Instability wave patterns generated by-inter action of sound waves with three-dimensional wall suction or roughness

Receptivity processes by which free-stream acoustic waves generate three dimensional instability waves in boundary layers are investigated. Concentration is placed on mechanisms associated with local regions of short scale variation in wall suction, admittance or height. Time harmonic interactions are analysed using the asymptotic, high Reynolds number, triple deck structure. A similarity transform in the Fourier transform wavenumber space, which reduces the three-dimensional receptivity problem to an equivalent two-dimensional problem with a complex frequency, is found. The acoustic wave orientation and the geometry of the wall inhomogeneity are found to significantly influence the amplitudes of the generated instability waves. For an isolated, three-dimensional wall inhomogeneity, instability wave growth is confined to a downstream, wedge shaped region. The saddle point method is utilised to calculate the characteristics of this instability wave pattern. In some ranges of parameter space, two saddle points are found to make comparable contributions. The instability wave pattern in these directions exhibits a beat phenomemon, due to constructive and destructive interference of the contributions from the two saddle points.