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Rigorous justification of a localized approximation to encode on-axis Gaussian acoustical waves.

Gérard Gouesbet¹, Leonardo André Ambrosio²

¹CORIA-UMR 6614 - Normandie Université. CNRS-Université et INSA de Rouen, Campus Universitaire du Madrillet. 76800, Saint-Etienne du Rouvray, France.

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|August 22, 2023

Summary

A new acoustical framework, analogous to Generalized Lorenz-Mie theory, enables acoustic scattering analysis. The localized approximation method efficiently calculates acoustical beam shape coefficients for Gaussian beams.

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Area of Science:

Acoustics
Wave Scattering
Electromagnetics

Background:

Generalized Lorenz-Mie theory (GLMT) models electromagnetic wave interactions with particles.
Acoustic wave scattering requires analogous theoretical frameworks.

Purpose of the Study:

To develop and justify an acoustical framework similar to GLMT.
To evaluate acoustical beam shape coefficients (BSCs) using the localized approximation.

Main Methods:

Developed a GLMT-like framework for acoustical wave scattering.
Applied a variant of the localized approximation to evaluate acoustical BSCs.
Rigorous justification for on-axis Gaussian beams.

Main Results:

Acoustical BSCs were derived and justified.
Demonstrated field reconstruction and remodeling using the localized approximation.
Confirmed method robustness for small confinement parameters.

Conclusions:

The localized approximation is a robust method for acoustic scattering.
Encourages wider adoption of localized approximation schemes in acoustics.
Provides a foundation for advanced acoustic wave analysis.