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Analyse multifractale pratique : coefficients dominants et ordres critiques. Applications à la turbulence pleinement développée. Effets de nombre de Reynolds fini

Abstract : Multifractal description of signals has been developed during the last 20 years, mainly in the fully developed turbulence. Pointwise regularity properties are characterized by the singularity spectrum. Multifractal analysis consists in the singularity spectrum measurement using multifractal formalisms. Simultaneous introduction of wavelet transforms allowed finer practical multifractal analysis, sometimes without receiving well-founded mathematical basis.
S. Jaffard recently introduced the wavelet leaders yielding a mathematical well-founded multifractal formalism, that allows the measurement of the whole singularity spectrum and remains valid when performing the analysis of signals with oscillating singularities. This new tool is for the first time implemented, numerically characterized and applied to turbulent velocity data.
On the other hand this work rises the important issue of the practical use of multifractal formalisms, that reduce in fine in structure function scaling exponent measurement. Extensive numerical study using reference synthetical multifractal processes illustrates and characterizes the existence of a critical order. An estimator of the critical order is built and numerically characterized. Previous results in turbulence then receive rereading.
Finally, the universality of structure function scaling exponents in fully developed turbulence is tackled. Third order structure function scaling exponent modelling is proposed and compared to experimental results, emphasizing its non-universal value.
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https://tel.archives-ouvertes.fr/tel-00011012
Contributor : Bruno Lashermes <>
Submitted on : Wednesday, November 16, 2005 - 7:36:36 PM
Last modification on : Thursday, November 21, 2019 - 2:22:08 AM
Long-term archiving on: : Friday, April 2, 2010 - 10:22:39 PM

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  • HAL Id : tel-00011012, version 1

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Bruno Lashermes. Analyse multifractale pratique : coefficients dominants et ordres critiques. Applications à la turbulence pleinement développée. Effets de nombre de Reynolds fini. Dynamique des Fluides [physics.flu-dyn]. Ecole normale supérieure de lyon - ENS LYON, 2005. Français. ⟨tel-00011012⟩

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