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, φ) with respect to the local mean magnetic field B0. 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 B0 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 B0 is more consistent with the Goldreich & Sridhar scaling P⊥/P‖ ∝ ν than with the Boldyrev scaling ν. 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⊥ρi ≃ 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⊥ρi ≃ 4. Subject headings: Solar wind — turbulence, magnetohydrodynamics, scaling laws