Investigation of a single-point nonlinearity indicator in one-dimensional propagation

The influence of nonlinear effects in the propagation of jet noise 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 Q _p2p, which is the imaginary part of the crossspectral density of the square of the pressure and the pressure. With the proper normalization, geometrical spreading and attenuation effects can be removed, and the normalized quantity represents only spectral changes due to nonlinearity. Despite its potential applicability to jet noise analysis, the physical significance and utility of Q _p2p have not been thoroughly studied. This work examines a normalization of Q _p2p and its dependence on distance for the propagation of plane waves in a shock tube. The use of a simple, controlled environment allows for a better understanding of the significance of Q _p2p. [Work supported by the National Science Foundation, the Office of Naval Research, and the Strategic Environmental Research and Development Program.].