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We show in this article direct evidence for the presence of an inertial energy cascade, the most characteristic signature of hydromagnetic turbulence (MHD), in the solar wind as observed by the Ulysses spacecraft. After a brief rederivation of the equivalent of Yaglom's law for MHD turbulence, we show that a linear relation is indeed observed for the scaling of mixed third order structure functions involving Elsässer variables. This experimental result, confirming the prescription stemming from a theorem for MHD turbulence, firmly establishes the turbulent character of low-frequency velocity and magnetic field fluctuations in the solar wind plasma.Space flights have shown that the interplanetary medium is permeated by a supersonic, highly turbulent plasma flowing out from the solar corona, the so called solar wind [1,2]. The turbulent character of the flow, at frequencies below the ion gyrofrequency f ci ≃ 1Hz, has been invoked since the first Mariner mission [3]. In fact, velocity and magnetic fluctuations power spectra are close to the Kolmogorov's -5/3 law [2,6]. However, even if fields fluctuations are usually considered within the framework of magnetohydrodynamic (MHD) turbulence [2], a firm established proof of the existence of an energy cascade, namely the main characteristic of turbulence, remains a conjecture so far [4]. This apparent lack could be fulfilled through the evidence for the existence of the only exact and nontrivial result of turbulence [6], that is a relation between the third order moment of the longitudinal increments of the fields and the separation [5]. This observation would firmly put low frequency solar wind fluctuations within the framework of MHD turbulence. The importance of such question stands beyond the understanding of the basic physics of solar wind turbulence. For example, it is well known that turbulence is one of the main obstacles to the confinement of plasmas in the fusion devices [7,8]. The understanding of interplanetary turbulence and its effects on energetic particle transport is of great importance also for Space Weather research [9], which is a relevant issue for spacecrafts and communication satellites operations, and for the security of human beings. Finally, more theoretical problems are concerned, such as the puzzle of solar coronal heating due to the turbulent flux toward small scales [10].Incompressible MHD equations are more complicated than the standard neutral fluid mechanics equations because the velocity of the charged fluid is coupled with the magnetic field generated by the motion of the fluid itself. However, written in terms of the Elsässer variables defined as z ± = v ± (4πρ) −1/2 b (v and b are the velocity and magnetic field respectively and ρ the mass density), they have the same structure as the Navier-Stokes equations [4]where P is the total hydromagnetic pressure, while ν is the viscosity and κ the magnetic diffusivity. In particular, the nonlinear term appears as z ∓ · ∇z ± , suggesting the form of a transport process, in which Alfvé...

Non-intrusive measurements of the streamwise velocity in turbulent round jets in air are performed by recording short-time displacements and distorsions of very thin tagging lines written spanwise into the flow. The lines are written by Raman-exciting oxygen molecules and are interrogated by laser-induced electronic fluorescence (relief). This gives access to the spatial structure of transverse velocity increments without recourse to the Taylor hypothesis. The resolution is around 25 μm, less than twice the Kolmogorov scale η for the experiments performed (with Rλ≈360–600).The technique is validated by comparison with results obtained from other techniques for longitudinal or transverse structure functions up to order 8. The agreement is consistent with the estimated errors – a few percent on exponents determined by extended-self-similarity – and indicates significant departures from Kolmogorov (1941) scaling.Probability distribution functions of transverse velocity increments Δu over separations down to 1:8η are reported for the first time. Violent events, with Δu comparable to the r.m.s. turbulent velocity fluctuation, are found to take place with statistically significant probabilities. The shapes of the corresponding lines suggest the effect of intense slender vortex filaments.

Astrophysical Journal, 677, pp. L71-L74, http://dx.doi.org./10.1086/587957International audienc

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