Scale-dependent normalized amplitude and weak spectral anisotropy of magnetic field fluctuations in the solar wind turbulence

Turbulence in the solar wind was recently reported to be anisotropic, with the average power spectral index close to ?2 when sampling parallel to the local mean magnetic field B₀ and close to ?5/3 when sampling perpendicular to the local B₀. This result was widely considered to be observational evidence for the critical balance theory (CBT), which is derived by making the assumption that the turbulence strength is close to one. However, this basic assumption has not yet been checked carefully with observational data. Here we present for the first time the scaledependent magnetic-field fluctuation amplitude, which is normalized by the local B₀ and evaluated for both parallel and perpendicular sampling directions, using two 30-day intervals of Ulysses data. From our results, the turbulence strength is evaluated as much less than one at small scales in the parallel direction. An even stricter criterion is imposed when selecting the wavelet coefficients for a given sampling direction, so that the time stationarity of the local B₀ is better ensured during the local sampling interval. The spectral index for the parallel direction is then found to be ?1.75, whereas the spectral index in the perpendicular direction remains close to ?1.65. These two new results, namely that the value of the turbulence strength is much less than one in the parallel direction and that the angle dependence of the spectral index is weak, cannot be explained by existing turbulence theories, like CBT, and thus will require new theoretical considerations and promote further observations of solar-wind turbulence.