Bicoherence analysis of model-scale jet noise

Abstract

Bicoherence analysis has been used to characterize nonlinear effects in the propagation of noise from a model-scale, Mach-2.0, unheated jet. Nonlinear propagation effects are predominantly limited to regions near the peak directivity angle for this jet source and propagation range. The analysis also examines the practice of identifying nonlinear propagation by comparing spectra measured at two different distances and assuming far-field, linear propagation between them. This spectral comparison method can lead to erroneous conclusions regarding the role of nonlinearity when the observations are made in the geometric near field of an extended, directional radiator, such as a jet.

Asymptotic behavior of a frequency-domain nonlinearity indicator for solutions to the generalized Burgers equation

“…The calculated quadspectrum of the pressure and squared pressure reveals phase coupling between two different frequencies, which occurs from sum and difference-frequency nonlinear harmonic generation in steepening waves. 6,18 The indicator is derived from the time-domain version of the GBE for an arbitrarily diverging pressure waveform, p(t), in thermoviscous media, which may be written as…”

“…Examples of nonlinearity indicators include the pressure waveform derivative skewness, 1,2 average and wave steepening factors, [3][4][5] bicoherence, 6 and the Morfey and Howell-derived Q/S.…”

Near-field shock formation in noise propagation from a high-power jet aircraft

“…Higher-order spectral analysis techniques, including the bispectrum 11 and quadspectrum-based indicators, 3,[12][13][14] have proven useful in nonlinearity analysis. However, because wave steepening and shock formation result in large changes in the waveform's time derivative, derivative-based measures for analysis of nonlinear propagation seem convenient.…”

Skewness and shock formation in laboratory-scale supersonic jet data

“…[8][9][10][11] However, authors have disagreed on the attribution of observed phenomena to nonlinearity. Recent work by Gee et al 12,13 has examined unheated, Mach-2.0 data in the geometric near field using higher-order spectral analysis methods. Both bispectral analysis 12 and a quadspectrum indicator, 13 based on work by Morfey and Howell, 2 showed distinct evidence of quadratic phase coupling and nonlinear propagation.…”

“…Recent work by Gee et al 12,13 has examined unheated, Mach-2.0 data in the geometric near field using higher-order spectral analysis methods. Both bispectral analysis 12 and a quadspectrum indicator, 13 based on work by Morfey and Howell, 2 showed distinct evidence of quadratic phase coupling and nonlinear propagation. This Letter examines the same data set using a different analysis method-the skewness of the pressure waveform and of its time derivative-to compare with the analysis in Ref.…”