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In homogeneous and isotropic turbulence, the relative contributions of different physical mechanisms to the energy cascade can be quantified by an exact decomposition of the energy flux (Johnson, Phys. Rev. Lett., vol. 124, 2020, 104501; J. Fluid Mech., vol. 922, 2021, A3). We extend the formalism to the transfer of kinetic helicity across scales, important in the presence of large-scale mirror‐breaking mechanisms, to identify physical processes resulting in helicity transfer and quantify their contributions to the mean flux in the inertial range. All subfluxes transfer helicity from large to small scales. Approximately 50 % of the mean flux is due to the scale-local vortex flattening and vortex twisting. We derive a new exact relation between these effects, similar to the Betchov relation for the energy flux, revealing that the mean contribution of the former is three times larger than that of the latter. Multi-scale effects account for the remaining 50 % of the mean flux, with approximate equipartition between multi-scale vortex flattening, twisting and entangling.

The solar wind (SW) and local interstellar medium (LISM) are turbulent media. Their interaction is governed by complex physical processes and creates heliospheric regions with significantly different properties in terms of particle populations, bulk flow and turbulence. Our knowledge of the solar wind turbulence \nature and dynamics mostly relies on near-Earth and near-Sun observations, and has been increasingly improving in recent years due to the availability of a wealth of space missions, including multi-spacecraft missions. In contrast, the properties of turbulence in the outer heliosphere are still not completely understood. In situ observations by Voyager and New Horizons, and remote neutral atom measurements by IBEX strongly suggest that turbulence is one of the critical processes acting at the heliospheric interface. It is intimately connected to charge exchange processes responsible for the production of suprathermal ions and energetic neutral atoms. This paper reviews the observational evidence of turbulence in the distant SW and in the LISM, advances in modeling efforts, and open challenges., 82 pages, 31 figures. Paper accepted by Space Science Reviews (collection: The Heliosphere in the Local Interstellar Medium: Into the Unknown), and presented at the ISSI Workshop on November 8-12, 2021

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 turbulence. After an initial transient period, the ratio of parallel to perpendicular length scales fluctuates around a steady value during the decay of the eddies. We show further that a Taylor--K\'arm\'an-like similarity decay holds for MHD turbulence in the presence of a mean magnetic field. The effect of different parameters, including Reynolds number, DC field strength, and cross-helicity, on the nature of similarity decay is discussed., Comment: Accepted for publication in Journal of Fluid Mechanics

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 turbulence permits quantitative assessment of the behavior of theoretically relevant timescales in Fourier wavevector space. We discuss the distribution of nonlinear times, Alfv\'en times, and estimated spectral transfer rates. Attention is called to the potential significance of special regions of the spectrum, such as the two-dimensional limit and the "critical balance" region. A formulation of estimated spectral transfer in terms of a suppression factor supports a conclusion that the quasi two-dimensional fluctuations (characterized by strong nonlinearities) are not a singular limit, but may be in general expected to make important contributions., Comment: In Press at Physics of Plasmas

For the solar wind, a wealth of observational evidence indicates that turbulence is an important dynamical process for velocity (v), magnetic (b), and other related fluctuations at MHD (fluid) scales. Here we review such observations and turbulence features, including discussion of when wave or turbulence descriptions can (or cannot) explain the observations. The relevance of properties of MHD turbulence to the acceleration and transport of energetic particles is emphasized. A summary of different classes of models for solar wind fluctuations is presented, followed by reviews of transport models for (i) solar wind fluctuations and (ii) cosmic rays. In connection with cosmic ray transport models, recent developments in terms of cosmic ray transport coefficients, as well as their application in cosmic ray modulation models, are discussed in detail.

We employ spectral method numerical simulations to examine the dynamical development of anisotropy of the variance, or polarization, of the magnetic and velocity field in compressible magnetohydrodynamic (MHD) turbulence. Both variance anisotropy and spectral anisotropy emerge under influence of a large-scale mean magnetic field B0; these are distinct effects, although sometimes related. Here we examine the appearance of variance parallel to B0, when starting from a highly anisotropic state. The discussion is based on a turbulence theoretic approach rather than a wave perspective. We find that parallel variance emerges over several characteristic nonlinear times, often attaining a quasi-steady level that depends on plasma beta. Consistency with solar wind observations seems to occur when the initial state is dominated by quasi-two-dimensional fluctuations.

