一种水平变化可穿透波导中声传播问题的耦合简正波方法

杨春梅; 骆文于; 张仁和; 秦继兴

doi:10.7498/aps.62.094302

摘要

通过利用标准简正波程序KRAKEN计算本地简正波解及耦合矩阵, 进一步发展了求解水平变化波导中声场的全局矩阵耦合简正波方法(Luo et al., "A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides," Sci. China-Phys. Mech. Astron. 55, 572 (2012)), 使得该方法可以处理具有可穿透海底及随深度变化声速剖面等实际问题, 并提供声场的完全双向解. 本文还给出了双层波导中耦合矩阵的解析表达式, 并利用其验证了本方法中耦合矩阵数值算法的精度. 最后, 利用改善后的全局矩阵耦合简正波模型(DGMCM)计算了美国声学学会(ASA)提出的可穿透楔形波导标准问题, 将所得数值解与参考解比较, 结果表明DGMCM方法可以精确处理水平变化波导中声传播实际问题.

关键词:

Abstract

The coupled-mode method based on the direct global matrix (DGMCM) approach for sound propagation in range-dependent waveguides [Luo et al., "A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides," Sci. China-Phys. Mech. Astron. 55, 572 (2012)] is further developed. The normal mode model KRAKEN is adopted to provide local modal solutions and their associated coupling matrices. As a result, the model DGMCM is capable of providing full two-way solutions for the two-dimensional realistic problems characterized by a penetrable bottom and a depth-varying sound speed profile. In addition, the closed-form expressions of coupling matrices for sound propagation in a range-dependent, two-layer waveguide are proposed. The numerical solutions of the coupling matrices by DGMCM agree well with the analytical solutions. Sound propagation in a penetrable wedge is solved by the updated DGMCM model. The numerical results indicate that the updated DGMCM model is numerically stable and accurate, and can provide benchmark solutions for realistic range-dependent problems.

Keywords:

作者及机构信息

1.
中国科学院声学研究所声场声信息国家重点实验室, 北京 100190;

2.
中国科学院大学, 北京 100049

基金项目: 国家自然科学基金(批准号:11125420,11174312)和中国科学院知识创新工程资助的课题.

Authors and contacts

1.
State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China;

2.
University of Chinese Academy of Sciences, Beijing 100049, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11125420, 11174312), and the Knowledge Innovation Program of the Chinese Academy of Sciences.

参考文献

[1]	Collis J M, Siegmann W L, Jensen F B, Zampolli M, KÜsel E T, Collins M D 2008 J. Acoust. Soc. Am. 123 51
[2]	Evans R B 1983 J. Acoust. Soc. Am. 74 188
[3]	Pierce A D 1965 J. Acoust. Soc. Am. 37 19
[4]	Luo W Y, Schmidt H 2009 J. Acoust. Soc. Am. 125 52
[5]	Collins M D, Schmidt H, Siegmann W L 2000 J. Acoust. Soc. Am. 107 1964
[6]	Thompson L L 2006 J. Acoust. Soc. Am. 119 1315
[7]	Zampolli M, Tesei A, Jensen F B, Malm N, Blottman III J B 2007 J. Acoust. Soc. Am. 122 1472
[8]	Peng Z H, Zhang R H 2005 Acta Acustica 30 97 (in Chinese) [彭朝晖, 张仁和 2005 声学学报 30 97]
[9]	Milder D M 1969 J. Acoust. Soc. Am. 46 1259
[10]	Rutherford S R, Hawker K E 1981 J. Acoust. Soc. Am. 70 554
[11]	Fawcett J A 1992 J. Acoust. Soc. Am. 92 290
[12]	Godin O A 1998 J. Acoust. Soc. Am. 103 159
[13]	Athanassoulis G A, Belibassakis K A, Mitsoudis D A, Kampanis N A, Dougalis V A 2008 J. Comp. Acoust. 16 83
[14]	Ferla C M, Porter M B, Jensen F B 1993 C-SNAP: Coupled SACLANTCEN normal mode propagation loss model (La Spezia, Italy: SACLANT Undersea Research Center) Technical Report SM-274
[15]	Porter M B, Jensen F B, Ferla C M 1991 J. Acoust. Soc. Am. 89 1058
[16]	Evans R B 1986 J. Acoust. Soc. Am. 80 1414
[17]	Luo W Y, Yang C M, Zhang R H 2012 Chin. Phys. Lett 29 014302
[18]	Luo W Y, Yang C M, Qin J X, Zhang R H 2012 Sci. China-Phys. Mech. Astron. 55 572
[19]	Schmidt H, Jensen F B 1985 J. Acoust. Soc. Am. 77 813
[20]	Schmidt H 1993 J. Acoust. Soc. Am. 94 2420
[21]	Ricks D C, Schmidt H 1994 J. Acoust. Soc. Am. 95 3339
[22]	Jensen F B, Kuperman W A, Porter M B, Schmidt H 2011 Computational Ocean Acoustics (2nd Ed.) (New York: Springer)
[23]	Porter M B 1991 The KRAKEN normal mode program (La Spezia, Italy: SACLANT Undersea Research Centre) Technical Report SM-245
[24]	Stotts S A 2002 J. Acoust. Soc. Am. 111 1623
[25]	Felsen L B 1986 J. Acoust. Soc. Am. Suppl. 1 80 S36
[26]	Felsen L B 1987 J. Acoust. Soc. Am. Suppl. 1 81 S39
[27]	Jensen F B 1998 J. Acoust. Soc. Am. 104 1310
[28]	Evans R B, Gilbert K E 1985 Comp. Maths. Appl. 11 795

