Scattering of aerodynamic noise by a semi-infinite compliant plate

Abstract

The acoustic scattering properties of a semi-infinite compliant plate immersed in turbulent flow are considered in the context of Lighthill's theory of aerodynamic noise. The turbulent eddies are replaced by a volume distribution of quadrupoles, and the reciprocal theorem used to transform the quadrupole scattering problem into one of the diffraction of a plane acoustic wave. This problem is solved by the Wiener–Hopf technique for the case when elastic forces in the plate are negligible, so that a local impedance condition relates the plate velocity to the pressure difference across the plate. Strong scattering of the near-field into propagating sound occurs when certain types of quadrupole lie sufficiently close to the plate edge, and we derive explicit expressions for the scattered fields in various cases. When fluid loading effects are small, and the plate relatively rigid, the results of Ffowcs Williams & Hall (1970) are recovered, in particular the U⁵ law for radiated intensity. A quite different behaviour is found in the case of high fluid loading, when the plate appears to be relatively limp. The radiated intensity then increases with flow velocity U according to a U⁶ law. In aeronautical situations, surface compliance is negligible in its effect on the scattering process, and the U⁵ law must then apply provided the surface is sufficiently large. On the other hand, the effect of appreciable surface compliance is to greatly inhibit the near-field scattering from the surface edge. This weaker scattering is likely to be observed in underwater applications, where fluid loading effects are generally so high as to render unattainable the condition for a plate to be effectively rigid.