Asymmetric multifractal model for solar wind intermittent turbulence

Szczepaniak, Anna; Macek, Wiesław M.

doi:10.5194/npg-15-615-2008

Cited by 38 publications

(33 citation statements)

References 50 publications

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“…It can be observed that the model fits the data well. The values estimated for multifractality and symmetry are slightly different from those obtained by Szczepaniak and Macek (2008). The discrepancy is primarily due to the differences in the fractal dimensions at the right end of the spectra.…”

Section: Example 2: Szczepaniak and Macek's Solar Wind Datamentioning

confidence: 45%

“…The discrepancy is primarily due to the differences in the fractal dimensions at the right end of the spectra. It is noteworthy that the model that Szczepaniak and Macek (2008) used to fit the data with the curve reaches zero at both ends, whereas the curve fitted by the new model reaches zero only at one end but not at the other end. The results also indicate that the distribution has strong multifractality and a left-skewed asymmetry.…”

Section: Example 2: Szczepaniak and Macek's Solar Wind Datamentioning

confidence: 99%

“…Szczepaniak and Macek (2008) The curve fitted by the model with the five values above is superimposed on the results obtained by Szczepaniak and Macek (2008) (see Fig. 3b).…”

Section: Example 2: Szczepaniak and Macek's Solar Wind Datamentioning

confidence: 99%

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Generalized binomial multiplicative cascade processes and asymmetrical multifractal distributions

Cheng

2014

Nonlin. Processes Geophys.

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Abstract.The concepts and models of multifractals have been employed in various fields in the geosciences to characterize singular fields caused by nonlinear geoprocesses. Several indices involved in multifractal models, i.e., asymmetry, multifractality, and range of singularity, are commonly used to characterize nonlinear properties of multifractal fields. An understanding of how these indices are related to the processes involved in the generation of multifractal fields is essential for multifractal modeling. In this paper, a fiveparameter binomial multiplicative cascade model is proposed based on the anisotropic partition processes. Each partition divides the unit set (1-D length or 2-D area) into h equal subsets (segments or subareas) and m 1 of them receive d 1 (> 0) and m 2 receive d 2 (> 0) proportion of the mass in the previous subset, respectively, where m 1 + m 2 ≤ h. The model is demonstrated via several examples published in the literature with asymmetrical fractal dimension spectra. This model demonstrates the various properties of asymmetrical multifractal distributions and multifractal indices with explicit functions, thus providing insight into and an understanding of the properties of asymmetrical binomial multifractal distributions.

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Section: Example 2: Szczepaniak and Macek's Solar Wind Datamentioning

confidence: 45%

Section: Example 2: Szczepaniak and Macek's Solar Wind Datamentioning

confidence: 99%

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Generalized binomial multiplicative cascade processes and asymmetrical multifractal distributions

Cheng

2014

Nonlin. Processes Geophys.

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“…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 have analysed time series of velocities of the solar wind measured by Voyager 2 at various distances from the Sun, 2.5, 25, and 50 AU, selecting longer (13-day) 1978-1988-1997(Macek and Wawrzaszek, 2009.…”

Section: Solar Wind Datamentioning

confidence: 99%

“…In particular, the multifractal spectrum has been investigated using Voyager (magnetic field fluctuations) data in the outer heliosphere (Burlaga, 1991(Burlaga, , 2001) and using Helios (plasma) data in the inner heliosphere (Marsch et al, 1996). The multifractal scaling has also been investigated using Ulysses observations, e.g., (Horbury and Balogh, 2001; and with Advanced Composition Explorer (ACE) and WIND data, e.g., (Hnat et al, 2003;Szczepaniak and Macek, 2008).…”

Section: Introductionmentioning

confidence: 99%

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

Macek

Wawrzaszek

2011

Nonlin. Processes Geophys.

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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.

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THEMIS observation of intermittent turbulence behind the quasi‐parallel and quasi‐perpendicular shocks

2015

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Turbulence is complex behavior that is ubiquitous in nature, but its mechanism is still not sufficiently clear. Therefore, the main aim of this paper is analysis of intermittent turbulence in magnetospheric and solar wind plasmas using a statistical approach based on experimental data acquired from space missions. The quintet spacecraft of Time History of Events and Macroscale Interactions during Substorms (THEMIS) allows us to investigate the details of turbulent plasma parameters behind the collisionless shocks. We investigate both the solar wind and magnetospheric data by using statistical probability distribution functions of Elsässer variables that can reveal the intermittent character of turbulence in space plasma. Our results suggest that turbulence behind the quasi‐perpendicular shock is more intermittent with larger kurtosis than that behind the quasi‐parallel shocks, which are immersed in a relatively quiet solar wind plasma, as confirmed by Wind measurements. It seems that behind the quasi‐perpendicular shock the waves propagating outward from the Sun are larger than possibly damped waves propagating inward. In particular, we hope that this difference in characteristic behavior of the fluctuating space plasma parameters behind both types of shocks can help identify complex plasma structures in the future space missions. We also expect that the results obtained in this paper will be important for general models of turbulence.

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Asymmetric multifractal model for solar wind intermittent turbulence

Cited by 38 publications

References 50 publications

Generalized binomial multiplicative cascade processes and asymmetrical multifractal distributions

Generalized binomial multiplicative cascade processes and asymmetrical multifractal distributions

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

THEMIS observation of intermittent turbulence behind the quasi‐parallel and quasi‐perpendicular shocks

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