Aerodynamic Noise and the Plane Boundary

Abstract

In an earlier paper entitled “Thoughts on Boundary Layer Noise” (Aeronautical Research Council Report 16727, 1954), it was pointed out that while the fluctuating pressures exerted upon a rigid boundary by a contiguous unsteady flow can be shown in a formal manner to generate sound as of a distribution of dipoles, it can be argued by means of the reflection principle that all such dipole effects cancel out in the case of the boundary being plane; yet observations of aeolian tones adequately confirm the presence of effective dipole-like generators in that case. Here the image principle is developed in a rigorous manner and the apparent paradox is resolved with the help of an extension of Lighthill's and Curle's analyses to include boundaries which are not wholly immersed in the noise-generating flow. In particular, it is shown that the pressures exerted on a plane boundary are simply reflections of the quadrupole generators of the flow itself; thus the pressure dipoles account for an enhancement of the quadrupole power, in fact a quadrupling when the wavelength is relatively large, except that degeneration into octupoles occurs for those lateral quadrupoles of the type that would be associated with fluctuations across the shear of an adjacent boundary layer. Under these circumstances it should be possible to estimate the noise of a plane turbulent boundary layer with satisfactory accuracy from sufficient knowledge of the principal quadrupole source strength alone (provided that it is reasonable to neglect the contribution of the fluctuating shear stresses acting on the boundary).