What determines the direction of minimum variance of the magnetic field fluctuations in the solar wind?

The solar wind is not an isotropic medium; two symmetry axis are provided, first the radial direction (because the mean wind is radial) and second the spiral direction of the mean magnetic field, which depends on heliocentric distance. Observations show very different anisotropy directions, depending on the frequency waveband; while the large-scale velocity fluctuations are essentially radial, the smaller scale magnetic field fluctuations are mostly perpendicular to the mean field direction, which is not the expected linear (WkB) result. We attempt to explain how these properties are related, with the help of numerical simulations.