Mechanism of sound generation by low Mach number flow over a wall cavity

An analysis is made of the mechanism of sound production by nominally steady low Mach number flow over a rigid shallow wall cavity. At very low Mach numbers the dominant source of sound is the unsteady drag, and the aeroacoustic dipole source accompanying this force. A monopole source dependent on the compression of fluid within the cavity is smaller by a factor of the order of the flow Mach number M. The directivity of the dipole sound peaks in directions upstream and downstream of the cavity, and there is a radiation null in the direction normal to the plane of the wall. However, numerical simulations for M as small as 0.1 have predicted significant radiation in directions normal to the wall. This anomaly is investigated in this paper by means of an acoustic Greenʹs function tailored to cavity geometry that accounts for possible aeroacoustic contributions from both the drag-dipole and from the lowest order cavity resonance. The Greenʹs function is used to show that these sources are correlated and that their strengths are each proportional to the unsteady drag generated by vorticity interacting with the cavity trailing edge. When M∼0.01, the case in most underwater applications, the monopole strength is always negligible (for a cavity with rigid walls). At low Mach numbers exceeding about 0.05 it is shown that the cavity monopole radiation is O(M2)≪1 relative to the dipole at low frequencies. At higher frequencies, near the resonance frequency of the cavity, the monopole and dipole have similar orders of magnitude, and the combination produces a relatively uniform radiation directivity, with substantial energy radiated in directions normal to the wall. Illustrative numerical results are given for a wall cavity subject to ‘shear layer mode’ excitation by the Rossiter ‘feedback’ mechanism.