Spectral broadening of acoustic waves by convected vortices

The scattering of acoustic waves by a moving vortex is studied in two dimensions to bring further insight into the physical mechanisms responsible for the spectral broadening caused by a region of turbulence. When propagating through turbulence, a monochromatic sound wave will be scattered over a range of frequencies, resulting in typical spectra with broadband sidelobes on either side of the tone. This spectral broadening, also called 'haystacking', is of importance for noise radiation from jet exhausts and for acoustic measurements in open-jet wind tunnels. A semianalytical model is formulated for a plane wave scattered by a vortex, including the influence of the convection of the vortex. This allows us to perform a detailed parametric study of the properties and evolution of the scattered field. A time-domain numerical model for the linearised Euler equations is also used to consider more general sound fields, such as that radiated by a point source in a uniform flow. The spectral broadening stems from the combination of the spatial scattering of sound due to the refraction of waves propagating through the vortex, and two Doppler shifts induced by the motion of the vortex relative to the source and of the observer relative to the vortex. The fact that the spectrum exhibits sidebands is directly explained by the directivity of the scattered field which is composed of several beams radiating from the vortex. The evolution of the acoustic spectra with the parameters considered in this paper is compared with the trends observed in previous experimental work on acoustic scattering by a jet shear layer.