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Equation d'Euler tronquée : de la dynamique des singularités complexes à la relaxation turbulente.

Abstract : This theoretical work presents numerical simulations of Euler equation by spectral methods that conserves energy and usually enables to study complex singularities dynamic. The study of Kida-Pelz flow enables to point out interferences of complex singularities and to extend usual analysis methods. Approximation of a continuous flow by ordinary differential equations leads to a validity limit of temporal integration. Beyond, the system converges to a statistical equilibrium, known as absolute equilibrium.

The study of relaxation to absolute equilibrium shows a spontaneous scale separation due to a progressive thermalisation of the flow, and a pseudo-dissipative effect on large scales. Studying characteric time-scales of equilibrium, analytically and by Monte-Carlo simulations, leads to a scale law. A Fluctuation-Dissipation relation enables a dissipative estimation of the scale separation. The behavior of large scales is finally compatible with a Kolmogorov Turbulence.
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https://tel.archives-ouvertes.fr/tel-00070819
Contributor : Cyril Cichowlas <>
Submitted on : Saturday, May 20, 2006 - 10:37:18 PM
Last modification on : Thursday, December 10, 2020 - 12:37:21 PM
Long-term archiving on: : Sunday, April 4, 2010 - 9:57:14 PM

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  • HAL Id : tel-00070819, version 1

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Cyril Cichowlas. Equation d'Euler tronquée : de la dynamique des singularités complexes à la relaxation turbulente.. Analyse de données, Statistiques et Probabilités [physics.data-an]. Université Pierre et Marie Curie - Paris VI, 2005. Français. ⟨tel-00070819⟩

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