On a stability of the shear flow with a tangential discontinuity in the presence of a small scatterer

It is well known a tangential discontinuity of velocity in the shear flow is unstable. That instability is convective i.e. all disturbances of the tangential discontinuity grow exponentially but they are carried away by the flow downstream so that after all the amplitude of sound field generated by the tangential discontinuity will decrease at any fixed point. In the presented paper we consider the problem when a small scatterer is placed near the tangential discontinuity. It appears this system can be absolutely unstable under the definite position of the scatterer. It means that the appearance of any disturbance of the tangential discontinuity will result in rising of the amplitude of sound field at every point of space. The cause of absolute instability is a feedback provided by the scatterer and the type of instability does not depend on the size of the scatterer. An absolutely unstable system behaves as an autogenerator and radiates tone or multitone sound. So the obtained result explains the possibl...