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浅海波导中的非线性声传播问题是声波在复杂海洋环境中传播的基本问题，在水下非线性声场控制与目标探测等领域具有重要意义。针对波导中的非线性声传播问题建立了理论分析模型与数值计算方法，研究了非线性互作用过程中差频波束在波导界面发生反射的物理特性。首先，基于非线性波动方程的准线性理论，通过引入高精度的非近轴近似方法，利用镜像源方法对波导中的非线性声场进行分析，提出了可以精确计算大掠射角情况下非线性声场广角信息的理论模型。研究了波导中多种因素对非线性声传播特性的影响。研究结果表明：频率的提升会增强非线性波束的定向性能，从而进一步提升其在波导中的抗干涉能力；当声源靠近波导界面时，非线性波束在靠近该边界的一侧区域内出现旁瓣，原本集中于声轴附近且均匀变化的波束能量出现明显的间断现象；声源掠射角会直接影响波束发生界面反射的先后次序，并对声场的能量分布产生影响；波导界面通过影响非线性虚源的空间幅值和相位分布来决定最终的声场结构。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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