Distribution of Magnetic Discontinuities in the Solar Wind and in MHD Turbulence

The statistical properties of magnetic discontinuities in the solar wind are investigated by measuring fluctuations in the magnetic field direction, given by the rotation Delta theta that the magnetic field vector undergoes during time interval Delta t. We show that the probability density function for rotations, P(Delta theta), can be described by a simple model in which the magnetic field vector rotates with a relative increment (Delta B)/B that is lognormally distributed. We find that the probability density function of increments, P((Delta B)/B), has a remarkable scaling property: the normalized variable x=[(Delta B)/B]*[(Delta t)/(Delta t_0)]^-a has a universal lognormal distribution for all time intervals Delta t. We then compare measurements from the solar wind with those from direct numerical simulations of magnetohydrodynamic (MHD) turbulence. We find good agreement for P(Delta theta) obtained in the two cases when the magnetic guide-field to fluctuations ratio B_0/b_rms is chosen accordingly. However, the scale invariance of P((Delta B)/B) is broken in the MHD simulations with relatively limited inertial interval, which causes P(Delta theta) to scale with measurement interval differently than in the solar wind.