Wavelet analysis can be used to measure the power spectrum of solar wind fluctuations along a line in any direction (θ, φ) with respect to the local mean magnetic field B 0 . This technique is applied to study solar wind turbulence in high-speed streams in the ecliptic plane near solar minimum using magnetic field measurements with a cadence of eight vectors per second. The analysis of nine high-speed streams shows that the reduced spectrum of magnetic field fluctuations (trace power) is approximately azimuthally symmetric about B 0 in both the inertial range and dissipation range; in the inertial range the spectra are characterized by a power-law exponent that changes continuously from 1.6 ± 0.1 in the direction perpendicular to the mean field to 2.0 ± 0.1 in the direction parallel to the mean field. The large uncertainties suggest that the perpendicular power-law indices 3/2 and 5/3 are both consistent with the data. The results are similar to those found by Horbury et al. (2008) at high heliographic latitudes. Comparisons between solar wind observations and the theories of strong incompressible MHD turbulence developed by Goldreich & Sridhar (1995) and Boldyrev (2006) are not rigorously justified because these theories only apply to turbulence with vanishing cross-helicity although the normalized cross-helicity of solar wind turbulence is not negligible. Assuming these theories can be generalized in such a way that the 3D wavevector spectra have similar functional forms when the cross-helicity is nonzero, then for the interval of Ulysses data analyzed by Horbury et al. (2008) the ratio of the spectra perpendicular and parallel to B 0 is more consistent with the Goldreich & Sridhar scaling P ⊥ /P ∝ ν 1/3 than with the Boldyrev scaling ν 1/2 . The analysis of high speed streams in the ecliptic plane does not yield a reliable measurement of this scaling law. The transition from a turbulent MHD-scale energy cascade to a kinetic Alfvén wave (KAW) cascade occurs when k ⊥ ρ i ≃ 1 which coincides with the spectral break. At slightly higher wavenumbers, in the dissipation range, there is a peak in the power ratio with P ⊥ /P ≫ 1. The decay of this peak may be caused by the damping of KAWs which is predicted to occur near k ⊥ ρ i ≃ 4.

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The question is addressed to what extent incompressible magnetohydrodynamics (MHD) can describe random magnetic and velocity fluctuations measured in the solar wind. It is demonstrated that distributions of spectral indices for the velocity, magnetic field, and total energy obtained from high resolution numerical simulations are qualitatively and quantitatively similar to solar wind observations at 1 AU. Both simulations and observations show that in the inertial range the magnetic field spectrum E b is steeper than the velocity spectrum Ev with E b > ∼ Ev and that the residual energy ER = E b − Ev decreases nearly following a k −2 ⊥ scaling.PACS numbers: 52.35.RaIntroduction.-Plasma motions in astrophysical systems are usually magnetized and turbulent. At scales larger than characteristic plasma kinetic scales, one-fluid magnetohydrodynamics provides a satisfactory framework for studying such systems [1,2]. Magnetohydrodynamic turbulence has long been invoked to explain the properties of the solar wind, where velocity and magnetic field fluctuations are measured in situ over a wide range of scales [e.g., 3-5]. Recent high-resolution numerical simulations, however, reported intriguing contradictions with the observational data. The Fourier energy spectrum of MHD turbulence obtained from numerical simulations appears to have a different scaling compared to the scaling inferred from observations. This raises some serious questions. Do the numerical simulations correctly represent the physics of solar wind fluctuations and, if so, then why doesn't solar wind turbulence exhibit the same universal scaling found in 3D MHD simulations?To formulate the problem, we rewrite the incompressible MHD equations in terms of the Elsässer variables,

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[1] Under certain conditions, freely decaying magnetohydrodynamic (MHD) turbulence evolves in such a way that velocity and magnetic field fluctuations dv and dB approach a state of alignment in which dv / dB. This process is called dynamic alignment. Boldyrev has suggested that a similar kind of alignment process occurs as energy cascades from large to small scales through the inertial range in strong incompressible MHD turbulence. In this study, plasma and magnetic field data from the Wind spacecraft, data acquired in the ecliptic plane near 1 AU, are employed to investigate the angle q(t) between velocity and magnetic field fluctuations in the solar wind as a function of the time scale t of the fluctuations and to look for the scaling relation hq(t)i $ t 1/4 predicted by Boldyrev. We find that the angle hq(t)i appears to scale like a power law at large inertial range scales, but then deviates from power law behavior at medium to small inertial range scales. We also find that small errors in the velocity vector measurements can lead to large errors in the angle measurements at small time scales. As a result, we cannot rule out the possibility that the observed deviations from power law behavior arise from errors in the velocity measurements. When we fit the data from 2 Â 10 3 s to 2 Â 10 4 s with a power law of the form hq(t)i / t p , our best fit values for p are in the range 0.27-0.36.