On the aerodynamic surface sound from a plane turbulent boundary layer

Abstract When a fluid in irregular or turbulent motion moves across the surface of a rigid body, dipole sound radiation can be produced by the fluctuating stress distribution set up at the boundary. This radiation, generated by the interaction of fluid in motion with rigid surfaces, can be called aerodynamic surface sound. It is the purpose of this paper to investigate some of the properties of the generation of sound in this manner from a turbulent boundary layer. An integral theorem is derived which relates the motion of a fluid about a body of arbitrary shape to the stress distribution over the surface. This can be applied to obtain properties of the surface radiation field in given flows. When turbulent fluid moves across an infinite flat plate, and the motion is statistically homogeneous in planes parallel to the plate, the dipole sound radiated per unit area is shown to vanish. This is a consequence of the vanishing of the mean-square momentum per unit area of the shear layer, defined as the momentum of the fluid in a large area of the layer, squared, averaged and then divided by that large area. However, when the motion is not homogeneous in planes parallel to the plate, a non-zero acoustic radiation field may be set up. Therefore it is suggested that a semi-infinite flat plate placed in a uniform stream should produce a finite dipole radiation per unit area which becomes vanishingly small with increasing distance down the plate.