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一种能量守恒的双向耦合简正波水声传播模型

An energy-conserving two-way coupled mode model for underwater acoustic propagation

  • 摘要: 针对非水平边界条件近似处理所引起的双向声场能量不守恒问题,提出了一种满足能量守恒的双向耦合简正波模型。在模型的建立中,严格考虑了非水平界面的边界条件,并依据介质运动方程和连续性方程推导了便于数值计算的耦合微分方程。同时,结合能量守恒方程和不同海底参数下的数值计算,对模型的准确性进行了研究。由理论分析和仿真结果可以看出,边界条件的严格考虑将导致边界修正项的产生,而边界修正项的引入确保了耦合系数满足对称性和模型所计算的声场满足能量守恒,使得本模型可充分考虑边界水平变化对声场的影响,实现非水平分层波导中双向场的准确计算。

     

    Abstract: In order to avoid the energy non-conservation in two-way sound field calculation, which results from cer- tain approximations of non-horizontal boundaries, an energy-conserving two-way coupled mode propagation model is developed. During the deriving of this model, the non-horizontal boundary condition is considered strictly instead of approximately. The coupling equations, which are easy to numerical implementation, are derived from the equation of motion and the equation of continuity. Moreover, the veracity of this model is proved by several numerical examples of different bottom parameters and the equation of energy conservation. It is shown that a boundary correcting term is involved in this model due to the strict formulizing of the boundary condition. And this boundary correcting term guarantees the coupling coefficients be symmetrical and makes the sound field satisfy the law of conservation of energy. Thus, the energy-conserving coupled model is able to handle non-horizontal boundaries adequately, and the two-way sound field in a non-horizontal stratified media can be calculated exactly by this model.

     

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