Published online by Cambridge University Press: 29 March 2006
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, θr 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 cos2 ½θ if the half plane is rigid and sin2 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.
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