| The stability of a boundary layer along a curved wall was first studied by Gortler (27) in 1940. Further investigations have been conducted since 1980. An important contribution was made by Hall (29), when he first proposed a more rigorous approach to this problem. Gortler had used a simple approximation which allowed him to reduce the problem to a set of ordinary differential equations. However such an assumption ignored the growth of the boundary layer, which Hall showed could not be neglected. Hall then rederived the formulation to obtain a set of partial differential equations.;We solved the system of equations, including the nonlinear terms, with a method proposed by Herbert (3), called the Parabolic Stability Equations (PSE). The flow is divided into a basic profile, which satisfies the Prandtl boundary layer equations, and a perturbation. We compared our results for the Blasius profile with those of Bottaro, Klinnmann, and Zebib (8) and found excellent agreement between our calculations and their finite-volume simulations.;We then applied our code to the wall jet profile. We were able to capture the growth of steady vortices, located in the inner region of the jet for a concave wall, and the outer region for a convex wall, as predicted by Florian's (20) linear inviscid argument. Our calculations were in good agreement with Matsson's (49) experimental results.;We also studied the influence of crossflow on a boundary layer. Crossflow might lead to streamwise vortices along a flat plate, and contrary to Gortler vortices, crossflow vortices are co-rotating instead of counter-rotating. We investigated the interactions between these two types of vortices and compared the results with experimental measurements obtained by Bippes (4).;The final part of the thesis is the simulation of the secondary time-dependent instability originating from the shear profiles created by the primary streamwise vortices. The onset of the instability is studied by marching both in space and time. If no forcing is prescribed the time-dependent code predicts a steady solution. Time-dependent boundary conditions are then applied by solving the linear stability problem at some streamwise location to obtain the most dangerous streamwise perturbation velocity and the corresponding frequency. We found that the varicose mode is more amplified in the streamwise direction than the sinuous mode. Similarly, if both modes are included in the initial conditions, the varicose mode is still dominant. Furthermore, as the flow evolves downstream, the unsteady behavior exhibits a more complex time-dependence, which was also observed in the experiments of Swearingen and Blackwealder (66). In our computations, higher harmonics are observed near the wall and propagate into the boundary layer. |
