黎曼流形下的水声测地线程函方程  

Underwater acoustic geodesic Eikonal equation on Riemannian manifold

作　　者：郭肖晋 马树青[1] 张理论[1] 蓝强 黄创霞 GUO Xiaojin;MA Shuqing;ZHANG Lilun;LAN Qiang;HUANG Chuangxia(College of Meteorology and Oceanography,National University of Defense Technology,Changsha 410073,Hunan,China;School of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410114,Hunan,China)

机构地区：[1]国防科技大学气象海洋学院,湖南长沙410073 [2]长沙理工大学数学与统计学院,湖南长沙410114

出　　处：《声学技术》2024年第3期318-322,共5页Technical Acoustics

基　　金：国防基础科研计划项目(JCKY2020550C011);水声对抗技术国防科技重点实验室基金(6412214200403)。

摘　　要：介质的天然非均匀性和时变等因素决定了水声传播信道是弯曲的黎曼流形。文章基于黎曼几何理论给出了水声射线程函方程在黎曼流形上的广义形式,该形式对于欧氏空间仍然适用。通过比较介质均匀的平面与弯曲球面两种理想场景,揭示了欧氏空间与弯曲流形上声传播存在差异。基于测地线程函方程和Bellhop-3D模式的Munk声速剖面射线仿真结果基本一致,验证了文中理论的正确性。文中结果为进一步开展弯曲水声信道的建模与计算奠定了概念基础。The inhomogeneity of medium,time-varying and other factors determine that the underwater acoustic propagation channel is a curved Riemannian manifold.Based on Riemannian geometry theory,a generalized form of underwater acoustic Eikonal equation on Riemannian manifold is given in this paper,which is still applicable to Euclidean space.By comparing two ideal scenes of a plane and a curved sphere with homogeneous medium,the difference of underwater acoustic ray propagation between curved Riemannian manifold and flat Euclid space is revealed.The ray simulation results for Munk sound speed profile based on geodesic eikonal equation and Bellhop-3D model are basically consistent,which verifies the correctness of the theory presented in this paper.The results of this paper lay a conceptual foundation for further modeling and calculation on the curved underwater acoustic channels.

关 键 词：黎曼度规 测地线 程函方程 

分 类 号：O427[理学—声学]