Intermittency, non-Gaussian statistics and fractal scaling of MHD fluctuations in the solar wind

Abstract

This paper gives a review of some recent work on intermittency, non-Gaussain statistics, and fractal scaling of solar wind magnetohydrodynamic turbulence. Model calculations and theories are discussed and put in their context with the in-situ observations of solar wind fluctuations, essentially of the flow velocity and magnetic field. Emphasis is placed more on a comparison of the data with theory than on a complete derivation of the model results, which are treated in a more tutorial fashion. The introduction reminds of some important observations and key aspects of solar wind turbulence. Then structure functions are defined and observational results discussed. The probabiltity density functions provide a direct means to analyse the statistical properties of the fluctuations. Evidence for non-Gaussian statistics is provided. Intermittency and simple scaling models are discussed, which yield algebraic expressions for the scaling exponents of the structure functions. The concept of extended self-similarity is presented and corresponding observational evidence for its existence in the solar wind is provided. Subsequently, an extended structure function model, including the p-model scaling and a scale-dependent cascade, is discussed and compared with selected measurements. The basics of multifractals are presented and applied to solar wind data. The multifractal scaling of the kinetic energy flux as a proxy for the unknown cascading rate is established observationally, and the so-called multifractal spectrum is obtained. Finally, the scaling exponents of the associated correlation functions are derived and analysed. The paper concludes with a discussion of the empirical results and prospects for future research in this field and in solar wind MHD turbulence in general.