Observation of the multifractal spectrum in solar wind turbulence by Ulysses at high latitudes

Abstract

The aim of our study is to examine the question of multifractal scaling properties of turbulence in the solar wind at high latitudes. We analyze time series of the velocities of the solar wind during solar minimum (1994–1997, 2006–2007) at various heliographic latitudes measured in situ by Ulysses, which is the only mission that has investigated parameters of the solar wind out of the ecliptic plane also in the polar regions of the Sun. We consider the non‐homogeneous energy transfer rate in the turbulent cascade leading to the phenomenon of intermittency. To quantify the degree of multifractality and the degree of asymmetric scaling of solar wind turbulence, we consider a generalized two‐scale weighted Cantor set with two different scales describing nonuniform distribution of the kinetic energy flux between cascading eddies of various sizes. It is worth noting that both characteristics exhibit latitudinal dependence with some symmetry with respect to the ecliptic plane. Generally, at high latitudes during solar minimum in the fast solar wind streams we observe a somewhat smaller degree of multifractality and intermittency as compared with those at the ecliptic and a roughly symmetric multifractal singularity spectrum. The minimum of intermittency is observed at midlatitudes, possibly related to the transition from the region where the interaction of the fast and slow streams takes place to a more homogeneous region of the pure fast solar wind.