Measurements made with the Voyager 1 spacecraft indicate that significant levels of compressive fluctuations exist in the inner heliosheath. Some studies have already been performed with respect to the mirror-mode instability in the downstream region close to the solar wind termination shock, and here we extend the investigation to the whole inner heliosheath. We employ quasilinear theory and results from a global magnetohydrodynamic model of the heliosphere to compute the time evolution of both the temperature anisotropy and the energy density of the corresponding magnetic fluctuations, and we demonstrate their likely presence in the inner heliosheath. Furthermore, we compute the associated, locally generated density fluctuations. The results can serve as inputs for future models of the transport of compressible turbulence in the inner heliosheath., Comment: 7 pages, 5 figures

In presence of an externally supported, mean magnetic field a turbulent, conducting medium, such as plasma, becomes anisotropic. This mean magnetic field, which is separate from the fluctuating, turbulent part of the magnetic field, has considerable effects on the dynamics of the system. In this paper, we examine the dissipation rates for decaying incompressible magnetohydrodynamic (MHD) turbulence with increasing Reynolds number, and in the presence of a mean magnetic field of varying strength. Proceeding numerically, we find that as the Reynolds number increases, the dissipation rate asymptotes to a finite value for each magnetic field strength, confirming the K\'arm\'an-Howarth hypothesis as applied to MHD. The asymptotic value of the dimensionless dissipation rate is initially suppressed from the zero-mean-field value by the mean magnetic field but then approaches a constant value for higher values of the mean field strength. Additionally, for comparison, we perform a set of two-dimensional (2DMHD) and a set of reduced MHD (RMHD) simulations. We find that the RMHD results lie very close to the values corresponding to the high mean-field limit of the three-dimensional runs while the 2DMHD results admit distinct values far from both the zero mean field cases and the high mean field limit of the three-dimensional cases. These findings provide firm underpinnings for numerous applications in space and astrophysics wherein von K\'arm\'an decay of turbulence is assumed., Comment: Accepted for publication in Physical Review X

MHD-scale fluctuations in the velocity, magnetic, and density fields of the solar wind are routinely observed. The evolution of these fluctuations, as they are transported radially outwards by the solar wind, is believed to involve both wave and turbulence processes. The presence of an average magnetic field has important implications for the anisotropy of the fluctuations and the nature of the turbulent wavenumber cascades in the directions parallel and perpendicular to this field. In particular, if the ratio of the rms magnetic fluctuation strength to the mean field is small, then the parallel wavenumber cascade is expected to be weak and there are difficulties in obtaining a cascade in frequency. The latter has been invoked in order to explain the heating of solar wind fluctuations (above adiabatic levels) via energy transfer to scales where ion-cyclotron damping can occur.Following a brief review of classical hydrodynamic and magnetohydrodynamic (MHD) cascade theories, we discuss the distinct nature of parallel and perpendicular cascades and their roles in the evolution of solar wind fluctuations.

We argue that the hypothesis of preservation of shape of dimensionless second- and third-order correlations during decay of incompressible homogeneous magnetohydrodynamic (MHD) turbulence requires, in general, at least two independent similarity length scales. These are associated with the two Elsässer energies. The existence of similarity solutions for the decay of turbulence with varying cross-helicity implies that these length scales cannot remain in proportion, opening the possibility for a wide variety of decay behaviour, in contrast to the simpler classic hydrodynamics case. Although the evolution equations for the second-order correlations lack explicit dependence on either the mean magnetic field or the magnetic helicity, there is inherent implicit dependence on these (and other) quantities through the third-order correlations. The self-similar inertial range, a subclass of the general similarity case, inherits this complexity so that a single universal energy spectral law cannot be anticipated, even though the same pair of third-order laws holds for arbitrary cross-helicity and magnetic helicity. The straightforward notion of universality associated with Kolmogorov theory in hydrodynamics therefore requires careful generalization and reformulation in MHD.

A review of spectral anisotropy and variance anisotropy for solar wind fluctuations is given, with the discussion covering inertial range and dissipation range scales. For the inertial range, theory, simulations and observations are more or less in accord, in that fluctuation energy is found to be primarily in modes with quasi-perpendicular wavevectors (relative to a suitably defined mean magnetic field), and also that most of the fluctuation energy is in the vector components transverse to the mean field. Energy transfer in the parallel direction and the energy levels in the parallel components are both relatively weak. In the dissipation range, observations indicate that variance anisotropy tends to decrease towards isotropic levels as the electron gyroradius is approached; spectral anisotropy results are mixed. Evidence for and against wave interpretations and turbulence interpretations of these features will be discussed. We also present new simulation results concerning evolution of variance anisotropy for different classes of initial conditions, each with typical background solar wind parameters.

