Multifractal structure of turbulence in magnetospheric cusp

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Multifractal structure of turbulence in
magnetospheric cusp
E.Yordanova (1, 2), M. Grzesiak (1), A.W.Wernik
(1), B. Popielawska (1), K.Stasiewicz (3) (1)
Space Research Centre, Polish Academy of
Science (2)Space Research Institute, Bulgarian
Academy of Science (3)Swedish Institute of Space
Physics, Uppsala, Sweden
Oulu Space Physics Text Book
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CALCULATION OF THE SCALING PROPERTIES OF
TURBULENCE
Structure functions of a measured fluctuating
parameter g(x)
Singularity spectrum D(h) (Legendre
transformation)
Wavelet transform
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Wavelet Transform Modulus Maxima Method (WTMM)
Wavelet based partition function
Scaling law of the partition function along the
maxima line
Singularity spectrum D(h) of the WTMM function
?(q)
The relation between ?(q) and WTMM exponent ?(q)
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INTERMITTENCY MODELS
P-model (Meneveau and Sreenivasan, 1987, 1991)
P1 0.5 - no intermittency P11 - fully
intermittent turbulence
Extended intermittency models (Tu et al., 1996,
Marsch and Tu, 1997)
- scaling functions for the Kolmogorov-like
cascade
P10.5 - ? ? ?(q) -1 (?-1)q/2
- scaling functions for the Kraichnan-like
cascade
P11 - ??1/3 ? ?1/2 ? (q)
(-1 ? /2)q
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..Kolmogorov-like Kraicnan-like ----
p-model
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