The description of the turbulent spectrum of magnetic fluctuations in the solar wind in the kinetic range of scales is not yet completely established. Here, we perform a statistical study of 100 spectra measured by the STAFF instrument on the Cluster mission, which allows to resolve turbulent fluctuations from ion scales down to a fraction of electron scales, i.e. from ∼ 10 2 km to ∼ 300 m. We show that for k ⊥ ρ e ∈ [0.03, 3] (that corresponds approximately to the frequency in the spacecraft frame f ∈ [3, 300] Hz), all the observed spectra can be described by a general lawwhere k ⊥ is the wave-vector component normal to the background magnetic field and ρ e the electron Larmor radius. This exponential tail found in the solar wind seems compatible with the Landau damping of magnetic fluctuations onto electrons.

Spectral direct numerical simulations of incompressible MHD turbulence at a resolution of up to 1024 3 collocation points are presented for a statistically isotropic system as well as for a setup with an imposed strong mean magnetic field. The spectra of residual energy, E (anisotropic case, perpendicular to the mean field direction). A model of dynamic equilibrium between kinetic and magnetic energy, based on the corresponding evolution equations of the eddy-damped quasi-normal Markovian (EDQNM) closure approximation, explains the findings. The assumed interplay of turbulent dynamo and Alfvén effect yields E R k ∼ kE 2 k which is confirmed by the simulations.The nonlinear behavior of turbulent plasmas gives rise to a variety of dynamical effects such as self-organization of magnetic confinement configurations in laboratory experiments [1], generation of stellar magnetic fields [2] or structure formation in the interstellar medium [3]. The understanding of these phenomena is incomplete as the same is true for many inherent properties of the underlying turbulence.Large-scale low-frequency plasma turbulence is treated in the magnetohydrodynamic (MHD) approximation describing the medium as a viscous and electrically resistive magnetofluid neglecting additional kinetic effects. Incompressiblity of the flow is assumed for the sake of simplicity. In this setting the nature of the turbulent energy cascade is a central and still debated issue with different phenomenologies being proposed [4,5,6,7,8] (cf.[9] for a review). The associated spectral dynamics of kinetic and magnetic energy, in spite of its comparable importance, has received less attention (as an exception see [10]).This Letter reports a spectral relation between residual and total energy,respectively, as well as the influence of an imposed mean magnetic field on the spectra. The proposed physical picture, which is confirmed by accompanying direct numerical simulations, embraces two-dimensional MHD turbulence, globally isotropic three-dimensional systems as well as turbulence permeated by a strong mean magnetic field.In the following reference is made to two highresolution pseudospectral direct numerical simulations of incompressible MHD turbulence which we regard as paradigms for isotropic (I) and anisotropic (II) MHD turbulence. The dimensionless MHD equationsare solved in a 2π-periodic cube with spherical mode truncation to reduce numerical aliasing errors [11]. The equations include the flow vorticity, ω = ∇ × v, the magnetic field expressed in Alfvén speed units, b, as well as dimensionless viscosity, µ, and resistivity, η. In simulation II forcing is applied by freezing the largest spatial scales of velocity and magnetic field. Simulation I evolves globally isotropic freely decaying turbulence represented by 10243 Fourier modes. The initial fields are smooth with random phases and fluctuation amplitudes following exp(−k 2 /(2k 2 0 )) with k 0 = 4. Total kinetic and magnetic energy are initially equal with also decreases during turbulence decay from 0.7...

