Sound Produced When a Vortex Pair is Swallowed by a Jet

An analysis is made of the sound generated during the high-Reynolds-number convection of a vortex pair in a jet of water exhausting from a large vessel through a slit aperture. The equations of motion are linearized about the classical free-streamline solution describing steady flow through the aperture. It is assumed that the vortex pair is swept through the aperture into the jet by the steady mean flow, with no account taken of the nonlinear influence on the motion of ‘images’ in the boundaries. Additional vorticity is shed from the edges of the aperture in order that the flow should remain smooth and continuous (the Kutta condition). This vorticity is convected away within a sheet of ‘bound’ vorticity on the mean free streamlines of the jet. A strong peak in the bound vorticity is established when the vortex pair enters the aperture. Both the incident and the shed vorticity generate sound, but their respective contributions to the acoustic pressure are of opposite phase. The dominant radiation in the water above the aperture is produced as the vortex enters the jet, and has the form of a pressure pulse of width ~h/M and monopole strength , where h is the width of the aperture, ρ _o the density of the water, v a typical flow velocity, and M is the jet Mach number.