Explosive Acoustics

The influence of nonlinear effects in jet noise propagation is typically characterized by examining changes in the power spectral density (PSD) of the noise as a function of propagation distance. The rate of change of the PSD is an indicator of the importance of nonlinearity. Morfey and Howell [AIAA J. 19, 986–992 (1981)] introduced an analysis technique that has the potential to extract this information from a measurement at a single location. They develop an ensemble‐averaged Burgers equation that relates the rate of change of the PSD with distance to the quantity Qp2p , which is the imaginary part of the cross‐spectral density of the pressure and the square of the pressure. With the proper normalization, spreading and attenuation effects can be removed, and the normalized quantity represents only spectral changes which are due to nonlinearity. Despite its potential applicability to jet noise analysis, the physical significance and utility of Qp2p have not been thoroughly studied. This work examines a normalization of Qp2p and its dependence on distance for the propagation of plane waves in a shock tube. The use of such a controlled environment allows for better understanding of the significance of Qp2p .

One issue of interest pertaining to the development of a numerical model applicable to the nonlinear propagation of jet noise is the behavior of spectral predictions at large distances. In this study, a recorded noise waveform from a military jet aircraft is numerically propagated via a hybrid time‐frequency domain solution to the generalized Burgers equation that incorporates spherical spreading and atmospheric absorption and dispersion. Numerical results show that the spatial rate of change of the difference between the nonlinearly‐ and linearly‐predicted power spectra appears to approach constant nonzero behavior at high frequencies. This asymptotic relationship is analogous to that predicted by analytical theory for initially‐sinusoidal plane and spherical waves.