A WKB method based on parabolic cylinder function for very-low-frequency sound propagation in deep ocean  

作　　者：Jian-Kang Zhan Sheng-Chun Piao Li-Jia Gong Yang Dong Yong-Chao Guo Guang-Xue Zheng 詹建康;朴胜春;龚李佳;董阳;郭永超;郑广学

机构地区：[1]National Key Laboratory of Underwater Acoustic Technology,Harbin Engineering University,Harbin 150001,China [2]Key Laboratory of Marine Information Acquisition and Security(Harbin Engineering University),Ministry of Industry and Information Technology,Harbin 150001,China [3]College of Underwater Acoustic Engineering,Harbin Engineering University,Harbin 150001,China

出　　处：《Chinese Physics B》2025年第3期433-446,共14页中国物理B(英文版)

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.12174048 and 12204128)。

摘　　要：A Wentzel-Kramers-Brillouin(WKB)method is introduced for obtaining a uniform asymptotic solution for underwater sound propagation at very low frequencies in deep ocean.The method utilizes a mode sum and employs the reference functions method to describe the solution to the depth-separated wave equation approximately using parabolic cylinder functions.The conditions for the validity of this approximation are also discussed.Furthermore,a formula that incorporates waveguide effects for the modal group velocity is derived,revealing that boundary effects at very low frequencies can have a significant impact on the propagation characteristics of even low-order normal modes.The present method not only offers improved accuracy compared to the classical WKB approximation and the uniform asymptotic approximation based on Airy functions,but also provides a wider range of depth applicability.Additionally,this method exhibits strong agreement with numerical methods and offers valuable physical insights.Finally,the method is applied to the study of very-low-frequency sound propagation in the South China Sea,leading to sound transmission loss predictions that closely align with experimental observations.

关 键 词：WKB method normal modes very-low-frequency sound propagation parabolic cylinder function 

分 类 号：O17[理学—数学]