Radiation from large-scale structures within a turbulent shear layer

We examine the acoustic radiation from multiple high-speed subsonic and supersonic free shear layers. We decompose the flow field into a base component (an average), a component associated with the spatially and temporarily growing and decaying instability waves, and the acoustic radiation associated from the instability waves. We find an analytical solution for the acoustic radiation through the use of an acoustic analogy. The arguments of the acoustic analogy involve the two-point cross-correlation of quantities associated with the base flow and instability waves. The instability waves are modeled with a newly proposed basis function. A combination of large eddy simulation, steady Reynolds-averaged Navier-Stokes solutions, and turbulence modeling is used to close the acoustic model. We compare our predictions to those of previous investigators and our predictions match previous theory. We find that the dominant acoustic radiation is due to the large-scale highly spatially coherent turbulence. The interaction of the instability waves causes secondary broadband radiation at higher observer angles.