Receptivity of supersonic boundary layers over smooth and wavy surfaces to impinging slow acoustic waves

In this talk, we investigate the receptivity of a supersonic boundary layer to impinging acoustic waves. Unlike previous studies of acoustic receptivity, where the sound waves have phase speeds comparable with or larger than the free-stream velocity U_\infty, the acoustic waves here have much slower (O(R^{-1/8}U_\infty)) phase velocity, and their wavelength and frequency are of O(R^{-3/8} L) and O(R^{1/4} U_\infty /L) respectively, compatible with the triple-deck structure, where L is the distance to the leading edge and R the Reynolds number based on L and U_\infty. The first receptivity mechanism is completely new, involving the interaction of two waves and operating in a boundary layer over a smooth wall. The second involves the interaction between an acoustic wave and the steady perturbation induced by a wavy wall. The sound-sound, or sound-roughness, interactions generate a forcing in resonance with a neutral T-S wave. The latter is thus excited near the lower branch of the neutral curve, and subsequently undergoes exponential amplification. The two receptivity processes are much more effective compared with those involving usual sound waves, with the coupling coefficient being greater by a factor of O(R^{1/4}) and O(R^{1/8}) in the S-S and S-R interactions, respectively.