation using an MHD turbulence phenomenology. Despite the basic differences between the models, their simulation results match remarkably well, yielding almost identical heating rates inside the corona.

Barrow entropy and stochastic gravitational wave background generated from cosmological QCD phase transition

In this work we investigate the stochastic gravitational wave background generated during the first-order cosmological QCD phase transition of the early universe in the framework of the Barrow entropy. We first derived the Barrow corrections to the expression of stochastic gravitational wave background spectrum in presence of trace anomaly. Then, by taking account of Bubble wall collisions, sound waves and magnetohydrodynamic turbulence as the sources of stochastic gravitational wave, an analysis of the influence of Barrow entropy on the total energy density and the peak signal of stochastic gravitational wave signal is carried out. Finally, we discuss the possibility of detectors for the detection of these stochastic gravitational wave signals. Our results show that effect of Barrow entropy plays an important role in the temporal evolution of temperature of the universe as a function of the Hubble parameter, which leads to the signal of stochastic gravitational wave to shift towards the lower frequency regime, making the signal of stochastic gravitational wave possible to be probed by relevant ongoing and upcoming gravitational waves experiments.

A Model for Gradual-phase Heating Driven by MHD Turbulence in Solar Flares

Coronal flare emission is commonly observed to decay on timescales longer than those predicted by impulsively driven, one-dimensional flare loop models. This discrepancy is most apparent during the gradual phase, where emission from these models decays over minutes, in contrast to the hour or more often observed. Magnetic reconnection is invoked as the energy source of a flare, but should deposit energy into a given loop within a matter of seconds. Models which supplement this impulsive energization with a long, persistent ad hoc heating have successfully reproduced long-duration emission, but without providing a clear physical justification. Here we propose a model for extended flare heating by the slow dissipation of turbulent Alfvén waves initiated during the retraction of newly reconnected flux tubes through a current sheet. Using one-dimensional simulations, we track the production and evolution of MHD wave turbulence trapped by reflection from high-density gradients in the transition region. Turbulent energy dissipates through nonlinear interaction between counter-propagating waves, modeled here using a phenomenological one-point closure model. Atmospheric Imaging Assembly EUV light curves synthesized from the simulation were able to reproduce emission decay on the order of tens of minutes. We find this simple model offers a possible mechanism for generating the extended heating demanded by observed coronal flare emissions self-consistently from reconnection-powered flare energy release.