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流体力学セミナー ２００８ No.7

日時： 10月30日（木）15:00から16:30

場所： 京都大学理学部５号館（物理学教室）４１３号室

講師： Prof. Wieslaw M. Macek
(Faculty of Mathematics and Natural Sciences,
Cardinal Stefan Wyszynski University,
Warsaw Space Research Centre, Polish Academy
of Sciences, Poland: visiting at
Faculty of Engineering Sciences, E.S.S.T.,
Kyushu University)
　　　
題目: Multifractal multiscale intermittency
in fully developed turbulence

概要： We consider a question of multifractality based
on an extended self-similarity that depends on scale.
We look into this concept of a multiscale multifractality
in the context of scaling properties of intermittent
turbulence in space plasmas. 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. To quantify scaling of this turbulence,
we use a generalized weighted Cantor set with two different
rescaling parameters describing with various probabilities
nonuniform intermittent multiplicative process of distribution
of the kinetic energy between cascading eddies of various sizes1.

We show that the universal shape of the multifractal spectrum
results not only from the nonuniform probability of the energy
transfer rate but also from the multiscale nature of the cascade.
It is worth noting that only in the case of the two-scale cascade
one can reproduce the entire experimental multifractal spectrum,
especially for the negative index of generalized dimensions2.
It appears that intermittent pulses are stronger for the model
with two different scales, where the singularity spectrum is often
asymmetric3. Therefore, we argue that there is a need to use the
multi-scale cascade model. Hence we hope that our new more general
asymmetric multifractal model could shed light on the nature of
turbulence and we propose this 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.

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世話人：山田 道夫(京大数理研)，松本 剛(京大理), 藤 定義(京大)，
アドバイザー：船越 満明（京大情報学）、水島 二郎(同志社大工)、
余田 成男（京大理）
連絡先：山田道夫 yamada@kurims.kyoto-u.ac.jp
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