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 Log-Poisson approach, ζp = p/g 2 + 1 − (1/g) p/g , is able to describe the observed structure function scalings. PACS: 47.27Gs; 47.65+a; 47.27Eq; 52.35.Ra Turbulence is the natural state of many plasma flows observed throughout the universe, its statistical properties being essential for the theoretical understanding of, e.g., star-forming regions in the interstellar medium, the convection in planetary and stellar interiors, as well as the dynamics of stellar winds. The solar wind, in particular, represents the only source of in-situ measurements, since laboratory experiments are far from generating fully-developed turbulence at high magnetic Reynolds numbers. A simplified nonlinear model of turbulent plasmas is incompressible magnetohydrodynamics (MHD) [1]. In this framework the kinetic nature of microscopic processes responsible for, e.g., energy dissipation, is neglected when studying the fluid-like macroscopic plasma motions.The spatial similarity of incompressible MHD turbulence is usually investigated by considering two-point statistics of the Elsässer variables z ± = v ± B [2] combining velocity v and magnetic field B (given in Alfvén-speed units). Restricting consideration to turbulence with small cross helicity H C = V dV(v · B), V being the volume of the system, allows to set z + ≃ z − = z. With δz ℓ = [z(r + ℓ) − z(r)] · ℓ/ℓ the longitudinal isotropic structure functions of order p are defined as S p (ℓ) = δz p ℓ , the angular brackets denoting spatial averaging. The structure functions exhibit self-similar scaling S p (ℓ) ∼ ℓ ζp in the inertial range where the dynamical influence of dissipation, turbulence driving and system boundaries is weak.The inertial range has been introduced in Kolmogorov's K41 phenomenology of incompressible hydrodynamic turbulence [3,4] which assumes a spectral energy-cascade driven by the break-up of turbulent eddies. This leads to the experimentally well-verified energy-spectrum E(k) ∼ k −5/3 [5] corresponding to ζ 2 = 2/3. Iroshnikov and Kraichnan (IK) [6,7] included the effect of a magnetic field by founding the energy-cascade on the mutual scattering of Alfvén waves triggered by velocity fluctuations. The IK picture phenomenologically yields E(k) ∼ k −3/2 , i.e., ζ 2 = 1/2.The validity of the two phenomenologies in MHD turbulence is still under discussion. Two-dimensional direct numerical simulations (DNS) support the IK picture [8,9] while three-dimensional simulations exhibit K41 s...

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The large-scale inhomogeneity of the solar wind is taken into account to estimate the turbulent flux due to nonlinear interactions among purely outward-traveling waves. The nonlinear interactions are mediated by secondary, incoming waves generated by the linear coupling of the dominant species to the large-scale gradients. A quasistationary self-similar turbulent cascade is possible, with a spectrum scaling as k ~\ close to what is found in the low-frequency range of solar-wind fluctuations near the sun. PACS numbers: 52.35.Mw, 52.35.Ra, 96.60.VgTwo prominent and seemingly contradictory features of solar-wind fluctuations are, first, that they seem for a large part of the time to be made up of incompressible, almost pure Alfven waves propagating outwards from the sun along the average spiral magnetic field; and, second, that they present a well developed power spectrum over many frequency decades. The spectrum varies with heliocentric distance in the inner heliosphere: Far from the sun, it is well represented by a quasi-Kolmogorov power law, while it is much less steep near the sun. 1 A natural hypothesis to explain the apparent contradiction is that the outgoing part of the turbulent spectrum formed beyond the Alfvenic point is simply advected without modifications by the solar wind. 2 The difficulty with this idea is that purely outgoing waves do not interact nonlinearly (in the limit of incompressible fluctuations) so that the extremely inhomogeneous region near the sun should leave its imprint on the spectrum in the form of, say, preferred excited scales or absorption lines. 3 Such features are not seen in the observed spectrum. A second problem with purely outgoing Alfven waves is that their spectrum should evolve with heliocentric distance only because of large-scale WKB effects, which have been shown to be insufficient to account for the observed changes. 4 In order for nonlinear interactions to occur starting from a spectrum of purely outgoing waves, some source of incoming waves is necessary. The source may be the large-scale shear instabilities at the interaction regions of In Eq. (1), the total time derivative operator d~/dt is defined by rf ± /A-3/drH-(U + Vj-V.In the case of homogeneous MHD turbulence, the zfields can be thought of as wave packets propagating in opposite directions in a frame of reference traveling with high-and low-speed streams. 5 Although this hypothesis of in situ generation may explain, for example, the observed variation of of the velocity-magnetic-field correlation with distance, 6 it cannot in itself predict a spectral slope different from that of the classical MHD phenomenology. 7 Indeed, the above explanations do not take into account the inhomogeneity deriving from the radial expansion of the solar wind. Tu, Pu, and Wei 8 have modeled the effect of large-scale systematic gradients on turbulence by mixing together the usual phenomenological expressions for the turbulent flux 3 (valid for homogeneous turbulence) and large-scale linear WKB terms. This allows them to predict t...