Acoustics of a two-dimensional compact jet impinging normally onto a flat plate

Vortex sound is revisited for two-dimensional compact jets. The interactions between the flow and the rigid boundaries of the nozzle are included. Jets with steady upstream conditions and with imposed forcing are considered. A multipole expansion for the acoustic radiation is derived by the method of matched asymptotic expansion. The processes are carried out to higher order to obtain the quadrupole impingement sound in addition to the leading monopole. The emitted sound is found to be related to the vortical flow motion and the scattering of the incoming forcing from the nozzle interior. The flow motion is simulated incompressibly using a point vortex model. The discretization of the continuous vortex shedding is carefully treated to fulfil the Kutta condition and to eliminate spurious sound radiation. Numerical calculations are given for both free and forced jets. For small forcing, the leading monopole is weak and, under some circumstances, the quadrupole sound can be dominant.