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The nonlinear acoustic propagation in shallow-sea waveguides is a fundamental issue for the propagation of sound waves in complex marine environments. It holds significant importance for applications such as underwater nonlinear sound field regulation and target detection. In this study, a theoretical model and a numerical method are established to investigate nonlinear sound propagation in waveguides. The physical characteristics of the reflection of difference-frequency beams at the waveguide boundaries during nonlinear interaction processes are examined. Based on the quasi-linear theory of the nonlinear wave equation, a theoretical model capable of accurately computing wide-angle sound field information at large grazing angles is developed by introducing a high-precision non-paraxial approximation approach and employing the image source method to analyze the nonlinear sound field in the waveguide. The effects of frequency (200–500 Hz), source depth (20 m and 80 m), and grazing angle (±60°) on nonlinear sound propagation are studied, and the underlying mechanisms are analyzed. Results indicate that an increase in frequency enhances the orientation performance of the nonlinear beam, thereby enhancing its resistance to interference in the waveguide. When the sound source is near a waveguide boundary, the nonlinear beam develops side lobes in the area close to this boundary. The beam energy that was originally concentrated near the sound axis and varies uniformly shows obvious discontinuity, and the sound pressure distribution along the sound axis shows fluctuations. The grazing angle of the source directly affects the sequence of boundary reflections, which in turn alters the sound energy distribution and leads to enhanced or weakened interference effects. Waveguide boundaries influence the spatial amplitude and phase distribution of the nonlinear virtual source, modifying the spatial accumulation process and significantly affecting the final sound field distribution. The model developed in this work accounts for the diffraction characteristics of beams emitted by real sources and ensures accuracy in wide-angle sound field modeling. It helps reveal the propagation laws of difference-frequency beams under waveguide boundary reflection during the nonlinear interaction process at large grazing angles, and provides theoretical support for fine regulation technologies of directional beams such as active noise control and low-frequency active detection in underwater waveguide environments.
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Keywords:
- shallow-sea waveguide /
- nonlinear acoustic propagation /
- difference-frequency beam /
- nonlinear acoustics
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