Abstract
Abstract. To quantify 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. We examine generalized dimensions and the corresponding multifractal singularity spectrum depending 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 wind measured in situ by Voyager 2 spacecraft in the outer heliosphere during solar maximum at 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 wind in the distant heliosphere. Namely, it appears that while the degree of multifractality for the solar wind during solar maximum is only weakly correlated with the heliospheric distance, but the multifractal spectrum could substantially be asymmetric in a very distant heliosphere beyond the planetary orbits. Therefore, one could expect that this scaling near the frontiers of the heliosphere should rather be asymmetric. It is worth noting that for the model with two different scaling parameters a better agreement with the solar wind data 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.
Highlights
Multifractality is commonly related to a probability measure that may have different fractal dimensions on different parts of the support of this measure Mandelbrot (1989)
In order to estimate the multifractal spectrum for solar wind turbulence, we should first calculate the multifractal measure given in Eq (4)
We have studied the inhomogeneous rate of the transfer of the energy flux indicating multifractal and intermittent behaviour of solar wind turbulence in the outer heliosphere
Summary
Multifractality is commonly related to a probability measure that may have different fractal dimensions on different parts of the support of this measure Mandelbrot (1989). To quantify scaling of this turbulence, we use a generalized weighted Cantor set with two different scales describing with various probabilities nonuniform intermittent multiplicative process of distribution of the kinetic energy between cascading eddies of various sizes (Macek, 2007; Macek and Szczepaniak, 2008). Starting from Richardson’s (1922) scenario of turbulence, many authors try to recover the observed scaling exponents, using some simple and more advanced fractal and multifractal models of turbulence describing distribution of the energy flux between cascading eddies at various scales, see for a review (e.g., Bruno and Carbone, 2005). The multifractal scaling has been investigated using Ulysses observations, e.g., (Horbury and Balogh, 2001; Wawrzaszek and Macek, 2010) and with Advanced Composition Explorer (ACE) and WIND data, e.g., (Hnat et al, 2003; Szczepaniak and Macek, 2008)
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