Aerodynamic sound generation by turbulent flow in the vicinity of a scattering half plane

Abstract

The presence of the edge of a half plane in a turbulent fluid results in a large increase in the noise generated by that fluid at low Mach numbers. The parameter which is important is the product $2k\overline{r}_0$ , where $\overline{r}_0$ is the distance of the centre of an eddy from the edge. Eddies which satisfy the inequality $2k\overline{r}_0\ll 1$ have the sound output of the quadrupoles associated with the fluid motion in a plane normal to the edge increased by the factor $(k\overline{r}_0)^{-3}$ . There is no enhancement of the sound from the longitudinal quadrupoles with axes parallel to the edge: the rr , θ r and θθ quadrupoles are the dominant sound sources. The far field sound intensity induced by these sources depends upon the fifth power of a typical fluid velocity. The intensity has a directional dependence on cos 2 ½θ if the half plane is rigid and sin 2 ½θ if it is a pressure release surface, θ = 0 being a direction in the half plane. If the eddies are far from the edge so that $(k\overline{r}_0)^{\frac{1}{2}} \gg 1$ then the farfield sound has the same features as would be predicted by geometrical acoustics. The edge does not produce any significant sound amplification.