On the generation of sound by turbulent boundary layer flow over a rough wall

Abstract

The production of sound by scattering of the near field of low Mach number boundary-layer turbulence by a rough, rigid wall is examined on the basis of Lighthill’s theory ( Proc. R. Soc. Lond . A 211, 564 (1952)) of aerodynamic noise. The radiation is expressed in terms of the turbulence pressure spectrum on a control surface that is parallel to the mean plane of the wall and at a stand-off distance equal to the height of the wall roughness elements, the surface irregularities being modelled by a distribution of hemispherical bosses on an otherwise plane wall. The intensity of the sound produced by unit area of the wall varies as the sixth power of the main stream velocity and, for given wall roughness, increases as the boundary-layer thickness decreases. These conclusions are in accord with experimental observations reported by Hersh { AIAA paper no. 83-0786) of the generation of high frequency sound by turbulent flow from sand-roughened pipes, and it is shown how, for moderately rough pipes, the theory reproduces the spectral characteristics of Hersh’s data.