Azimuthal Source Noncompactness and Mode Coupling in Sound Radiation from High-Speed Axisymmetric Jets

Acoustic analogy approaches can be used to express the sound radiation from a turbulent flow as the convolution product of a propagator and a source term. This paper presents an acoustic analogy-based analysis that properly accounts for circumferential variations of the propagator across the source correlation region in an axisymmetric jet. The analysis shows that including azimuthal source noncompactness effects leads to a formula for the acoustic spectrum in which each circumferential propagator mode couples only to its corresponding Fourier mode of the source term. This significantly affects the radiated sound field, because the lower-order propagator modes radiate much more efficiently than the higher-order modes, while the lower-order source modes usually contain significantly less energy than the higher-order modes. The resulting formula depends on the Reynolds stress autocovariance tensor, which must be accurately modeled in order to obtain realistic predictions of the sound field. A relatively simple, experimentally based model of this tensor is proposed and combined with Reynolds-averaged Navier-Stokes solutions to obtain predictions of the noise from a moderately supersonic cold round jet. The predictions are shown to be in good agreement with experimental data and the analysis is used to provide insights into the modal structures of the source and sound fields.