Multifractal two-scale Cantor set model for slow solar wind turbulence in the outer heliosphere during solar maximum

To quantify solar windturbulence, we consider a generalized two-scale weighted Cantor setwith two different scales describing nonuniform distribution of the kinetic energy flux between cascading eddies of various sizes. We examine generalized dimensions and the corresponding multifractal singularity spectrumdepending on one probability measure parameter and two rescaling parameters. In particular, we analyse time series of velocities of the slow speed streams of the solar windmeasured in situ by Voyager 2 spacecraft in the outer heliosphereduring solar maximumat various distances from the Sun: 10, 30, and 65 AU. This allows us to look at the evolution of multifractal intermittent scaling of the solar windin the distant heliosphere. Namely, it appears that while the degree of multifractality for the solar windduring solar maximumis only weakly correlated with the heliosphericdistance, but the multifractal spectrum could substantially be asymmetric in a very distant heliospherebeyond the planetary orbits. Therefore, one could expect that this scaling near the frontiers of the heliosphereshould rather be asymmetric. It is worth noting that for the model with two different scaling parameters a better agreement with the solar winddata is obtained, especially for the negative index of the generalized dimensions. Therefore we argue that there is a need to use a two-scale cascade model. Hence we propose this model as a useful tool for analysis of intermittent turbulence in various environments and we hope that our general asymmetric multifractal model could shed more light on the nature of turbulence.