An overview is given of important properties of spatial and temporal intermittency, including evidence of its appearance in fluids, magnetofluids and plasmas, and its implications for understanding of heliospheric plasmas. Spatial intermittency is generally associated with formation of sharp gradients and coherent structures. The basic physics of structure generation is ideal, but when dissipation is present it is usually concentrated in regions of strong gradients. This essential feature of spatial intermittency in fluids has been shown recently to carry over to the realm of kinetic plasma, where the dissipation function is not known from first principles. Spatial structures produced in intermittent plasma influence dissipation, heating, and transport and acceleration of charged particles. Temporal intermittency can give rise to very long time correlations or a delayed approach to steady-state conditions, and has been associated with inverse cascade or quasi-inverse cascade systems, with possible implications for heliospheric prediction. Fil: Matthaeus, W. H.. University of Delaware; Estados Unidos. Università della Calabria; Italia. Universita Degli Studi Di Firenze; Italia Fil: Minping Wan. University of Delaware; Estados Unidos Fil: Servidio, S.. Università della Calabria; Italia Fil: Greco, A.. Università della Calabria; Italia Fil: Osman, K. T.. University of Warwick; Reino Unido Fil: Oughton, S.. University of Waikato; Nueva Zelanda Fil: Dmitruk, Pablo Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina

We investigate the nonlinear evolution of Alfven waves in a radially stratified isothermal atmosphere with wind, from the atmospheric base out to the Alfvenic point. Nonlinear interactions, triggered by wave reflection due to the atmospheric gradients, are assumed to occur mainly in directions perpendicular to the mean radial magnetic field. The nonlinear coupling between waves propagating in opposite directions is modeled by a phenomenological term, containing an integral turbulent length scale, which acts as a dissipative coefficient for waves of a given frequency. Although the wind acceleration profile is not determined self-consistently one may estimate the dissipation rate inside the layer and follow the evolution of an initial frequency spectrum. Reflection of low frequency waves drives dissipation across the whole spectrum, and steeper gradients, i.e. lower coronal temperatures, enhance the dissipation rate. Moreover, when reasonable wave amplitudes are considered, waves of all frequencies damp at the same rate and the spectrum is not modified substantially during propagation. Therefore the sub-Alfvenic coronal layer acts differently when waves interact nonlinearly, no longer behaving as a frequency dependent filter once reflection-generated nonlinear interactions are included, at least within the classes of models discussed here.

Spacecraft measurements in the solar wind offer the opportunity to study magnetohydrodynamic (MHD) turbulence in a collisionless plasma in great detail. We review some of the key results of the study of this medium: the presence of large amplitude Alfven waves propagating predominantly away from the Sun; the existence of an active turbulent cascade; and the presence of intermittency similar to that in neutral fluids. We also discuss the presence of anisotropy in wavevector space relative to the local magnetic field direction. Some models suggest that MHD turbulence can evolve to a state with power predominantly in wavevectors either parallel to the magnetic field ('slab' fluctuations) or approximately perpendicular to it ('2D'). We review the existing evidence for such anisotropy, which has important consequences for the transport of energetic particles. Finally, we present the first results of a new analysis which provides the most accurate measurements to date of the wave-vector anisotropy of wavevector power in solar wind MHD turbulence.

The self-consistency of the reduced magnetohydrodynamics (RMHD) model is explored by examining whether (parallel) spectral transfer might invalidate the assumptions employed in deriving it. Using direct numerical simulations we find that transfer of energy to structures with high parallel wavenumber is in fact limited by ongoing perpendicular transfer. Thus, the dynamics associated with RMHD models remains consistent with the underlying assumptions of RMHD. In particular, in well-resolved simulations it is neither necessary nor correct to introduce additional dissipation terms that (artificially) damp spectral transfer parallel to the mean magnetic field B0.

