Three-wave non-linear interaction in a three-dimensional compressible boundary layer

A perturbation method for analysis of non-linear wave interaction in three-dimensional compressible boundary layer is developed. The method is based on a biorthogonal eigenfunction system for three-dimensional compressible boundary layers. It is assumed that characteristic space and time scales of the disturbances are much less than space and time scales of non-linear development and an averaging technique in intermediate scales may be applied. The method is a generalization of Zelman's results for two-dimensional incompressible boundary layer. As an example, a three-wave interaction is considered. A numerical example for so-called Tollmien - Schlichting wave interaction shows the possibility of amplification for rather broad packets without an exact resonance synchronizm for three-wave interaction.