Anisotropy up to and Beyond the Outer Scale of Turbulence and its Radial Dependence

We present the first study of the anisotropy of magnetic field (B) fluctuations over the whole inertial range of MHD turbulence. We use Ulysses fast polar solar wind data and a wavelet method (Horbury et al., Phys. Rev. Lett., 2008) to show that beyond the outer scale of turbulence, where the power spectral index of B is -1, both the power and spectral index are close to isotropic. As the turbulent cascade develops the power and spectral index become anisotropic in a way that is dependent on frequency. We show this is consistent with a “critical balance” approximation by comparing the power and estimated wave vector anisotropy to those predicted by critical balance. We also show that as distance from the Sun increases the isotropic outer scale moves to lower frequency and both the power and spectral index anisotropies move with it. Thus lower frequencies become more anisotropic with distance from the Sun. This shows that the anisotropy is an inherent local property of the turbulence and not a structure imposed by the Sun.