Nonlinear Acoustic Propagation of Broadband Noise

Broadband jet noise is invariably assumed to propagate according to linear acoustic laws, although there are clear indications from both a limited set of experimental data taken in unusual, though appropriate, circumstances, and from simple weakly nonlinear acoustic theory that nonlinear propagation effects may significantly distort the noise spectrum over ranges of importance in full-scale aircraft flyovers. This paper starts with a review of the experimental situation and discusses the implications for aircraft noise prediction and control that might follow recognition of the importance of nonlinear propagation effects. Three rational theoretical approaches to the problem are then examined. The first relies on a simple expansion in amplitude (or, equivalently, frequency or range), and despite its obvious limitations is useful in giving a quantitative indication of the frequency, range and OASPL at which nonlinear spectral distortion can be expected to be significant near the peak frequency (and, by implication, even more significant at the higher frequencies which are so important in the determination of Perceived Noise Levels). This method can also incorporate attenuation effects, along with those of spherical spreading, directional nonuniformity, and weak nonlinearity. From it are also derived scaling laws for the variation with jet speed of the nonlinearly induced contribution to the spectrum and its dependence on range.