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Cascades log-infiniment divisibles et analyse multiresolution. Application à l'étude des intermittences en turbulence.

Abstract : Log-infinitely divisible cascades provide a general framework to study the property of scale invariance. We introduce these objects through a historical presentation of some models proposed in the past to describe statistical intermittency in turbulence. We then aim at giving a precise and formal definition to log-infinitely divisible cascades. Moreover, we choose to use the wavelet transform coefficients associated to a multiresolution analysis,
specially dedicated to time-scale analysis, rather than the increments traditionally used in turbulence. A deep understanding of the formalism leads us to demonstrate its versatility for modelling, and its relations to multiplicative cascades, Markov processes, Langevin equation, Fokker-Planck equation... The particular case of log-compoung Poisson cascades provides us
with new insights in the phenomenon of statistical intermittency. Then, we study some estimates of (relative) power law scaling exponents with an emphasis on bias correction and confidence interval estimation. We apply this technique to internet traffic data. We explain as well why a usual procedure to estimate
a multifractal spectrum applied to a linear fractional stable motion may result misleading. Eventually, the link between statistical intermittency and spatio-temporal intermittency (coherent structures) is investigated in turbulence thanks to joint velocity/pressure measurements in a turbulent flow. Strong pressure drops due to vortices called filmaents are detected. A statistical analysis of the wavelet coefficients of the velocity signal
conditionned by those detected events allows us to quantify the influence of coherent structures on intermittency at different Reynolds numbers.
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https://tel.archives-ouvertes.fr/tel-00001584
Contributor : Pierre Chainais <>
Submitted on : Tuesday, August 27, 2002 - 12:45:37 PM
Last modification on : Thursday, November 21, 2019 - 2:38:14 AM
Long-term archiving on: : Friday, April 2, 2010 - 6:09:13 PM

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  • HAL Id : tel-00001584, version 1

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Pierre Chainais. Cascades log-infiniment divisibles et analyse multiresolution. Application à l'étude des intermittences en turbulence.. Dynamique des Fluides [physics.flu-dyn]. Ecole normale supérieure de lyon - ENS LYON, 2001. Français. ⟨tel-00001584⟩

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