Evolution of the derivative skewness for high-amplitude sound propagation

Abstract

The skewness of the first time derivative of a pressure waveform has been used as an indicator of shocks and nonlinearity in both rocket and jet noise data [e.g., Gee et al., J. Acoust. Soc. Am. 133, EL88–EL93 (2013)]. The skewness is the third central moment of the probability density function and demonstrates asymmetry of the distribution, e.g., a positive skewness may indicate large, infrequently occurring values in the data. In the case of nonlinearly propagating noise, a positive derivative skewness signifies occasional instances of large positive slope and more instances of negative slope as shocks form [Shepherd et al., J. Acoust. Soc. Am. 130, EL8–EL13 (2011)]. In this paper, the evolution of the derivative skewness, and its interpretation, is considered analytically using key solutions of the Burgers equation. This paper complements a study by Muhlestein et al. [J. Acoust. Soc. Am. 134, 3981 (2013)] that used similar methods but with a different metric. An analysis is performed to investigate the effect of a finite sampling frequency and additive noise. Plane-wave tube experiments and numerical simulations are used to verify the analytic solutions and investigate derivative skewness in random noise waveforms. [Work supported by ONR.]