Magnetic Discontinuities in Magnetohydrodynamic Turbulence and in the Solar Wind

Abstract

Recent measurements of solar wind turbulence report the presence of intermittent, exponentially distributed angular discontinuities in the magnetic field. In this Letter, we study whether such discontinuities can be produced by magnetohydrodynamic (MHD) turbulence. We detect the discontinuities by measuring the fluctuations of the magnetic field direction, $\ensuremath{\Delta}\ensuremath{\theta}$, across fixed spatial increments $\ensuremath{\Delta}x$ in direct numerical simulations of MHD turbulence with an imposed uniform guide field ${B}_{0}$. A large region of the probability density function (pdf) for $\ensuremath{\Delta}\ensuremath{\theta}$ is found to follow an exponential decay, proportional to $\mathrm{exp}(\ensuremath{-}\ensuremath{\Delta}\ensuremath{\theta}/{\ensuremath{\theta}}_{*})$, with characteristic angle ${\ensuremath{\theta}}_{*}\ensuremath{\approx}(14\ifmmode^\circ\else\textdegree\fi{})({b}_{\mathrm{rms}}/{B}_{0}{)}^{0.65}$ for a broad range of guide-field strengths. We find that discontinuities observed in the solar wind can be reproduced by MHD turbulence with reasonable ratios of ${b}_{\mathrm{rms}}/{B}_{0}$. We also observe an excess of small angular discontinuities when $\ensuremath{\Delta}x$ becomes small, possibly indicating an increasing statistical significance of dissipation-scale structures. The structure of the pdf in this case closely resembles the two-population pdf seen in the solar wind. We thus propose that strong discontinuities are associated with inertial-range MHD turbulence, while weak discontinuities emerge from dissipation-range turbulence. In addition, we find that the structure functions of the magnetic field direction exhibit anomalous scaling exponents, which indicates the existence of intermittent structures.