Non-Gaussian statistics in space plasma turbulence: Fractal properties and pitfalls

Abstract

Statistical properties of collisionless plasmas in the vicinity of the Earth's bow shock are investigated with the aim to characterize the intermittent behaviour of non-magnetohydrodynamic turbulence. The structure functions of the fluctuating magnetic field reveal an increasing departure from Gaussianity at small scales, which is similar to that observed in solar wind turbulence and is surprisingly little affected by the abrupt shock transition. While these results may be the signature of a multifractal process, a deeper inspection reveals caveats in such an interpretation. Several effects, including the anisotropy of the wavefield, the violation of the Taylor hypothesis and the occasional occurrence of coherent wave packets, strongly affect the higher order statistical properties. Most of the small differences observed between the up- and downstream sides of the shock can be ascribed to the occurrence of discrete whistler wavetrains, while the wavefield itself is much less intermittent. It is also shown how the finite length of the records prohibits a reliable estimation of structure functions beyond the fourth order. These results preclude an unambiguous identification of underlying models for intermittency.