Acoustic Radiation from a Vortex Approaching a Circular Cylinder with Surface Suction

This paper concerns an unsteady two-dimensional inviscid flow about a circular cylinder, a flow containing, a concentrated line vortex which interacts with the body to generate sound. Using potential theory, we determine the force that would act on the cylinder if there was uniform surface suction that attracted the vortex towards the cylinder. We determine the far field sound generated by the unsteady vortex motion and show that the sound field is still dipole with its axis rotating at the angular speed of the vortex. Of course this is only a model of the processes that might occur at high Reynolds number, a model selected to be anlaytically traceable at low Mach number. The singular nature of the flow induces singular speeds and a singular rate of change as the vortex enters the cylinder; that aspect is hardly likely to simulate realizable aeroacoustic flows. It is the scarcity of exact model problems that gives this example its interest.