When acoustic waves are propagating through turbulence, a scattering phenomenon occurs leading to a broadening of the acoustic spectrum. This phenomenon has been observed experimentally for a harmonic source radiating through the shear layer of a cold jet at low speed. The observed spectra are displaying a characteristic shape consisting in a more or less reduced peak amplitude at the source frequency, surrounded by sidebands (also called haystacks). The levels and width of these sidebands appear to be evolving with the source and flow parameters. This spectral broadening is studied in this paper for a simplified configuration consisting in a monopole radiation propagating through a turbulent layer with a constant thickness and convected by a uniform mean flow. The numerical method used relies on a finite difference code solving the linearized Euler equations in the time domain. The turbulence is synthesized using a stochastic method based on the filtering of white noise to impose prescribed statistical properties to the turbulent velocity field. These turbulent fluctuations are then added to the steady mean flow to form an unsteady base flow around which the Euler equations are linearized. This new set of equations contains terms involving products between the turbulent and acoustic fluctuations, which are responsible for the scattering. In this paper, the trends deduced from this numerical study can be compared to analytical models and experimental data obtained for a jet shear layer. They can also be related to the trends observed in a previous study on the scattering of sound by a single convected vortex.
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