Abstract.Intermittency in fluid turbulence can be emphasized through the analysis of Probability Distribution Functions (PDF) for velocity fluctuations, which display a

Magnetic fluctuations in the solar wind are distributed according to Kolmogorov's power law f À5/3 below the ion cyclotron frequency f ci . Above this frequency, the observed steeper power law is usually interpreted in two different ways, as a dissipative range of the solar wind turbulence, or another turbulent cascade, the nature of which is still an open question. Using the Cluster magnetic data we show that after the spectral break the intermittency increases toward higher frequencies, indicating the presence of nonlinear interactions inherent to a new inertial range and not to the dissipative range. At the same time the level of compressible fluctuations rises. We show that the energy transfer rate and intermittency are sensitive to the level of compressibility of the magnetic fluctuations within the small-scale inertial range. We conjecture that the time needed to establish this inertial range is shorter than the eddy-turnover time, and is related to dispersive effects. A simple phenomenological model, based on the compressible Hall MHD, predicts the magnetic spectrum $k À7/3þ2 , which depends on the degree of plasma compression .

Solar wind is probably the best laboratory to study turbulence in astrophysical plasmas. In addition to the presence of magnetic field, the differences with neutral fluid isotropic turbulence are: (i) weakness of collisional dissipation and (ii) presence of several characteristic space and time scales. In this paper we discuss observational properties of solar wind turbulence in a large range from the MHD to the electron scales. At MHD scales, within the inertial range, turbulence cascade of magnetic fluctuations develops mostly in the plane perpendicular to the mean field, with the Kolmogorov scaling k −5/3 ⊥ for the perpendicular cascade and k −2 for the parallel one. Solar wind turbulence is compressible in nature: density fluctuations at MHD scales have the Kolmogorov spectrum. Velocity fluctuations do not follow magnetic field ones: their spectrum is a power-law with a −3/2 spectral index. Probability distribution functions of different plasma parameters are not Gaussian, indicating presence of intermittency. At the moment there is no global model taking into account all these observed properties of the inertial range. At ion scales, turbulent spectra have a break, compressibility increases and the density fluctuation spectrum has a local flattening. Around ion scales, magnetic spectra are variable and ion instabilities occur as a function of the local plasma parameters. Between ion and electron scales, a small scale turbulent cascade seems to be established. It is characterized by a well defined power-law spectrum in magnetic and density fluctuations with a spectral index close to −2.8. Approaching electron scales, the fluctuations are no more self-similar: an exponential cut-off is usually observed (for time intervals without quasi-parallel whistlers) indicating an onset of dissipation. The small scale inertial range between ion and electron scales and the electron dissipation range can be together described by ∼ k −α ⊥ exp(−k ⊥ d ), with α 8/3 and the dissipation scale d close to the electron Larmor radius d ρ e . The nature of this small scale cascade and a possible dissipation mechanism are still under debate.

[1] We analyzed intermittency in the solar wind, as observed on the ecliptic plane, looking at magnetic field and velocity fluctuations between 0.3 and 1 AU, for both fast and slow wind and for compressive and directional fluctuations. Our analysis focused on the property that probability distribution functions of a fluctuating field affected by intermittency become more and more peaked at smaller and smaller scales. Since the peakedness of a distribution is measured by its flatness factor we studied the behavior of this parameter for different scales to estimate the degree of intermittency of our time series. We confirmed that both magnetic field and velocity fluctuations are rather intermittent and that compressive magnetic fluctuations are generally more intermittent than the corresponding velocity fluctuations. In addition, we observed that compressive fluctuations are always more intermittent than directional fluctuations and that while slow wind intermittency does not depend on the radial distance from the Sun, fast wind intermittency of both magnetic field and velocity fluctuations clearly increases with the heliocentric distance. We propose that the observed radial dependence can be understood if we imagine interplanetary fluctuations made of two main components: one represented by coherent, nonpropagating structures convected by the wind and, the other one made of propagating, stochastic fluctuations, namely Alfvén waves. While the first component tends to increase the intermittency level because of its coherent nature, the second one tends to decrease it because of its stochastic nature. As the wind expands, the Alfvénic contribution is depleted because of turbulent evolution and, consequently, the underlying coherent structures convected by the wind, strengthen further on by stream-stream dynamical interaction, assume a more important role increasing intermittency, as observed. Obviously, slow wind does not show a similar behavior because Alfvénic fluctuations have a less dominant role than within fast wind and the Alfvénicity of the wind has already been frozen by the time we observe it at 0.3 AU. Finally, our analysis suggests that the most intermittent magnetic fluctuations are distributed along the local interplanetary magnetic field spiral direction while, those relative to wind velocity seem to be located along the radial direction.