Numerical study of the scattering of acoustic waves by an elliptic vortex

Abstract

The scattering of the acoustic waves generated by a monopolar source propagating through a two-dimensional elliptic vortex, fixed or convected by a uniform flow, is studied by solving the Linearized Euler Equations in Cartesian coordinates using the Discontinuous Galerkin Method. For a fixed vortex position, the number, amplitudes, and angular spreads of the acoustic interference beams resulting from the sound scattering are found to significantly depend on the orientation of the vortex major axis with respect to the direction of the incident waves and on the vortex maximum tangential velocity. In particular, additional interference beams are obtained at large observation angles for a more elliptical vortex. For a convected elliptic vortex, the interference beams are curved as the angle between the incident acoustic wave and the vortex major axis varies when the vortex travels in the downstream direction. As expected, the scattering of the acoustic waves leads to spectral broadening in this case. Moreover, the widths and the frequencies of the lateral lobes obtained in the spectra on both sides of the peak at the source frequency are different for elliptic and round vortices.