A characteristic nonlinear distortion length for broadband Gaussian noise

Area of Science:

• Acoustics
• Fluid Dynamics
• Psychoacoustics

Background:

• Nonlinear evolution of high-amplitude broadband noise significantly impacts high-speed jet noise perception, often causing annoyance.
• Characterizing nonlinear evolution typically involves a waveform distortion length scale, commonly the shock formation distance for sinusoidal signals.
• Applying sinusoidal-based scales to broadband noise can underestimate overall nonlinear distortion, as indicated by derivative skewness.

Purpose of the Study:

• To introduce an alternative, more appropriate length scale for analyzing the nonlinear evolution of broadband noise.
• To derive this new length scale directly from the evolution of derivative skewness in Gaussian noise.
• To establish a useful metric for broadband noise analysis with improved consistency and physical interpretation.

Main Methods:

• Derived a novel Gaussian-based length scale from the statistical evolution of derivative skewness for broadband noise.
• Utilized analytical predictions for the evolution of derivative skewness.
• Employed an ensemble of numerical simulations to model noise propagation and validate the new length scale.

Main Results:

• The proposed Gaussian-based length scale provides a more accurate assessment of nonlinear waveform distortion in broadband noise compared to traditional methods.
• This new metric demonstrates relative consistency and possesses a clear physical interpretation.
• The length scale effectively captures the nonlinear evolution dynamics of broadband acoustic signals.

Conclusions:

• The Gaussian-based length scale is a more suitable metric for quantifying nonlinear distortion in broadband jet noise.
• This metric aids in better understanding the psychoacoustic perception, including annoyance, associated with high-speed jet noise.
• The derived length scale offers a valuable tool for future research in aeroacoustics and noise mitigation.