Abstract
It has been shown that the quantity Qp2p, the cross-spectral density of the square of the pressure and the pressure, is related to the strength of nonlinear effects in a propagating acoustic signal. Morfey and Howell [AIAA J. 19, 986–992, (1981)] derive from the Burgers equation an expression that relates Qp2p to the rate of change of the power spectral density (PSD) of a signal. They suggest a propagation scheme based on this expression that makes assumptions about the Gaussian nature of the signal. These assumptions are invalid for many finite-amplitude signals, so a new propagation scheme is proposed and validated. This scheme uses an expression for the rate of change of the phase of the signal as well as its amplitude. These two expressions are combined into a finite-difference equation that is used to step the signal to the desired propagation distance. The method is shown to compare favorably with the Fubini solution for lossless plane waves. Comparisons are also made with a numerical split-step algorithm for the nonlinear propagation of a broadband source, and with experimental data obtained in a plane wave tube. [Work supported by ONR, GE.]
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