Analysis of the linear stability of compressible boundary layers using the PSE (Q1182726)

The parabolic stability equations (PSE) have been developed recently to take into account mean-flow nonparallelism in the stability analysis of convectively unstable flows. This is done in an ad-hoc manner, avoiding the order-of-magnitude analysis of more rational perturbation methods. Due to the parabolic character in streamwise direction a marching procedure can be utilized to solve these equations numerically, using only a fraction of the time and memory requirements of direct numerical simulations. In the present paper the linearized PSE are applied to supersonic boundary layers. Results are presented for two- and three- dimensional first-mode waves. While the effect of mean-flow nonparallelism is found to be small for two-dimensional waves, it is pronounced for a three-dimensional wave similar to findings in the incompressible case.