南京大学学报(自然科学版) ›› 2015, Vol. 51 ›› Issue (6): 1210–1216.

• • 上一篇    下一篇

均匀可穿透楔形波导中的三维声场解析解

杨春梅1*,骆文于2,乔方利1,吕连港1   

  • 出版日期:2015-11-14 发布日期:2015-11-14
  • 作者简介:(1. 国家海洋局第一海洋研究所海洋环境与数值模拟重点实验室,青岛,266061; 2. 中国科学院声学研究所声场声信息国家重点实验室,北京,100190)
  • 基金资助:
    基金项目:中国博士后科学基金(2014M561882),国家自然科学基金(11125420,U1406404),山东省博士基金(BS2012HZ015)
    收稿日期:2015-07-05
    *通讯联系人,E-mail:ycm@fio.org.cn

Three-dimensional analytical solution for sound propagation in a homogeneous penetrable wedge

Yang Chunmei1*, Luo Wenyu2, Qiao Fangli1, Lyu Liangang1   

  • Online:2015-11-14 Published:2015-11-14
  • About author:(1. Key Laboratory of Marine Science and Numerical Modeling, The First Institute of Oceanography, State Oceanic Administration, Qingdao, 266061, China; 2. State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing, 100190, China)

摘要: 研究可穿透楔形波导中的三维声传播问题,旨在求得该问题的三维标准解析解,可用于检验三维数值模型的计算精度.应用虚源法获得楔形海域海水以及海底中的三维声场解析解:对于海水中的声场,计算时只需考虑声波的反射问题;而对于海底中的声场,计算时不仅需要考虑声波的反射问题,还需要考虑声波的折射问题.鉴于球面波在两种介质分界平面上反射和折射机理的复杂性,将单个虚源辐射的球面波分解为一系列平面波,进而应用平面波的反射和折射原理得到整个海域中的声场解析解.该解析解适用于整个海域,包括海水和海底.最后,通过一个楔形波导标准问题验证了该解析解的正确性.

Abstract: A benchmark analytical solution for three-dimensional sound propagation excited by a point source in a penetrable wedge-shaped ocean is presented in this paper. This analytical solution presented in this paper is based on the method of source images, and it applies to the acoustic fields in both water and the bottom. For the acoustic field in water, only acoustic reflection needs to be considered. However, for the acoustic field in the bottom, both acoustic reflection and acoustic refraction need to be considered. Due to the complexity of spherical wave reflection and refraction on the interface of two media, the spherical wave radiated from each source image is expressed in terms of plane waves. Therefore, the analytical solution in the whole sea area can be obtained by using the plane wave reflection and refraction principles. The new solution is accurate throughout both water and the bottom, including the normally difficult modal cutoff regions, where energy propagates through the wedge at grazing angles close to the critical grazing angle; and so the analytical solution could be as a benchmark to validate the accuracy of three-dimensional numerical models. Consequently this analytical solution is also validated through a benchmark penetrable wedge problem.

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