This paper discusses the possibility that heating of the solar corona in open field-line regions emanating from coronal holes is due to a nonlinear cascade, driven by low-frequency or quasi-static magnetohydrodynamic fluctuations. Reflection from coronal inhomogeneities plays an important role in sustaining the cascade. Physical and observational constraints are discussed. Kinetic processes that convert cascaded energy into heat must occur in regions of turbulent small-scale reconnection, and may be similar in some respects to ion heating due to intense electron beams observed in the aurora.

Originally proposed as an efficient approach to computation of nonlinear dynamics in tokamak fusion research devices, reduced magnetohydrodynamics (RMHD) has subsequently found application in studies of coronal heating, flux tube dynamics, charged particle transport, and, in general, as an approximation to describe plasma turbulence in space physics and astrophysics. Given the diverse set of derivations available in the literature, there has emerged some level of discussion and a lack of consensus regarding the completeness of RMHD as a turbulence model, and its applicability in contexts such as the solar wind. Some of the key issues in this discussion are examined here, emphasizing that RMHD is properly neither 2D nor fully 3D, being rather an incomplete representation that enforces at least one family of extraneous conservation laws. Fil: Oughton, S.. University Of Waikato; Nueva Zelanda Fil: Matthaeus, W. H.. University Of Delaware; Estados Unidos Fil: Dmitruk, Pablo Ariel. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina

We determine that the sizes of bursts in mean-square current density in a reduced magnetohydrodynamic (RMHD)simulation follow power-law probability density function (PDF). The PDFs for burst durations and waiting time between bursts are clearly not exponential and could also be power-law. This suffices to distinguish their behaviour from the original Bak et al. sandpile model which had exponential waiting time PDFs. However, it is not sufficient to distinguish between turbulence, some other SOC-like models, and other red noise sources., Comment: In press, Planetary and Space Science. Proceedings of a session at European Geophysical Society General Assembly, Nice, 2000

We test a theory presented previously to account for the turbulent transport of magnetic fluctuation energy in the solar wind and the related dissipation and heating of the ambient ion population. This theory accounts for the injection of magnetic energy through the damping of large-scale flow gradients, such as wind shear and compression, and incorporates the injection of magnetic energy due to wave excitation by interstellar pickup ions. The theory assumes quasi-two-dimensional spectral transport of the fluctuation energy and subsequent dissipation that heats the thermal protons. We compare the predictions of this theory with Voyager 2 and Pioneer 11 observations of magnetic fluctuation energy, magnetic correlation lengths, and ambient proton temperatures. Near-Earth Omnitape observations are used to adjust for solar variability, and the possibility that high-latitude effects could mask possible radial dependences is considered. We find abundant evidence for in situ heating of the protons, which we quantify, and show that the observed magnetic energy is consistent with the ion temperatures.

In a number of space and astrophysical plasmas, turbulence is driven by the supply of wave energy. In the context of incompressible magnetohydrodynamics (MHD) there are basic physical reasons, associated with conservation of cross helicity, why this kind of driving may be ineffective in sustaining turbulence. Here an investigation is made into some basic requirements for sustaining steady turbulence and dissipation in the context of incompressible MHD in a weakly inhomogeneous open field line region, driven by the supply of unidirectionally propagating waves at a boundary. While such wave driving cannot alone sustain turbulence, the addition of reflection permits sustainment. Another sustainment issue is the action of the nonpropagating or quasi-two dimensional part of the spectrum; this is particularly important in setting up a steady cascade. Thus, details of the wave boundary conditions also affect the ease of sustaining a cascade. Supply of a broadband spectrum of waves can overcome the latter difficu...

The issue of dynamical anisotropy in helical three-dimensional magnetohydrodynamic turbulence with a mean magnetic field B0 is investigated. Using high-resolution direct numerical simulations, we follow the evolution of various isotropic initial states characterized by their different values of the kinetic helicity. The cross helicity and magnetic helicity of the initial conditions are also varied. In agreement with earlier work, we find that such initial states become anisotropic in of order an eddy-turnover time, with correlation lengths parallel to B0 remaining largely unchanged while finer scales are excited in the perpendicular directions. Moreover, it is found that the development of both the anisotropy and the energy are essentially independent of the initial level of kinetic helicity. The physics associated with this latter feature is discussed.

