| This thesis investigates acoustic wave propagation phenomena in transversely-sheared flows theoretically and computationally. As model problems, four types of aero-acoustic problems are considered: (i) sound radiation from a time-harmonic point source in a steady mixing layer; (ii) that in a steady boundary layer; (iii) acoustic scattering of plane waves in an unsteady subsonic mixing layer; and (iv) shock wave leakage across an unsteady supersonic mixing layer. In each problem, theoretical predictions are compared with direct numerical simulation (DNS) in two dimensions.; In the first problem, Green's functions in a transversely-sheared mixing layer are re-derived or newly formulated including three types of waves: direct waves, refracted arrival waves, and instability waves. Likewise, in the second problem, Green's functions in a transversely-sheared boundary layer are derived including direct waves, channeled waves, and diffracted waves. Green's functions of direct waves, refracted arrival waves, and diffracted waves are derived based on the third order convective wave equation using asymptotic theories, i.e. low and high frequency limits as well as far field asymptotes. Green's functions of instability waves and channeled waves are formulated using the adjoint operator of the third order convective wave equation and the corresponding bi-orthogonal system. These theoretical predictions show fairly good agreement with DNS in most cases.; In the third problem, the interaction between acoustic plane waves and an unsteady vortex-laden mixing layer is investigated. Here, scattered acoustic field and frequency broadening are numerically analyzed using DNS. The scattered acoustic field is also calculated using geometrical acoustics, and its comparison with DNS shows good agreement. In the fourth problem, the interaction between a weak shock wave and a supersonic unsteady vortex laden mixing layer is studied for the application to jet screech noise. The shock leakage across a mixing layer is analyzed based on geometrical acoustics, and the wave-front evolution of the leaked shock noise and its amplitude are predicted. |
