Excitation of instability waves in a two-dimensional shear layer by sound

Abstract

The excitation of instability waves in a plane compressible shear layer by sound waves is studied. The problem is formulated mathematically as an inhomogeneous boundary-value problem. A general solution for arbitrary incident sound wave is found by first constructing the Green's function of the problem. Numerical values of the coupling constants between incident sound waves and excited instability waves for a range of flow Mach numbers are calculated. The effect of the angle of incidence in the case of a beam of acoustic waves is analysed. It is found that for moderate subsonic Mach numbers a narrow beam aiming at an angle between 50 to 80° to the flow direction is most effective in exciting instability waves.