Mechanisms for the deposition of heat in the lower coronal plasma are discussed, emphasizing recent attempts to reconcile the —uid and kinetic perspectives. Structures at magnetohydrodynamic (MHD) scales may drive a nonlinear cascade, preferentially exciting high perpendicular wavenumber —uctuations. Relevant dissipative kinetic processes must be identi—ed that can absorb the associated energy —ux. The relationship between the MHD cascade and direct cyclotron absorption, including cyclotron sweep, is discussed. We conclude that for coronal and solar wind parameters the perpendicular cascade cannot be neglected and may be more rapid than cyclotron sweep. Solar wind observational evidence suggests the relevance of the ion inertial scale, which is associated with current sheet thickness during reconnection. We conclude that a signi—cant fraction of dissipation in the corona and solar wind likely proceeds through a perpendicular cascade and small-scale reconnection, coupled to kinetic processes that act at oblique wavevectors. Subject headings: MHDsolar windSun: coronaSun: magnetic —eldsturbulence

A phenomenological theory describes radial evolution of plasma turbulence in the solar wind from 1 to 50 astronomical units. The theory includes a simple closure for local anisotropic magnetohydrodynamic turbulence, spatial transport, and driving by large-scale shear and pickup ions. Results compare well to plasma and magnetic field data from the Voyager 2 spacecraft, providing a basis for a concise, tractable description of turbulent energy transport in a variety of astrophysical plasmas.

Space plasma measurements, laboratory experiments, and simulations have shown that magnetohydrodynamic (MHD) turbulence exhibits a dynamical tendency towards spectral anisotropy given a sufficiently strong background magnetic field. Here the undriven decaying initial-value problem for homogeneous MHD turbulence is examined with the purpose of characterizing the variation of spectral anisotropy of the turbulent fluctuations with magnetic field strength. Numerical results for both incompressible and compressible MHD are presented. A simple model for the scaling of this spectral anisotropy as a function of the fluctuating magnetic field over total magnetic field is offered. The arguments are based on ideas from reduced MHD (RMHD) dynamics and resonant driving of certain non-RMHD modes. The results suggest physical bases for explaining variations of the anisotropy with compressibility, Reynolds numbers, and spectral width of the (isotropic) initial conditions.

In an evolving turbulent medium, a natural timescale can be defined in terms of the energy decay time. The time evolution may be complicated by other effects such as energy supply due to driving, and spatial inhomogeneity. In the solar wind the turbulence appears not to be simply engaging in free decay, but rather the energy level observed at a particular position in the hellosphere is affected by expansion, "mixing," and driving by stream shear. Here we discuss a new approach for estimating the "age" of solar wind turbulence as a function of heliocentric distance, using the local turbulent decay rate as the natural dock, but taking into account expansion and driving effects. The simplified formalism presented here is appropriate to low cross hellcity (non-Alfvnic) turbulence in the outer hellosphere especially at low hello-latitudes. We employ Voyager data to illustrate our method, which improves upon the familiar estimates in terms of local eddy turnover times.

The properties and structure of second-order ~Cartesian! correlation tensors are derived for the general case of two solenoidal random vector fields. The theory is intended to describe homogeneous magnetohydrodynamic turbulence, with no assumed rotational or reflectional symmetries. Each correlation tensor can be written in terms of four scalar generating functions and the relationship of these functions to the potentials that generate the poloidal and toroidal components of the underlying vector fields is derived. The physical nature of the scalar functions is investigated and their true or pseudoscalar character is ascertained. In our general discussion we clarify several misleading statements dating back to Robertson’s original paper in the field @Proc. Camb. Philos. Soc. 36, 209 ~1940!#. It is also shown that using the one-dimensional correlation function, it is possible to obtain spectral information on the induced electric field in directions perpendicular to the measurement direction. @S1063-651X~97!09208-8#

Power spectra of the components of the magnetic field parallel (Pzz) and perpendicular (Pzz+Pyy) to the local mean magnetic field direction were determined by wavelet methods from Ulysses’ MAG instrument data during eighteen 10-day segments of its first North Polar pass at high latitude at solar minimum in 1995. The power depends on frequency f and the angle θ between the solar wind direction and the local mean field, and with distance from the Sun. This data includes the solar wind whose total power (Pxx + Pyy + Pzz) in magnetic fluctuations we previously reported depends on f and the angle θ nearly as predicted by the GS95 critical balance model of strong incompressible MHD turbulence. Results at much wider range of frequencies during six evenly-spaced 10-day periods are presented here to illustrate the variability and evolution with distance from the Sun. Here we investigate the aniso tropic scaling of Pzz(f,θ) in particular because it is a reduced form of the Poloidal (pseudo-Alfvenic) component of th...

