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Biau, Damien (2006)
Languages: French
Types: Article
Subjects: Mécanique des fluides, Transition laminaire turbulent, Stabilité hydrodynamique, Réceptivité, Ecoulement de couche limite, Méthodes spectrales, 532
Ce travail est, consacré à la modélisation des stries dans une couche limite laminaire et à l’étude de leur influence sur la transition. Dans une première partie, on présente une modélisation de ces structures longitudinales en utilisant les équations de Navier-Stokes paraboliques. La résolution numérique est basée sur des schémas de projection, de type Chorin-Temam, associés à des méthodes de discétisation spectrales. Ce modèle parabolique est appliqué au problème de réceptivité de la couché limite laminaire vis-a-vis de différentes perturbations extérieures. La dernière étape du processus de transition vers la turbulence est abordée par une étude de stabilité linéaire ainsi qu’une simulation numérique directe. Enfin on propose un modèle pragmatique pour reproduire la dynamique des stries et estimer le seuil de transition ’bypass’. Sur l'ensemble, on a cherché à comparer les résultats à différents travaux expérimentaux existants. Streamwise elongated structures, called streaks, are observed in boundary layers exposed to significant levels of external perturbations. The effect of these streaks on the transition process is investigated in this thesis. The equations for the streaks' dynamics are obtained using the streamwise parabolic form of the Navier-Stokes equations. The numerical resolution is based on projection schemes associated to spectral spatial discretization. SImulations of a boundary layer subject to different external perturbations have been performed. The receptivity of the boundary layer is studied in detail for different inflow conditions : optimal vortices, single tip-vortex and two-dimensional turbulence fields. The breakdown of an isolated streak is investigated by linear stability analysis and direct numerical simulation. The instability, characterised by a short streamwise wavelength, regenerates streamwise structures by non-linear interactions. The streak's breakdown is then characterised by the appearance of quasi-streamwise vortices following the meandering of the streak. This mechanism shows some similarities with the near-wall cycle of fully developed turbulent flows. In the last part, a model is proposed to mimic the streaks' dynamics in laminar boundary layers subject to free-stream turbulence. This empirical model is then applied to estimate the bypass transition position. Throughout the thesis, numerical results are compared, as much as possible, to existing experimental data.

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