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)

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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

CALCULATION OF THE SCALING PROPERTIES OF TURBULENCE Structure functions of a measured fluctuating parameter g(x): Singularity spectrum D(h) (Legendre transformation): Wavelet transform:

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): Wavelet Transform Modulus Maxima Method (WTMM)

INTERMITTENCY MODELS P-model (Meneveau and Sreenivasan, 1987, 1991): P 1 = no intermittency P 1 =1 - fully intermittent turbulence Extended intermittency models (Tu et al., 1996, Marsch and Tu, 1997): - scaling functions for the Kolmogorov-like cascade: - scaling functions for the Kraichnan-like cascade: P 1 =0.5 -  =  ’  (q) = -1+ (  -1)q/2 P 1 =1 -  =  ’+1/3  =  ’+1/2  (q)= (-1+  /2)q

…..Kolmogorov-like Kraicnan-like ---- p-model

E. Yordanova acknowledges the financial support provided through the European Community's Human Potential Programme under contract HPRN-CT , ‘Turbulent Boundary Layers’ Acknowledgements: