Etude numérique à petite et grande échelle de la bande laminaire-turbulente de l'écoulement de Couette plan transitionnel

Abstract : The thesis proposes a numerical study and modelling of the transition to turbulence in plane Couette flow. It is focused on the laminar-turbulent oblique bands regime at the centre of the transition. Two types of approaches are taken, based on the scales considered. On the one hand, one can study the microscopic details of the flow. Direct Numerical simulations are used to identify and characterise a shear instability that creates spanwise vorticity, and allows to measure the advection velocity of these perturbations. The modelling of the background turbulent flow is used to study the instability in term of linear analysis. The convective/absolute transition in the intermediate zone between turbulent and pseudo-laminar flow is emphasised. From these data, a description of the sustaining of turbulence in term of a cycle is proposed. On the other hand, the flow can be seen at the scale of the band. Statistical tools are used to study the oblique band in term of pattern formation. The effect of the intrinsic turbulent noise is studied, particularly with the orientation fluctuation of the band. The modelling in term of Landau--Langevin and corresponding Fokker--Planck equation draws a parallel with the noisy pattern formation and critical phenomena. Using this model, the orientation fluctuations can be understood in term of mean first passage time. Eventually, several topics are considered from both points of view. The study of relaminarisations both at the threshold of disappearance of turbulence and of appearance of the bands helps to identify the mechanisms of local death of turbulence. The study of turbulent spots presents part of their zoology and helps to study the small scale mechanisms at higher Reynolds numbers.
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Joran Rolland. Etude numérique à petite et grande échelle de la bande laminaire-turbulente de l'écoulement de Couette plan transitionnel. Dynamique des Fluides [physics.flu-dyn]. Ecole Polytechnique X, 2012. Français. ⟨pastel-00755414⟩

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