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Multifractal Scaling in the Solar Wind
Wieslaw Macek, Anna Wawrzaszek

The aim of our work is to examine the question of scaling properties of turbulence in the solar wind. We focus on the non-homogeneous energy transfer rate in the turbulent cascade leading to the phenomenon of intermittency. In particular, we consider time series of the velocities of the slow and fast solar wind measured in situ by the following space satellites: (a) Helios mission (ESA) exploring the inner heliosphere at the ecliptic plane, (b) Advanced Composition Explorer mission (NASA) near Earth's orbit, (c) Voyager mission (NASA) investigating the outer heliosphere and (d) Ulysses which is the only mission that measured parameters of the solar wind out of the ecliptic plane (also in the polar regions of the Sun). We analyse solar wind data obtained during solar minimum and maximum at various distances from the Sun.

In order to look into the multifractality and intermittency in the context of turbulence cascade, we consider generalized weighted Cantor set. This model describe a standard scenario of cascading eddies, each breaking down into two new ones, but not necessarily equal and twice smaller. Our model involves two scaling parameters and one probability measure parameter allowing to describe more intermittent data.

We verify the proposed model and possibility of its application for a better modeling of the irregular solar wind energy transfer. In particular, we focus on determination of multifractal characteristics, such as generalized dimensions, singularity spectra and parameters describing the degree of multifractality and the degree of asymmetry. We compare the calculated generalized dimensions and singularity spectra for the solar wind with that for the generalized two-scale Cantor set model. We demonstrate that the universal shape of the multifractal spectrum resulting from the multiscale nature of the cascade in the solar wind is often rather asymmetric. It worth noting that we observe the evolution of multifractal scaling of the solar wind in the inner and outer heliosphere. Moreover, we use our model to consider large-scale fluctuations in magnetic field intensity before and after crossing the termination shock by the Voyager spacecraft. We also discuss the importance of this model for the description of the attractor properties determined from the solar wind data.

Our analysis show that the model with different scales is in a very good agreement with the experimental data in the whole range of the multifractal spectra for both positive and negative values 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. We hope that our new more general asymmetric multifractal model can shed light on the nature of turbulence and will be usefull for the construction of the global picture of the multifractal scaling in heliosphere.

Last modification: May 25, 2006