Sensitivity of a supersonic boundary layer to acoustic disturbances

Abstract

The results obtained by the authors in [1] are extended to the case of arbitrary angles of incidence of the external wave. This is not a trivial generalization, since the acoustic scattering undergoes a qualitative change. It is possible to distinguish two excitation channels: the first is connected with the diffraction of the acoustic wave by the spatial inhomogeneity resulting from the displacing action of the boundary layer, and the second with the presence of concentrated acoustic field sources associated with the scattering of the wave at the leading edge. The latter makes the principal contribution to the initial amplitude of the unstable modes when the angles of incidence of the sound are substantially different from zero. At low angles of incidence there is a singularity which can be revealed by introducing narrow intervals in the neighborhood of the limiting values of the wave numbers, where the two excitation channels are approximately equivalent. It is possible to obtain composite expressions for the initial amplitudes of the unstable modes uniformly valid for all angles of incidence of the acoustic wave.