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Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

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Statistical wave field theory: Anisotropic wave fields under Robin's boundary condition.

Roland Badeau¹

¹Laboratoire Traitement et Communication de l'Information, Télécom Paris, Institut Polytechnique de Paris, Palaiseau 91120, France.

The Journal of the Acoustical Society of America

|June 17, 2026

Summary

This study unifies statistical wave field theory for semi-mixing billiards. It reveals directional reverberation time, improving upon Eyring

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Area of Science:

Physics
Acoustics
Mathematical Physics

Background:

Statistical wave field theory describes wave equations in bounded domains.
Previous work focused on diffuse wave fields (mixing rooms) and anisotropic fields (special polyhedra).
Existing theories rely on dynamical billiards, Weyl-like laws, and crystallographic approaches.

Purpose of the Study:

To develop a unified statistical wave field theory for semi-mixing billiards.
To analyze wave field characteristics under Robin's boundary conditions.
To derive a generalized formula for directional reverberation time.

Main Methods:

Extension of statistical wave field theory to semi-mixing billiards.
Application of Robin's boundary conditions.
Derivation of closed-form expressions for wave field properties.

Main Results:

Characterization of wave fields by directional reverberation time.
Reverberation time is independent of receiver position but dependent on orientation.
A closed-form expression for directional reverberation time is provided.

Conclusions:

The unified theory provides a comprehensive framework for semi-mixing billiards.
The derived directional reverberation time generalizes Eyring's formula.
This work advances the understanding of wave propagation in complex acoustic environments.