Singularity formation in the strongly nonlinear wide-vortex/ Tollmien-Schlichting-wave interaction equations

A combined numerical/analytical study of the wide-vortex/wave interaction e quations, describing boundary-layer instability, is presented. Depending on the obliqueness beta of the wave input, different solution properties are obtained. For beta = 1, oscillations in the wave amplitude lead to the evol ution of a strongly three-dimensional mean flow, while for beta = 2 the int eraction is characterized by the development of a singularity in the wave p ressure amplitude. This latter behaviour is modelled using an approximate f orm for the mean flow skin friction and the resulting amplitude equation is analysed using a combination of numerical and asymptotic techniques. A sim ple method is described for determining the singularity location for a give n spanwise wavenumber, and the asymptotic behaviour of the pressure amplitu de as the singularity is approached is deduced.