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Développement d'un nouveau modèle dynamique pour la turbulence: application aux écoulements bidimensionnels et aux écoulements plans.

type de publication      thèse de doctorat
date de publication 1999
auteur(s) Laval Jean-Philippe
jury Bérengère DUBRULLE; Bernard LEGRAS; Maurice MENEGUZZI; Annick POUQUET; Olivier THUAL, Vladimir TSEITLINE
  
résumé We developed a turbulent model based on asymptotic developpement of the Navier-Stokes equations within the hypothesis of non-local interactions at small scales. This model provides expressions of the turbulent Reynolds subgrid stresses via estimates of the subgrid velocities rather than velocities correlations as is usually done. The model involves the coupling of two dynamical equations: one for the resolved scales of motions, which depends upon the Reynolds stresses generated by the sub-grid motions, and one for the subgrid scales of motions, which can be used to compute the subgrid Reynolds stresses. The non-locality of interaction at subgrid scales allows to modelise their evolution with a linear inhomogenous equation where the forcing occurs via the energy cascade from resolved to subgrid scales. This model was solved using a decomposition of sub-grid scales on Gabor's modes and implemented numericaly in 2D with periodic boundary conditions. A particles method (PIC) was used to compute the sub-grid scales. The results were compared with results of direct simulations for several typical flows. The model was also applied to plane parallel flows. An analytical study of the equations allows a description of mean velocity profiles in agreement with experimental results and theoritical results based on the symetries of the Navier-Stokes equation. Possible applications and improvements of the model are discussed in the conclusion.
mots clés two-dimensional turbulence, modelisation, numerical simulation
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