Evolution of the average steepening factor for nonlinearly propagating waves

Area of Science:

• Acoustics
• Fluid Dynamics
• Signal Processing

Background:

• Nonlinearity complicates near-field jet noise measurements.
• Quantifying waveform distortion is crucial for understanding high-velocity jet acoustics.

Purpose of the Study:

• Introduce and validate the average steepening factor (ASF) as a measure of waveform nonlinearity.
• Assess the ASF's sensitivity to measurement parameters and signal types.

Main Methods:

• Analytical derivation of ASF evolution for sinusoidal waves.
• Numerical and experimental analysis of ASF for broadband Gaussian noise.
• Investigation of effects from finite sampling rates and measurement noise.

Main Results:

• ASF quantifies nonlinearity in waveform propagation.
• ASF is sensitive to measurement noise but robust to limited sampling rates.
• Gaussian noise signals exhibit slower waveform distortion than sinusoidal signals.

Conclusions:

• The ASF provides a valuable tool for analyzing nonlinear effects in acoustic measurements.
• Understanding ASF evolution aids in interpreting complex jet noise phenomena.
• The measure's robustness allows for practical application in experimental acoustics.