Radiation from a double layer jet

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Abstract
The paper deals with the radiation of aerodynamic sound due to two symmetrically placed point sources on either side of a double layer jet flow. These sources are regarded as the driving forces in the acoustic medium. In consequence, the illumination due to a point source on one side is supplemented by the transmission due to the point source on the other side, which results in an enhanced radiation on each side. The analysis provides an expression for the reflexion coefficient which is valid at an interface that separates a fluid at rest from a fluid in motion [which is in perfect agreement with the one obtained by Miles, J. Acoust. Soc. Am. 29, 226–228 (1957), Ffowcs Williams, J. Fluid Mech. 66, 791–816 (1974), and Dash, J. Sound Vib. 49, 365–377; 379–392 (1976)] and predicts an aerodynamic zone of silence, also known as the valley of relative silence, which prevails parallel to the vortex interface off the source locations and appears in the form of sharp clefts around the jet axis. This deep valley in the directivity pattern deepens as the jet velocity or the ambient-to-jet density ratio ( ρ0/ρ1) increases. Marked by the conspicuous absence of highly directional beams, the formation of symmetric directivity patterns around the jet axis resembling a kidney-shaped, lung-shaped, or heart-shaped structure has been vividly illustrated in Figs. 5–8. The emergence of these structures depends on the jet speed and the ambient-to-jet density ratio ( ρ0/ρ1). This investigation also suggests that the sharp, steep, dual dimples formed in the directivity pattern are characteristics to the transonic and supersonic flows at ρ0/ρ1=1 whereas the balloon-type, puffed-up, dual loops formed symmetrically at close angles to the jet axis in the forward flow direction are solely characteristics to the supersonic flows at all values of the ambient-to-jet density ratio, ρ0/ρ1≥1.

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