Scattering and diffraction of sound by moving bodies

Abstract

A scattering configuration consists of a primary acoustic source S and a scattering body B, and we examine the effect of convection of S and B, at a uniform subsonic Mach number M, on the scattered field, for various types of source and scatterer. It is shown that if B is a compact rigid body scattering the near field of the source S it is not equivalent to a convected point dipole, but rather its pressure field is augmented by the quadrupole convection factor (1 − M cosθ)⁻³. If, on the other hand, the compact body B scatters the distant field of S, convective effects introduce an O(M) monopole field which does not vanish in the sideline directions. A number of problems are examined in which B is a rigid half-plane, and there it is shown that the effect of convection is to augment the pressure by $(1 - M \cos \theta)^{-\frac{3}{2}}$ in the case of diffraction of the field of a distant source S, and by $(1 - M \cos \theta)^{-\frac{5}{2}}$ for scattering of the near field of S. Effects associated with the multipole order of S are discussed, as are those arising from the satisfaction of a Kutta condition at the trailing edge of the half-plane, and the application of these results to current problems in aerodynamic sound is mentioned.