On strongly nonlinear vortex/wave interactions in boundary-layer transition

The interactions between longitudinal vortices and accompanying waves considered are strongly nonlinear, in the sense that the mean-flow profile throughout the boundary layer is completely altered from its original undisturbed state. Nonlinear interactions between vortex flow and Tollmien-Schlichting waves are addressed first, and some analytical and computational properties are described. These include the possibility in the spatial-development case of a finite-distance break-up, inducing a singularity in the displacement thickness. Second, vortex/Rayleigh wave nonlinear interactions are considered for the compressible boundary-layer, along with certain special cases of interest and some possible solution properties. Both types, vortex/Tollmien-Schlichting and vortex/Rayleigh, are short-scale/long-scale interactions and they have potential applications to many flows at high Reynolds numbers. The strongly nonlinear nature is believed to make them very relevant to fully fledged transition to turbulence.