Evolution of higher-order spectra of nonlinear random waves

Гурбатов, С. Н.; Malakhov, A. N.; Pronchatov-Rubtsov, N. V.

doi:10.1007/bf01035089

Cited by 6 publications

(2 citation statements)

References 7 publications

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“…3,4,13 Furthermore, a great deal of literature discusses the limiting and asymptotic cases of the spectra (and associated correlation functions) of propagating noise, both narrow and broadband. 6,[14][15][16] While other potentially useful measures of the importance of nonlinearity have been defined, not all of these measures have been thoroughly documented. The purpose of this paper is to document analytically, numerically, and experimentally obtained values of a statistically based metric, called the average steepening factor (ASF), for waveforms propagating with prominent nonlinear effects.…”

Section: Introductionmentioning

confidence: 99%

Evolution of the average steepening factor for nonlinearly propagating waves

Muhlestein

Gee

Neilsen

et al. 2015

The Journal of the Acoustical Society of America

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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.

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Section: Introductionmentioning

confidence: 99%

Evolution of the average steepening factor for nonlinearly propagating waves

Muhlestein

Gee

Neilsen

et al. 2015

The Journal of the Acoustical Society of America

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“…These measures have been developed in the time domain, using both the pressure waveform [9][10][11] and its first time derivative, [12][13][14][15] and in the frequency domain using higher order spectral analysis. 2,16,17 Although these various measures have been used as qualitative indicators of nonlinearity, a quantitative understanding of the values obtained has been lacking. This paper provides quantitative insight into the meaning of skewness values of the first time derivative of the pressure waveform, using analytical, experimental, and numerical methods.…”

Section: Introductionmentioning

confidence: 99%

Evolution of the derivative skewness for nonlinearly propagating waves

Reichman

Muhlestein

Gee

et al. 2016

The Journal of the Acoustical Society of America

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The skewness of the first time derivative of a pressure waveform, or derivative skewness, has been used previously to describe the presence of shock-like content in jet and rocket noise. Despite its use, a quantitative understanding of derivative skewness values has been lacking. In this paper, the derivative skewness for nonlinearly propagating waves is investigated using analytical, numerical, and experimental methods. Analytical expressions for the derivative skewness of an initially sinusoidal plane wave are developed and, along with numerical data, are used to describe its behavior in the preshock, sawtooth, and old-age regions. Analyses of common measurement issues show that the derivative skewness is relatively sensitive to the effects of a smaller sampling rate, but less sensitive to the presence of additive noise. In addition, the derivative skewness of nonlinearly propagating noise is found to reach greater values over a shorter length scale relative to sinusoidal signals. A minimum sampling rate is recommended for sinusoidal signals to accurately estimate derivative skewness values up to five, which serves as an approximate threshold indicating significant shock formation.

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On the Inverse Problems of Nonlinear Acoustics and Acoustic Turbulence

Гурбатов

Руденко

2015

Radiophys Quantum El

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Evolution of higher-order spectra of nonlinear random waves

Cited by 6 publications

References 7 publications

Evolution of the average steepening factor for nonlinearly propagating waves

Evolution of the average steepening factor for nonlinearly propagating waves

Evolution of the derivative skewness for nonlinearly propagating waves

On the Inverse Problems of Nonlinear Acoustics and Acoustic Turbulence

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