Dependence of Solar-Wind Power Spectra on the Direction of the Local Mean Magnetic Field

Wavelet analysis can be used to measure the power spectrum of solar-wind fluctuations along a line in any direction (θ, ) 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. at high heliographic latitudes. Comparisons between solar-wind observations and the theories of strong incompressible MHD turbulence developed by Goldreich & Sridhar and Boldyrev 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 three-dimensional wavevector spectra have similar functional forms when the cross-helicity is nonzero, then for the interval of Ulysses data analyzed by Horbury et al. the ratio of the spectra perpendicular and parallel to B 0 is more consistent with the Goldreich & Sridhar scaling P ⊥/P ∥ ∝ ν1/3 than with the Boldyrev scaling ν1/2. 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 Alfven 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.