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Diffusion, étirement et intermittence dans le transport turbulent

Abstract : This thesis is divided in two parts. The first one is dedicated to deterministic chaos and, in particular, to the properties of a class of dynamical systems generalising the Lorenz model. The time evolution of the Lorenz system can be interpreted as the oscillating motion of a classical particle moving in a bistable potential. This interpretation yields a systematic analysis of the properties of this model and allows to obtain an example of one-dimensional deterministic diffusion.
The second part is devoted to passive turbulent transport. The transport of a scalar field, examples being the temperature or the concentration of a colorant, is the simplest case of transport. It turns out, studying the dynamics of lagrangian particles, that the large fluctuations of a scalar decaying in an incompressible turbulent flow are more frequent than those predicted by a Gaussian distribution. A more complex case is the transport of a vector field like the magnetic field. The problem of the magnetic dynamo effect can be transformed, within the context of the Kraichnan model, in a quantum mechanics problem. This allows to analyze how the scaling properties of the advecting flow affect the growth of the magnetic field. Finally, the last considered case of passive transport refers to the coil-stretch transition of a polymer. When the advecting flow is defined by the Kraichnan model, the probability distribution of the polymer elongation satisfies a Fokker-Planck equation. This last equation is solved exactly by means of an eigenfunction expansion.
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Contributor : Dario Vincenzi <>
Submitted on : Saturday, March 27, 2004 - 7:55:57 PM
Last modification on : Wednesday, October 14, 2020 - 4:22:22 AM
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  • HAL Id : tel-00005476, version 1


Dario Vincenzi. Diffusion, étirement et intermittence dans le transport turbulent. Dynamique des Fluides [physics.flu-dyn]. Université Nice Sophia Antipolis, 2003. Français. ⟨tel-00005476⟩



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