The generation of sound by the convection of inhomogeneities through space‐varying flows, by analogy with the scattering of acoustic and evanescent waves

Abstract

It is pointed out that the scattering theory of Rayleigh for sound waves interacting with inhomogeneities of a stationary medium can also be applied to evanescent waves. By considering the fluid to be moving and the wave system stationary and caused by a fixed wavy wall, the problem of the sound generated by inhomogeneities of a fluid carried through a supersonic or subsonic space‐varying flow field past the wall can then be addressed. As in that scattering theory, the inhomogeneities must be small in extent compared to the scale of the pressure gradient of the basic flow and also of the resultant sound: This is the low‐frequency approximation (which excludes application of the theory to shockwaves). It is found that inhomogeneities in density and compressibility of the gas (i.e., of the gas constant) both result in sound power that varies as the sixth power of the speed in all the cases of supersonic and subsonic flow, and when the interaction takes place far from, or close to, the wall or body, except that, at supersonic speed, interactions close to the body result in the sound power due to density fluctuations varying with only the fourth power of the Mach number and that due to the gas constant (compressibility) at subsonic speeds varying as the eighth power. In all cases, the sound power depends acutely on the shortness of the length characterizing the pressure gradients in the flow; specifically, it varies inversely as the sixth power of the characteristic length. It is pointed out that, in most engineering applications, the effects of density inhomogeneities are likely to overwhelm those due to variations in the compressibility of the gas, and interactions in the subsonic case must be close to the body to be significant, due to the very rapid decay of the pressure field away from the body.