Non-linear propagation of broadband noise signals

Abstract

Measurements of aircraft flyover noise have strongly suggested that non-linear propagation effects can significantly modify the noise spectrum. The data show that over ranges of 500 to 1000 m the attenuation in the range 5 to 10 kHz may fall considerably short of that predicted on the basis of linear propagation, if the noise is sufficiently intense. Such distances are comparable to those used in aircraft noise certification measurements, and the frequencies involved have an important influence on the perceived noise level. Therefore a scheme is required for predicting the finite amplitude propagation of random signals over a wide range of source and atmospheric conditions. Taylor series solutions to a generalized Burgers' equation are generated for stationary noise signals. The expansions are in powers of the range variable, and any frequency dependence of attenuation and dispersion is allowed. The limitations of such an approach are discussed, and it is found that the number of terms needed increases rapidly with range. For propagation over a long range, when non-linear effects are important, it is recommended that one of the differential equations derived for the power spectrum be used, together with a closure hypothesis. Individual terms in the series may be treated separately as local spectrum evolution equations, valid at all points along the propagation path. With appropriate modelling of the non-linear terms, such an equation can form a basis for aircraft noise prediction schemes.