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

doi:10.1088/1674-1056/ada886

中国物理B ›› 2025, Vol. 34 ›› Issue (3): 34301-034301.doi: 10.1088/1674-1056/ada886

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

Jian-Kang Zhan(詹建康)^1,2,3, Sheng-Chun Piao(朴胜春)^1,2,3,†, Li-Jia Gong(龚李佳)^1,2,3, Yang Dong(董阳)^1,2,3, Yong-Chao Guo(郭永超)³, and Guang-Xue Zheng(郑广学)³

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

收稿日期:2024-11-11 修回日期:2025-01-06 接受日期:2025-01-10 发布日期:2025-03-15
通讯作者: Sheng-Chun Piao E-mail:piaoshengchun@hrbeu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12174048 and 12204128).

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

Jian-Kang Zhan(詹建康)^1,2,3, Sheng-Chun Piao(朴胜春)^1,2,3,†, Li-Jia Gong(龚李佳)^1,2,3, Yang Dong(董阳)^1,2,3, Yong-Chao Guo(郭永超)³, and Guang-Xue Zheng(郑广学)³

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

Received:2024-11-11 Revised:2025-01-06 Accepted:2025-01-10 Published:2025-03-15
Contact: Sheng-Chun Piao E-mail:piaoshengchun@hrbeu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12174048 and 12204128).

摘要/Abstract

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

Abstract: 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.

Key words: WKB method, normal modes, very-low-frequency sound propagation, parabolic cylinder function

中图分类号: (Underwater sound)

43.30.+m

43.30.-k (Underwater sound)

Jian-Kang Zhan(詹建康), Sheng-Chun Piao(朴胜春), Li-Jia Gong(龚李佳), Yang Dong(董阳), Yong-Chao Guo(郭永超), and Guang-Xue Zheng(郑广学). A WKB method based on parabolic cylinder function for very-low-frequency sound propagation in deep ocean[J]. 中国物理B, 2025, 34(3): 34301-034301.

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

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

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