Analysis of stability and viscous-inviscid interaction in compressible boundary layers

This work belongs to the theory of fluid flows at high Reynolds number, characterised by low viscosity and, to a lesser extent, high speeds. It is a mathematically intensive field covering most aspects of applied mathematics, from Partial Differential equations to Numerical Analysis and Complex Analysis. Two of the central areas of research within this particular branch of fluid dynamics are the boundary-layer laminar-turbulent transition and the boundary-layer separation. Both of these phenomena have a high impact on the aerodynamic performance of aircraft wings, turbine blades and other fast-moving objects such as rockets. As a consequence, their study is relevant both for industrial applications and to the scientific community as a whole. The mathematical element pertaining to the analysis of these two phenomena is the consistent use of asymptotic methods, such as matched asymptotic expansions and multiple scales analysis. In particular, this work will be based on the viscous-inviscid interaction theory originally discovered by Lin (1955) and further developed by the work of Neiland (1969) and Stewartson & Williams (1969). In the first chapter of this thesis, we will study the initial stages of the laminar-turbulent transition of a compressible boundary layer on a swept wing. The instability of interest will be the stationary crossflow vortex, which is known to be the main instability mode in three-dimensional boundary layers on a swept wing. We will focus on two specific aspects of the transition process, namely the receptivity and linear stability analysis of the flow. The receptivity mechanism introduced in our work is a roughness of size comparable with that of the boundary layer thickness. This justifies our restriction to the study of the inviscid instability of the flow and the use of the impermeability condition on the roughness. The remaining two chapters are concerned with the viscous-inviscid interaction of the boundary layer in the vicinity of a surface discontinuity. We will first study the behaviour of the subsonic flow exposed to the singular pressure gradient dp/dx = κ(x0 − x)−1/3, as x → x0. It forms when the body contour has a point x = x0 near which yw = (x0 − x)5/3. We will show how logarithmic terms need to be included in the solution. We then study a similar problem, this time in the context of an incoming transonic flow near a point of curvature discontinuity. We will show that in both cases the boundary layer experiences an “extreme acceleration”.Open Acces

Militaires en République, 1870-1962

Du maréchal de MacMahon au général de Gaulle, militaires et hommes politiques entretiennent des relations dominées par une mutuelle incompréhension et une large suspicion. Les premiers accusent les poli­tiques de diviser les Français en professionnels de la chicane, quand les seconds suspectent nombre d’officiers de rêver au renversement de la République. Ce livre dépasse les stéréotypes habituels. En une cinquantaine de contributions, il étudie toutes les formes de participation des officiers au pouvoir et à la vie publique, de rétablissement de la Troisième République aux débuts de la Cinquième, de la fin de la guerre de 1870-1871 à la conclusion du conflit algérien. Le métier des armes est, par essence, de nature politique en ce qu’il participe de la conduite de la cité. Certes la professionnalisation de l’action politique sans parler de la peur qu’inspire aux républicains le césarisme a contribué à maintenir les officiers dans les limites de l’expertise. Mais les grands chefs, au même titre qu’une poignée de hauts fonctionnaires, participent au pouvoir par leur contribution à la définition de la politique de défense et de certains aspects de la politique extérieure. Par une approche pluridisciplinaire, associant historiens, juristes, poli­tiques et sociologues, universitaires et militaires, ce colloque rompt défi­nitivement avec l’image simpliste de deux mondes étanches l’un à l’autre et renouvelle l’étude des relations entre les officiers et la vie politique