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Description multifractale unifiée du phénomène d'intermittence en turbulence Eulérienne et Lagrangienne

Abstract : The multifractal formalism of Parisi and Frisch, and the Propagator approach of Castaing et al., provide a quantitative description of the statistical behavior, in the inertial range, of velocity increments of fully developed turbulent flows. In this PhD thesis, we show that the physics of dissipative effects, that is completely governed by the local Reynolds number, has non trivial consequences on velocity increment statistics. Thanks to simple dimensional arguments, we propose a unified picture, in the framework of the multifractal formalism, of the "acceleration" of the propagator observed in the intermediate dissipative range, in between the inertial range and the dissipative range in which statistics become independent on scale. In particular, we show that it is possible to compute, for a given Reynolds number, the probability density function of velocity increments at every scale, a function that depends only on a single parameter function DE(h) that acquires the mathematical status of singularity spectrum in the limit of infinite Reynolds numbers. We discuss how to adapt our formalism in order to take into account the phenomenon of Skewness. We show that it is possible to generalize our formalism to describe the statistics of Lagrangian velocity fluctuations. We compare our theoretical predictions to experimental and numerical data. This study allows us to estimate the singularity spectrum DL(h) of Lagrangian velocity and to demonstrate its universal behavior. Then, we show that it is possible to establish a formal transformation between the singularity spectra DE(h) of Eulerian turbulence and DL(h) of Lagrangian turbulence. To conclude, we generalize our approach to higher order statistics in order to test various cascade model predictions on experimental and numerical data.
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Contributor : Laurent. Chevillard <>
Submitted on : Friday, November 19, 2004 - 1:16:09 PM
Last modification on : Thursday, November 21, 2019 - 2:27:24 AM
Long-term archiving on: : Thursday, September 13, 2012 - 1:00:16 PM


  • HAL Id : tel-00007454, version 1



Laurent Chevillard. Description multifractale unifiée du phénomène d'intermittence en turbulence Eulérienne et Lagrangienne. Dynamique des Fluides [physics.flu-dyn]. Université Sciences et Technologies - Bordeaux I, 2004. Français. ⟨tel-00007454⟩



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