Statistical analysis of a characteristic shock formation distance for high-amplitude noise

Abstract

Previous research involved investigating a characteristic shock formation distance for Gaussian, finite-amplitude noise propagating in a cylindrical plane wave tube [Muhlestein and Gee, POMA 12, (in press)]. In particular, the evolution of the probability density function of the pressure and the first-order time derivative of pressure along with the skewness of the pressure derivative were experimentally studied. It was concluded that a constant-factor modification to the nonlinear distortion length defined by Gurbatov and Rudenko may yield a suitable characteristic shock formation distance in a statistical sense. Additional Gaussian noise data with a broader frequency range have now been taken, and the effects of boundary layer dispersion considered. Furthermore, noise with other statistical distributions and pressure statistics mimicking high velocity jet noise have been examined. These data are analyzed statistically as before using probability density function estimates and the skewness of the pressur...