均匀可穿透楔形波导中的三维声场解析解  

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

作　　者：杨春梅[1] 骆文于[2] 乔方利[1] 吕连港[1] 

机构地区：[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

出　　处：《南京大学学报（自然科学版）》2015年第6期1210-1216,共7页Journal of Nanjing University（Natural Science）

基　　金：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)

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.A benchmark analytical solution for three-dimensional sound propagation excited by a point source in a pen-etrable wedge-shaped ocean was presented in this paper.This analytical solution 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 thenbsp;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.

关 键 词：楔形波导 虚源法 声反射 声折射 全局矩阵方法 

分 类 号：O427.1[理学—声学]