Radiation and Refraction of Sound Waves Through a 2-D Shear Layer: Numerical Solution

Acoustic propagation in sheared mean flows can be calculated using the linearized Euler equations (LEE). However the LEE also support instabilities. These instabilities are nonphysical since, in the real flow problem, they are suppressed by nonlinear effects. In fact, they constitute the fundamental driving mechanism in their nonlinear form, for turbulent free shear flows. These instabilities can overwhelm the acoustic solution thus complicating the prediction of mean flow/acoustic interaction effects. In this paper, a numerical solution for sound propagation through a 2-D shear layer is presented that suppresses the LEE instabilities. The solution is obtained using a direct frequency domain solver. A frequency domain buffer-zone is used to implement the boundary conditions. The numerical solution avoids the instability-wave solution and accurately captures the acoustic-wave solution. The rationale for the success of this technique is described in reference 1. The numerical algorithm is straightforward and is presented in this paper along with the results.