Aeroacoustics of vortex–wedge interaction

We consider the vortex–wedge interaction problem, taking as a departure point Howe’s model of a point vortex interacting with a semi-infinite half-plane, where the vortex path is influenced by its image and a closed-form analytical solution is obtained for the sound field. We generalise Howe’s model to consider wedges of arbitrary angles and explore the influence of vortex circulation, distance from the edge and the wedge half-angle. The effect of wedge angle on sound emission involves a reduced amplitude of the latter as the former is increased. An extension of the model is proposed to account for convection effects by a non-zero ambient flow. We identify a non-dimensional parameter that characterises the vortex kinematics close to the edge and the associated acoustic effect: high and low values of the parameter correspond, respectively, to high- and low-amplitude sound emission of high and low frequency.