The von Karman-Howarth (vKH) hierarchy of equations relate the second-order correlations of the turbulent fluctuations to the third-order ones, the third-order to the fourth-order, and so on. We recently demonstrated [1] that for MHD, self-similar solutions to the vKH equations seem to require at least two independent similarity lengthscales (one for each Elsasser energy), so that compared to hydrodynamics a richer set of behaviors seems likely to ensue. Moreover, despite the well-known anisotropy of MHD turbulence with a mean magnetic field (B0), the equation for the second-order correlation does not contain explicit dependence on B0. We show that there is, however, implicit dependence on B0 via the third-order correlations, which themselves have both explicit B0-dependence and also their own implicit dependence through fourth-order correlations. Some subtleties and consequences of this implicit-explicit balance are summarized here. In addition, we present an analysis of simulation results showing that t...

We report on results from direct numerical simulation of the incompressible three- dimensional magnetohydrodynamic (MHD) equations, modified to incorporate viscous dissipation via the strongly anisotropic ion-parallel viscosity term. Both linear and nonlinear cases are considered, all with a strong background magnetic field. It is found that spectral anisotropy develops in almost all cases, but that the contribution from effects associated with the ion-parallel viscosity is relatively weak compared with the previously reported nonlinear process. Furthermore, and in contrast to this earlier work, it is suggested that when B0 is large, the anisotropy will develop and persist for many large-scale turnover times even for non-dissipative runs. Resistive dissipation is found to dominate over viscous even when the resistivity is several orders of magnitude smaller than the ion parallel viscosity. A variance anisotropy effect and anisotropy dependence on the polarization of the fluctuations are also observed.

A simple phenomenology is developed for the decay and transport of turbulence in a constant-speed, uniformly expanding medium. The fluctuations are assumed to be locally incompressible, and either of the hydrodynamic or non-Alfvénic magnetohydrodynamic (MHD) type. In order to represent local effects of nonlinearities, a simple model of the Kaármá-Dryden type for locally homogeneous turbulent decay is adopted. A detailed discussion of the parameters of this familiar one-point hydrodynamic closure is given, which has been shown recently to be applicable to non-Alfvénic MHD as well. The effects of the large-scale flow and expansion are incorporated using a two-scale approach, in which assumptions of particular turbulence symmetries provide simplifications. The derived model is tractable and provides a basis for understanding turbulence in the outer heliosphere, as well as in other astrophysical applications.

Direct spectral method simulation of the three-dimensional magnetohydrodynamics (MHD) equations is used to explore anisotropy that develops from initially isotropic fluctuations as a consequence of a uniform applied magnetic field. Spectral and variance anisotropies are investigated in both compressible and incompressible MHD. The nature of the spectral anisotropy is consistent with the model of Shebalin et al. [1983] in which the spectrum broadens in the perpendicular wavenumber direction, the anisotropy being greater for smaller wavenumbers. Here this effect is seen for both incompressible and polytropic compressible MHD. In contrast, the longitudinal (compressive) velocity fluctuations remain isotropic. Variance anisotropy is observed for low plasma beta compressible MHD but not for incompressible MHD. Solar wind observations are qualitatively consistent with both variance and spectral anisotropies of the type discussed here.

We evaluate a number of simple, one‐point phenomenological models for the decay of energy‐containing eddies in magnetohydrodynamic (MHD) and hydrodynamic turbulence. The MHD models include effects of cross helicity and Alfvenic couplings associated with a constant mean magnetic field, based on physical effects well‐described in the literature. The analytic structure of three separate MHD models is discussed. The single hydrodynamic model and several MHD models are compared against results from spectral‐method simulations. The hydrodynamic model phenomenology has been previously verified against experiments in wind tunnels, and certain experimentally determined parameters in the model are satisfactorily reproduced by the present simulation. This agreement supports the suitability of our numerical calculations for examining MHD turbulence, where practical difficulties make it more difficult to study physical examples. When the triple‐decorrelation time and effects of spectral anisotropy are properly taken i...

Solar wind fluctuations admit well-documented anisotropies of the variance matrix, or polarization, related to the mean magnetic field direction. Typically, one finds a ratio of perpendicular variance to parallel variance of the order of 9:1 for the magnetic field. Here we study the question of whether a kinetic plasma spontaneously generates and sustains parallel variances when initiated with only perpendicular variance. We find that parallel variance grows and saturates at about 5% of the perpendicular variance in a few nonlinear times irrespective of the Reynolds number. For sufficiently large systems (Reynolds numbers) the variance approaches values consistent with the solar wind observations.

