Generalized two‐scale weighted Cantor set model for solar wind turbulence

Abstract

[1] In order to quantify the multifractality of solar wind turbulence, we consider a generalized weighted Cantor set with two different scales describing nonuniform compression of cascading eddies. We investigate the resulting multifractal spectrum of generalized dimensions depending on two scaling parameters and one probability measure parameter, especially for asymmetric scaling. In particular, we show that intermittent pulses are stronger for the model with two different scaling parameters and a much 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 new more general model as a useful tool for analysis of intermittent turbulence in various environments. Citation: Macek, W. M., and A. Szczepaniak

MAGNETIC FIELD STRENGTH FLUCTUATIONS AND THEq-TRIPLET IN THE HELIOSHEATH:VOYAGER 2OBSERVATIONS FROM 91.0 TO 94.2 AU AT LATITUDE 30° S

“…In the supersonic solar wind, the large-scale fluctuations of B have correlations on various scales. A multifractal structure on scales from one to several days was observed at all distances between 1 AU and the termination shock (Burlaga 1991a(Burlaga , 1991b, in the disturbed heliosheath just behind the termination shock (Burlaga et al 2006;Macek 2007;Macek & Szczepaniak (2008, and deep into the heliosheath Burlaga & Ness 2012a).…”

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

“…In our model of turbulence we consider a standard scenario of cascading eddies, each breaking down into two new ones, but not necessarily equal and twice smaller, as proposed by Macek and Szczepaniak (2008). In particular, space filling turbulence could be recovered for l 1 + l 2 = 1.…”

“…Namely, to study turbulence cascade Macek and Szczepaniak (2008) have selected four-day time intervals of v x samples in 1976 (solar minimum) for both slow and fast solar wind streams measured by Helios 2 at various distances from the Sun. The results for ACE data at 1 AU and dependence on solar cycle are discussed by Szczepaniak and Macek (2008).…”

“…We consider the concept of the multiscale multifractality in the context of scaling properties of intermittent turbulence in astrophysical and space plasmas Sreenivasan, 1987, 1991). 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).…”

Asymmetric multifractal model for solar wind intermittent turbulence

“…Using generalized dimensions and singularity spectra allow us a better description of energy turbulence cascade and the degree of multifractality in the solar wind plasma (Meneveau and Sreenivasan, 1991). It is well known that multifractal nature of solar wind has been observed in the inner heliosphere (Marsch et al, 1996;Macek, 1998Macek, , 2002Macek, , 2003Macek, , 2007Macek et al, 2005;Macek and Szczepaniak, 2008a), and in the outer heliosphere (Burlaga, 1991a(Burlaga, ,b,c, 2004Burlaga et al, 1993Burlaga et al, , 2003, also at various phases of the solar cycle (Burlaga, 2001;Burlaga et al, 1993) and various heliographic latitudes . However, 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).…”