Wave mode computing method using the step-split Padé parabolic equation

doi:10.1088/1674-1056/ac6940

中国物理B ›› 2022, Vol. 31 ›› Issue (9): 94301-094301.doi: 10.1088/1674-1056/ac6940

Wave mode computing method using the step-split Padé parabolic equation

Chuan-Xiu Xu(徐传秀)^1,† and Guang-Ying Zheng(郑广赢)^1,2

1 Hangzhou Applied Acoustics Research Institute, Hangzhou 310023, China;
2 Science and Technology on Sonar Laboratory, Hangzhou 310023, China

收稿日期:2022-01-29 修回日期:2022-03-22 接受日期:2022-04-22 出版日期:2022-08-19 发布日期:2022-09-03
通讯作者: Chuan-Xiu Xu E-mail:xuchuanxiu715@163.com
基金资助:
Project supported by Young Elite Scientist Sponsorship Program by CAST (Grant No. YESS20200330).

Wave mode computing method using the step-split Padé parabolic equation

Chuan-Xiu Xu(徐传秀)^1,† and Guang-Ying Zheng(郑广赢)^1,2

1 Hangzhou Applied Acoustics Research Institute, Hangzhou 310023, China;
2 Science and Technology on Sonar Laboratory, Hangzhou 310023, China

Received:2022-01-29 Revised:2022-03-22 Accepted:2022-04-22 Online:2022-08-19 Published:2022-09-03
Contact: Chuan-Xiu Xu E-mail:xuchuanxiu715@163.com
Supported by:
Project supported by Young Elite Scientist Sponsorship Program by CAST (Grant No. YESS20200330).

摘要/Abstract

摘要： Models based on a parabolic equation (PE) can accurately predict sound propagation problems in range-dependent ocean waveguides. Consequently, this method has developed rapidly in recent years. Compared with normal mode theory, PE focuses on numerical calculation, which is difficult to use in the mode domain analysis of sound propagation, such as the calculation of mode phase velocity and group velocity. To broaden the capability of PE models in analyzing the underwater sound field, a wave mode calculation method based on PE is proposed in this study. Step-split Padé PE recursive matrix equations are combined to obtain a propagation matrix. Then, the eigenvalue decomposition technique is applied to the matrix to extract sound mode eigenvalues and eigenfunctions. Numerical experiments on some typical waveguides are performed to test the accuracy and flexibility of the new method. Discussions on different orders of Padé approximant demonstrate angle limitations in PE and the missing root problem is also discussed to prove the advantage of the new method. The PE mode method can be expanded in the future to solve smooth wave modes in ocean waveguides, including fluctuating boundaries and sound speed profiles.

关键词: parabolic equation, propagation matrix, eigenvalue decomposition

Abstract: Models based on a parabolic equation (PE) can accurately predict sound propagation problems in range-dependent ocean waveguides. Consequently, this method has developed rapidly in recent years. Compared with normal mode theory, PE focuses on numerical calculation, which is difficult to use in the mode domain analysis of sound propagation, such as the calculation of mode phase velocity and group velocity. To broaden the capability of PE models in analyzing the underwater sound field, a wave mode calculation method based on PE is proposed in this study. Step-split Padé PE recursive matrix equations are combined to obtain a propagation matrix. Then, the eigenvalue decomposition technique is applied to the matrix to extract sound mode eigenvalues and eigenfunctions. Numerical experiments on some typical waveguides are performed to test the accuracy and flexibility of the new method. Discussions on different orders of Padé approximant demonstrate angle limitations in PE and the missing root problem is also discussed to prove the advantage of the new method. The PE mode method can be expanded in the future to solve smooth wave modes in ocean waveguides, including fluctuating boundaries and sound speed profiles.

Key words: parabolic equation, propagation matrix, eigenvalue decomposition

中图分类号: (Underwater sound)

43.30.-k

43.30.Bp (Normal mode propagation of sound in water)

Chuan-Xiu Xu(徐传秀) and Guang-Ying Zheng(郑广赢). Wave mode computing method using the step-split Padé parabolic equation[J]. 中国物理B, 2022, 31(9): 94301-094301.

Chuan-Xiu Xu(徐传秀) and Guang-Ying Zheng(郑广赢). Wave mode computing method using the step-split Padé parabolic equation[J]. Chin. Phys. B, 2022, 31(9): 94301-094301.

参考文献

[1] Pekeris C L 1948 Geol. Soc. Am. 27 1
[2] Labiance F M 1973 J. Acoust. Soc. Am. 53 1137
[3] Bartberger C L 1977 J. Acoust. Soc. Am. 61 1643
[4] Ellis D D 1985 J. Acoust. Soc. Am. 78 2087
[5] Evans R B 1992 J. Acoust. Soc. Am. 92 2024
[6] Westwood E K 1996 J. Acoust. Soc. Am. 100 3631
[7] Collins M D 1993 J. Acoust. Soc. Am. 93 1736
[8] Collins M D 1991 J. Acoust. Soc. Am. 89 1068
[9] Petrov P S and Ehrhardt M 2016 J. Comp. Phys. 313 144
[10] Porter M B and Bucker H P 1987 J. Acoust. Soc. Am. 82 1349
[11] DiNapoli F R 1971 Tech. Rpt. 4103 (New London:Naval Underwater Systems Center)
[12] Ewing W M, Jardetzky W S and Press F 1957 Elastic waves in layered media (New York:Mcgraw-Hill Book Company) pp. 328-330
[13] DiNapoli F R and Deavenport R L 1980 J. Acoust. Soc. Am. 67 92
[14] Collins M D 1989 J. Acoust. Soc. Am. 86 1459
[15] Jerzak W and Siegmann W L 2005 J. Acoust. Soc. Am. 117 3497
[16] Outing D A, Siegmann W L and Collins M D 2007 IEEE J. Oceanic. Eng. 32 620
[17] Frank S D, Odom R I and Collis J M 2013 J. Acoust. Soc. Am. 133 1358
[18] Frank S D, Collis J M and Odom R I 2015 J. Acoust. Soc. Am. 137 3534
[19] Collins M D 2015 J. Acoust. Soc. Am. 137 1557
[20] Fredricks A J, Siegmann W L and Collins M D 2000 Wave Motion. 31 139
[21] Metzler A M, Collins M D and Collis J M 2013 J. Acoust. Soc. Am. 134 246
[22] Brooke G H, Thomson D J and Ebbeson G R 2001 J. Comput. Acoust. 9 69
[23] Sturm F and Fawcett J A 2003 J. Acoust. Soc. Am. 113 3134
[24] Sturm F 2005 J. Acoust. Soc. Am. 117 1058
[25] Lin Y T and Duda T F 2012 J. Acoust. Soc. Am. 132 EL61
[26] Lin Y T, Collis J M and Duda T F 2012 J. Acoust. Soc. Am. 132 EL364
[27] Lin Y T 2013 J. Acoust. Soc. Am. 134 EL251
[28] Lin Y T, Duda T F and Newhall A E 2013 J. Comput. Acoust. 21 1250018
[29] Sturm F 2016 J. Acoust. Soc. Am. 139 263
[30] Tang J, Piao S C and Zhang H G 2017 Chin. Phys B. 26 114301
[31] Xu C X and Tang J 2019 J. Acoust. Soc. Am. 146 EL464
[32] Porter M 1991 Saclantcen Memorandum, SM-245 (La Spezia:SACLANT Undersea Research Centre)

Wave mode computing method using the step-split Padé parabolic equation

Wave mode computing method using the step-split Padé parabolic equation

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