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

Miller, Kyle; Gee, Kent L.; Reichman, Brent O.

doi:10.1121/1.4971880

Cited by 4 publications

(2 citation statements)

References 22 publications

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“…Furthermore, since higher pressures gives rise to greater phase speeds (Hamilton & Blackstock, ), we expect a positive correlation between maximum signal pressure and maximum

ν_{N_{t o t}}

and a negative correlation between maximum signal pressure and minimum

ν_{N_{t o t}}

. These relationships have been qualitatively observed in applications to computationally propagated waves (Reichman et al, ; Miller et al, ) and model‐scale jet noise (Miller & Gee, ), as shown in Figure c. This study is the first to extract quantitative metrics from

ν_{N}

.…”

Section: Methodssupporting

confidence: 59%

“…Various approaches have been used to investigate nonlinear propagation effects such as the statistics of the waveform (e.g., skewness) and its derivative (Anderson et al, ; Fee et al, ; Gee et al, , ), bicoherence (Gee et al, ; ; Kim & Powers, ), and quadspectral density (Gee et al, ; Miller et al, ; Miller & Gee, ; Morfey & Howell, ; Petitjean et al, ; Reichman et al, ). The quadspectral density refers here to the imaginary part of the cross spectrum of pressure and squared pressure (

Q_{p p^{2}}

).…”

Section: Introductionmentioning

confidence: 99%

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Investigating Spectral Distortion of Local Volcano Infrasound by Nonlinear Propagation at Sakurajima Volcano, Japan

et al. 2020

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Sound waves generated by erupting volcanoes can be used to infer important source dynamics, yet acoustic source‐time functions may be distorted during propagation, even at local recording distances ( <15 km). The resulting uncertainty in source estimates can be reduced by improving constraints on propagation effects. We aim to quantify potential distortions caused by wave steepening during nonlinear propagation, with the aim of improving the accuracy of volcano‐acoustic source predictions. We hypothesize that wave steepening causes spectral energy transfer away from the dominant source frequency. To test this, we apply a previously developed single‐point, frequency domain, quadspectral density‐based nonlinearity indicator to 30 acoustic signals from Vulcanian explosion events at Sakurajima Volcano, Japan, in an 8‐day data set collected by five infrasound stations in 2013 with 2.3‐ to 6.2‐km range. We model these results with a 2‐D axisymmetric finite‐difference method that includes rigid topography, wind, and nonlinear propagation. Simulation results with flat ground indicate that wave steepening causes up to ∼2 dB (1% of source level) of cumulative upward spectral energy transfer for Sakurajima amplitudes. Correction for nonlinear propagation may therefore provide a valuable second‐order improvement in accuracy for source parameter estimates. However, simulations with wind and topography introduce variations in the indicator spectra on order of a few decibels. Nonrandom phase relationships generated during propagation or at the source may be misinterpreted as nonlinear spectral energy transfer. The nonlinearity indicator is therefore best suited to small source‐receiver distances (e.g., <2 km) and volcanoes with simple sources (e.g., gas‐rich strombolian explosions) and topography.

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“…Furthermore, since higher pressures gives rise to greater phase speeds (Hamilton & Blackstock, ), we expect a positive correlation between maximum signal pressure and maximum

ν_{N_{t o t}}

and a negative correlation between maximum signal pressure and minimum

ν_{N_{t o t}}

ν_{N}

.…”

Section: Methodssupporting

confidence: 59%

Q_{p p^{2}}

).…”

Section: Introductionmentioning

confidence: 99%

Investigating Spectral Distortion of Local Volcano Infrasound by Nonlinear Propagation at Sakurajima Volcano, Japan

et al. 2020

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Model-scale jet noise analysis with a single-point, frequency-domain nonlinearity indicator

Miller

Gee

2018

The Journal of the Acoustical Society of America

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A single-point, frequency-domain nonlinearity indicator is calculated and analyzed for noise from a model-scale jet at Mach 0.85, Mach 1.8, and Mach 2.0. The nonlinearity indicator, ν, has been previously derived from an ensemble-averaged, frequency-domain version of the generalized Burgers equation (GBE) from Reichman, Gee, Neilsen, and Miller [J. Acoust. Soc. Am. 139, 2505-2513 (2016)]. The indicator gives the spatial rate of change due to nonlinear processes in sound pressure level (SPL) spectrum, and two other indicators from the GBE-ν and ν-give the same quantity due to geometric spreading and absorption, respectively. Trends with frequency, angle, distance, and jet condition-supported both by spectral analysis and by calculation of the GBE-derived indicators-reveal a concentration of nonlinear effects along radials close to the plume with large overall SPLs. The calculated indicators for nonlinearity and absorption effects far from the source combine to give the same decay predicted by nonlinear theory for monofrequency sources. Trends in the ν indicator are compared with trends observed for other indicators such as pressure-derivative skewness and bicoherence, revealing both the qualitative and quantitative advantages of the ν indicator.

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Single-point characterization of spectral amplitude and phase changes due to nonlinear propagation

Reichman

Gee

Ohm³

2018

Proceedings of Meetings on Acoustics

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

Cited by 4 publications

References 22 publications

Investigating Spectral Distortion of Local Volcano Infrasound by Nonlinear Propagation at Sakurajima Volcano, Japan

Investigating Spectral Distortion of Local Volcano Infrasound by Nonlinear Propagation at Sakurajima Volcano, Japan

Model-scale jet noise analysis with a single-point, frequency-domain nonlinearity indicator

Single-point characterization of spectral amplitude and phase changes due to nonlinear propagation

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