Building on results from two-dimensional magnetohydrodynamic (MHD) turbulence (Shebalin, Matthaeus & Montgomery 1983), the development of anisotropic states from initially isotropic ones is investigated numerically for fully three-dimensional incompressible MHD turbulence. It is found that when an external d.c. magnetic field (B0) is imposed on viscous and resistive MHD systems, excitations are preferentially transferred to modes with wavevectors perpendicular to B0). The anisotropy increases with increasing mechanical and magnetic Reynolds numbers, and also with increasing wavenumber. The tendency of B0 to inhibit development of turbulence is also examined.

We observe the anisotropy of the power spectral tensor of magnetic field fluctuations in the fast solar wind for the first time. In heliocentric RTN coordinates the power in each element of the tensor has a unique dependence on the angle between the magnetic field and velocity of the solar wind (\theta) and the angle of the vector in the plane perpendicular to the velocity (\phi). We derive the geometrical effect of the high speed flow of the solar wind past the spacecraft on the power spectrum in the frame of the plasma P(k) to arrive at the observed power spectrum P(f,\theta,\phi) based on a scalar field description of turbulence theory. This allows us to predict the variation in the \phi direction and compare it to the data. We then transform the observations from RTN coordinates to magnetic-field-aligned coordinates. The observed reduced power spectral tensor matches the theoretical predictions we derive in both RTN and field-aligned coordinates which means that the local magnetic field we calculate with wavelet envelope functions is an accurate representation of the physical axis of symmetry for the turbulence and implies that on average the turbulence is axi-symmetric. We also show that we can separate the dominant toroidal component of the turbulence from the smaller but significant poloidal component and that these have different power anisotropy. We also conclude that the magnetic helicity is anisotropic and mostly two-dimensional, arising from wavevectors largely confined to the plane perpendicular to B., Comment: 21 pages, 8 figures, 1 table

We present a new model for the transport of solar wind fluctuations which treats them as two interacting incompressible components: quasi-two-dimensional turbulence and a wave-like piece. Quantities solved for include the energy, cross helicity, and characteristic transverse length scale of each component, plus the proton temperature. The development of the model is outlined and numerical solutions are compared with spacecraft observations. Compared to previous single-component models, this new model incorporates a more physically realistic treatment of fluctuations induced by pickup ions and yields improved agreement with observed values of the correlation length, while maintaining good observational accord with the energy, cross helicity, and temperature.

We examine the effects of including effects of both protons and electrons on the heating of the fast solar wind through two different approaches. In the first approach, we incorporate the electron temperature in an MHD turbulence transport model for the solar wind. In the second approach, we adopt more empirically based methods by analyzing the measured proton and electron temperatures to calculate the heat deposition rates. Overall, we conclude that incorporating separate proton and electron temperatures and heat conduction effects provides an improved and more complete model of the heating of the solar wind.

We present a model for the transport of solar wind fluctuations, based on the assumption that they can be well‐represented using two distinct components: a quasi‐2D turbulence piece and a wave‐like piece. For each component, coupled transport equations for its energy, cross helicity, and characteristic lengthscale(s) are derived, along with an equation for the proton temperature. This energy‐containing “two‐component” model includes the effects of solar wind expansion and advection, driving by stream shear and pickup ions, and nonlinear cascades. Nonlinear effects are modeled using a recently developed one‐point phenomenology for such a two‐component model of homogeneous MHD turbulence [1]. Heating due to these nonlinear effects is included in the temperature equation. Numerical solutions are discussed and compared with observations.

A model is presented for generation of fast solar wind in coronal holes, relying on heating that is dominated by turbulent dissipation of MHD fluctuations transported upwards in the solar atmosphere. Scale-separated transport equations include large-scale fields, transverse Alfvenic fluctuations, and a small compressive dissipation due to parallel shears near the transition region. The model accounts for proton temperature, density, wind speed, and fluctuation amplitude as observed in remote sensing and in situ satellite data., accepted for publication in ApJL

We apply a recently developed 2‐component phenomenology to the turbulent heating of the core solar wind protons as seen at the Voyager 2 spacecraft. We find that this new description improves the model predictions of core temperature and correlation scale of the fluctuations, yielding excellent agreement with the Voyager measurements. However, the model fluctuation intensity substantially exceeds the Voyager measurements in the outer heliosphere, indicating that this picture needs further refinement.

