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The wave bivector formalism associated with circumferential leaky waves
1Groupe de Physique de Solides-CNRS UMR 7588, Universite Paris 7-Denis Diderot, France.
The Journal of the Acoustical Society of America
|August 3, 2000
Summary
Circumferential internal waves around elastic cylinders behave locally as plane evanescent waves. Analysis reveals curved phase paths and polarization ellipses, simplifying wave interpretation under low evanescence.
Area of Science:
- Acoustics
- Fluid Dynamics
- Solid Mechanics
Background:
- Internal waves in fluids are complex phenomena.
- Understanding wave propagation around elastic structures is crucial for various applications.
Purpose of the Study:
- To analyze circumferential internal waves around an elastic cylinder.
- To characterize wave behavior locally and globally.
- To establish a connection between wave phenomena and ray theory.
Main Methods:
- Direct calculation of the complex bivector.
- Detailed analysis of wave anatomy and phase paths.
- Investigation of polarization ellipses for acoustic displacement.
Main Results:
- Circumferential waves can be locally approximated as plane evanescent waves.
- Phase propagation paths are curved.
- Polarization ellipses of the acoustic displacement vector are described.
- Low evanescence assumption yields conventional ray interpretation.
Conclusions:
- The study provides a detailed understanding of internal wave propagation around elastic cylinders.
- Local plane evanescent wave approximation simplifies analysis.
- Wavefront geometry is identified as the involute of a circle.
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