title: Evolution of the average steepening factor for nonlinearly propagating waves.
abstract: Difficulties arise in attempting to discern the effects of nonlinearity in near-field jet-noise measurements due to the complicated source structure of high-velocity jets. This article describes a measure that may be used to help quantify the effects of nonlinearity on waveform propagation. This measure, called the average steepening factor (ASF), is the ratio of the average positive slope in a time waveform to the average negative slope. The ASF is the inverse of the wave steepening factor defined originally by Gallagher [AIAA Paper No. 82-0416 (1982)]. An analytical description of the ASF evolution is given for benchmark cases-initially sinusoidal plane waves propagating through lossless and thermoviscous media. The effects of finite sampling rates and measurement noise on ASF estimation from measured waveforms are discussed. The evolution of initially broadband Gaussian noise and signals propagating in media with realistic absorption are described using numerical and experimental methods. The ASF is found to be relatively sensitive to measurement noise but is a relatively robust measure for limited sampling rates. The ASF is found to increase more slowly for initially Gaussian noise signals than for initially sinusoidal signals of the same level, indicating the average distortion within noise waveforms occur more slowly.
authors.affiliation: Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602.
authors.forename: Michael B
authors.initials: MB
authors.lastname: Muhlestein
authors.affiliation: Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602.
authors.forename: Kent L
authors.initials: KL
authors.lastname: Gee
authors.affiliation: Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602.
authors.forename: Tracianne B
authors.initials: TB
authors.lastname: Neilsen
authors.affiliation: Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602.
authors.forename: Derek C
authors.initials: DC
authors.lastname: Thomas