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We consider the concept of the multiscale multifractality in
the context of scaling properties of intermittent turbulence
in space plasmas. 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
[1,2].
We examine the spectrum of generalized dimensions and the
corresponding multifractal singularity spectrum depending on
two rescaling parameters and one probability measure
parameter demonstrating that the multifractal scaling is
often strongly asymmetric [3]. We analyze time series of
plasma parameters of the slow and fast speed streams of the
solar wind plasma measured in situ by Helios 2 and Advanced
Composition Explorer spacecraft during solar minimum and
maximum. We show that the universal shape of the
multifractal spectrum results not only from the nonuniform
probability of the energy transfer rate but rather from the
multiscale nature of the cascade. It is worth noting that
intermittent pulses are stronger for the model with two
different rescaling parameters and a much better agreement
with the solar wind data is obtained. Only in the case of
the multiscale cascade one can reproduce the entire
multifractal spectrum, especially for the negative index of
the generalized dimensions. Therefore we argue that there
is a need to use the two-scale cascade model. Hence we
propose this new more general model as a useful tool for
analysis of intermittent turbulence in various environments.
[1] W. M. Macek, “Multifractality and intermittency in the
solar wind”, Nonlin. Processes Geophys., 14, 695-700, 2007.
[2] W. M. Macek and A. Szczepaniak, “Generalized two-scale
weighted Cantor set model for solar wind turbulence”,
Geophys. Res. Lett., 35, L02108, doi:10.1029/2007GL03263,
2008.
[3] A. Szczepaniak and W. M. Macek, “Asymmetric
multifractal model for solar wind intermittent turbulence”,
Nonlin. Processes. Geophys., 15, 615-620, 2008.