On the development and control of caustics in shear flows over elastic surfaces

The propagation of acoustic waves from a high-frequency line source in a shear layer flowing over an infinite elastic plate is considered. The fluid is inviscid and compressible. The Lagrange-Kirchhoff linear plate theory, including structural damping, is used to describe the small amplitude motions of the plate. The resulting problem is solved approximately by first obtaining the integral representation of the solution using Fourier transforms, and then obtaining asymptotic expansions of this expression for high-frequency sources, as we did previously for the shear flow over a rigid wall. An infinite sequence of caustics (localized noisy regions) are created, downstream of the source and adjacent to the elastic surface, by the refraction of rays from the source and their subsequent reflections from the plate. The acoustic fields on and off the caustics, and in the near and the far field, are obtained from the asymptotic solution. Because of the structural damping, large attenuation of the caustic sound field is obtained for special values of the plate and fluid parameters.