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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.

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

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

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.