| ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS |
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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, Dong Yang(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 |
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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.
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Received: 11 November 2024
Revised: 06 January 2025
Accepted manuscript online: 10 January 2025
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PACS:
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43.30.+m
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(Underwater sound)
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43.30.-k
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(Underwater sound)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12174048 and 12204128). |
Corresponding Authors:
Sheng-Chun Piao
E-mail: piaoshengchun@hrbeu.edu.cn
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Cite this article:
Jian-Kang Zhan(詹建康), Sheng-Chun Piao(朴胜春), Li-Jia Gong(龚李佳), Dong Yang(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 2025 Chin. Phys. B 34 034301
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