Edge scattering of aerodynamic sound by a lightly loaded elastic half-plane

Abstract

We investigate the acoustic field radiated when a compact turbulent eddy lies close to a semi-infinite wave-bearing surface, but many acoustic wavelengths from its edge. The Lighthill acoustic analogy is used to reduce the problem to the simpler one of the diffraction of a plane sound wave by a semi-infinite elastic plate. This is solved exactly in terms of a contour integral by means of the Wiener-Hopf technique. An explicit solution for the far sound field is then developed for the limiting case when a non-dimensional fluid loading parameter ϵ tends to zero. Particular attention is paid to the subsonic surface wave modes which couple the fluid and plate vibrations. At low frequencies the bulk of the elastic wave energy induced in the plate by the adjacent turbulent eddy propagates without attenuation in a subsonic surface wave mode. Interaction with the edge of the plate induces an indirect scattered field whose intensity exhibits the dependence on cos 2 ½ θ (the line θ = 0 defines the semi-infinite surface) typical of the acoustic field of an edge scattering half-plane. The acoustic power of the eddy is increased over its free space value by a factor ϵ 2 ( Ma s ) -1 , where Ma s = c p/ c represents the ratio of the natural speed of plate waves in vacuo to the speed of sound. In typical aeronautical applications e can be as large as 18 dB at characteristic eddy frequencies of 100 Hz.