Long‐time states of a turbulent, decaying, two‐dimensional, Navier–Stokes flow are shown numerically to relax toward maximum‐entropy configurations, as defined by the ‘‘sinh‐Poisson’’ equation. The large‐scale Reynolds number is about 14 000, the spatial resolution is (512)2, the boundary conditions are spatially periodic, and the evolution takes place over nearly 400 large‐scale eddy‐turnover times.

Previous formulations of heating and transport associated with strong magnetohydrodynamic (MHD) turbulence are generalized to incorporate separate internal energy equations for electrons and protons. Electron heat conduction is included. Energy is supplied by turbulent heating that affects both electrons and protons, and is exchanged between them via collisions. Comparison to available Ulysses data shows that a reasonable accounting for the data is provided when (i) the energy exchange timescale is very long and (ii) the deposition of heat due to turbulence is divided, with 60% going to proton heating and 40% into electron heating. Heat conduction, determined here by an empirical fit, plays a major role in describing the electron data.

Recent observations at comets Giacobini-Zinner and Halley suggest that simple nonreacting gas dynamics or MHD is an inappropriate description for the bow shock. The thickness of the observed (sub)shock implies that mass-loading is an important dynamical process within the shock itself, thereby requiring that the Rankine-Hugoniot conditions possess source terms. This leads to shocks with properties similar to those of combustion shocks. The paper considers parallel magnetized shocks subjected to mass-loading, describes some properties which distinguish them from classical MHD parallel shocks, and establishes the existence of a new kind of MHD compound shock. These results will be of importance both to observations and numerical simulations of the comet-solar wind interaction.

Numerical solution of two-dimensional incompressible hydrodynamics shows that states of a near-minimal ratio of enstrophy to energy can be attained in times short compared with the flow decay time, confirming the simplest turbulent selective decay conjecture, and suggesting that coherent vortex structures do not terminate nonlinear processes. After all possible vortex mergers occur, the vorticity attains a particlelike character, suggested by the late-time similarity of the streamlines to Ewald potential contours.

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 −2 k spectrum but is also consistent with the presence of a “critical balance” style turbulent cascade. We also find, in common with previous studies, that most of the power is contained in wavevectors at large angles to the local magnetic field and that this component of the turbulence has a spectral index of 5/3. Magnetised plasmas fill most of the Universe and in many regions, turbulence plays important roles in the transport of energy and momentum and the acceleration and scattering of charged particles. Many aspects of plasma turbulence remain poorly understood, however. Here we present results on one of these, the anisotropy of the energy spectrum of magnetohydrodynamic (MHD) turbulence with respect to the magnetic field. In classical hydrodynamics, velocity fluctuations δuk with a wavenumber k decay and transfer energy to smaller scales on the shear timescale, τS ≈ 1/(kδuk). Within the steady inertial range, far from the energy input (“outer”) and dissipation scales, this leads to the dimensional result (δuk) 3 ∝ ǫ/k, where ǫ is the energy dissipation rate per unit mass. This gives the familiar Kolmogorov energy spectrum P(k) ∝ k −5/3 , widely observed in hydrodynamic turbulence. In a plasma, fluc⊥ ! .

[1] We employ a turbulence transport model to compute distributions of turbulence throughout the heliosphere. The model determines the radial dependence of three (coupled) quantities that characterize interplanetary turbulence, the energy per unit mass, the cross helicity or Alfvenicity, and a similarity length scale. A fourth integrated quantity, the plasma temperature, is modified by heat deposition due to turbulent dissipation. The model includes advection, expansion, and reflection effects as well as the tendency toward dynamic alignment, and a von Karman type dissipation function that represents decay of turbulence due to cascade to small scales. Two types of forcing are also featured, one a simple model of stream shear, and the other a driving in the outer heliosphere associated with wave energy injection due to pickup protons of interstellar origin. Parameters for the model have been tuned using observation data from Voyager and Ulysses. We analyze the constraining observations to provide boundary conditions and parameters that vary with heliocentric latitude, with some extrapolations. The fully assembled model permits the computation of the distribution of turbulence throughout the entire heliosphere, and we present solutions for several appropriate parameter sets.