Abstract
Abstract. We consider nonuniform energy transfer rate for solar wind turbulence depending on the solar cycle activity. To achieve this purpose we determine the generalized dimensions and singularity spectra for the experimental data of the solar wind measured in situ by Advanced Composition Explorer spacecraft during solar maximum (2001) and minimum (2006) at 1 AU. By determining the asymmetric singularity spectra we confirm the multifractal nature of different states of the solar wind. Moreover, for explanation of this asymmetry we propose a generalization of the usual so-called p-model, which involves eddies of different sizes for the turbulent cascade. Naturally, this generalization takes into account two different scaling parameters for sizes of eddies and one probability measure parameter, describing how the energy is transferred to smaller eddies. We show that the proposed model properly describes multifractality of the solar wind plasma.
Highlights
The solar wind is a an example of turbulent and intermittent astrophysical plasma (Burlaga, 1991a, 1992a,b; Marsch, 1991; Carbone, 1993; Marsch and Liu, 1993; Marsch and Tu, 1997; Sorriso-Valvo et al, 2001; Biskamp, 2003; Bruno et al, 2003)
The results for the generalized dimensions Dq as a function of q, calculated from Eq (2) using the Advanced Composition Explorer (ACE) data and compared with those obtained from Eq (4) for solar wind turbulence at 1 AU during solar minimum (2006) and solar maximum (2001) are presented in Fig. 5a and b, correspondingly
Since the Cantor set is sensitive to initial conditions the multifractal spectrum for intermittent turbulence can be naturally related to the Lyapunov spectrum as discussed by Chian et al (2006)
Summary
The solar wind is a an example of turbulent and intermittent astrophysical plasma (Burlaga, 1991a, 1992a,b; Marsch, 1991; Carbone, 1993; Marsch and Liu, 1993; Marsch and Tu, 1997; Sorriso-Valvo et al, 2001; Biskamp, 2003; Bruno et al, 2003). The multifractal singularity spectrum obtained for the solar wind data has an asymmetric shape and shows a substantial departure from the standard p-model (Burlaga, 1993; Macek, 2007; Macek and Szczepaniak, 2008a). The nature of this departure is still unexplained.
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