Hydrodynamic instabilities and surface waves in a flow over an impedance wall

A two dimensional analysis of the surface waves in a subsonic compressible uniform mean flow along an impedance wall is made. It is found that a maximum of four surface waves is possible. The regions of existence in complex impedance and wave number planes are given. One wave is found to travel upstream, while the others, one of which is an instability, propagate downstream. A Wiener-Hopf solution of plane wave scattering at a hard/soft discontinuity of the wall impedance in which the instability wave provides the additional degree of freedom to satisfy the Kutta condition at the impedance jump is constructed. The waves are limiting forms of irregular acoustic duct modes.