施引文献

[1]	Collis J M, Siegmann W L, Jensen F B, Zampolli M, KÜsel E T, Collins M D 2008 J. Acoust. Soc. Am. 123 51
[2]	Evans R B 1983 J. Acoust. Soc. Am. 74 188
[3]	Pierce A D 1965 J. Acoust. Soc. Am. 37 19
[4]	Luo W Y, Schmidt H 2009 J. Acoust. Soc. Am. 125 52
[5]	Collins M D, Schmidt H, Siegmann W L 2000 J. Acoust. Soc. Am. 107 1964
[6]	Thompson L L 2006 J. Acoust. Soc. Am. 119 1315
[7]	Zampolli M, Tesei A, Jensen F B, Malm N, Blottman III J B 2007 J. Acoust. Soc. Am. 122 1472
[8]	Peng Z H, Zhang R H 2005 Acta Acustica 30 97 (in Chinese) [彭朝晖, 张仁和 2005 声学学报 30 97]
[9]	Milder D M 1969 J. Acoust. Soc. Am. 46 1259
[10]	Rutherford S R, Hawker K E 1981 J. Acoust. Soc. Am. 70 554
[11]	Fawcett J A 1992 J. Acoust. Soc. Am. 92 290
[12]	Godin O A 1998 J. Acoust. Soc. Am. 103 159
[13]	Athanassoulis G A, Belibassakis K A, Mitsoudis D A, Kampanis N A, Dougalis V A 2008 J. Comp. Acoust. 16 83
[14]	Ferla C M, Porter M B, Jensen F B 1993 C-SNAP: Coupled SACLANTCEN normal mode propagation loss model (La Spezia, Italy: SACLANT Undersea Research Center) Technical Report SM-274
[15]	Porter M B, Jensen F B, Ferla C M 1991 J. Acoust. Soc. Am. 89 1058
[16]	Evans R B 1986 J. Acoust. Soc. Am. 80 1414
[17]	Luo W Y, Yang C M, Zhang R H 2012 Chin. Phys. Lett 29 014302
[18]	Luo W Y, Yang C M, Qin J X, Zhang R H 2012 Sci. China-Phys. Mech. Astron. 55 572
[19]	Schmidt H, Jensen F B 1985 J. Acoust. Soc. Am. 77 813
[20]	Schmidt H 1993 J. Acoust. Soc. Am. 94 2420
[21]	Ricks D C, Schmidt H 1994 J. Acoust. Soc. Am. 95 3339
[22]	Jensen F B, Kuperman W A, Porter M B, Schmidt H 2011 Computational Ocean Acoustics (2nd Ed.) (New York: Springer)
[23]	Porter M B 1991 The KRAKEN normal mode program (La Spezia, Italy: SACLANT Undersea Research Centre) Technical Report SM-245
[24]	Stotts S A 2002 J. Acoust. Soc. Am. 111 1623
[25]	Felsen L B 1986 J. Acoust. Soc. Am. Suppl. 1 80 S36
[26]	Felsen L B 1987 J. Acoust. Soc. Am. Suppl. 1 81 S39
[27]	Jensen F B 1998 J. Acoust. Soc. Am. 104 1310
[28]	Evans R B, Gilbert K E 1985 Comp. Maths. Appl. 11 795

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