孤子内波环境下三维声传播建模

张泽众; 骆文于; 庞哲; 周益清

doi:10.7498/aps.68.20190478

摘要

提出了一种适用于存在孤子内波水平变化波导的高效三维水下声场计算模型. 该模型忽略反向散射, 一般情况下由于孤子内波的反向散射非常弱, 所以该模型能够提供精确的三维声场结果. 同时, 相对于双向三维耦合简正波模型, 该模型在计算效率上能够至少提高一个数量级. 除了孤子内波环境之外, 本模型还适用于存在小尺度海脊等反向散射比较弱的一般水平变化波导环境. 本文用该模型计算由KdV方程得到的孤子内波问题, 并用双向三维耦合简正波模型作为标准模型来验证本模型的计算精度. 计算结果表明本模型在反向散射比较弱的波导环境中具有非常高的计算精度.

关键词:

Abstract

An accurate and numerically efficient numerical model is very important for studying the effect of internal wave on underwawter sound propagation. A full-wave, three-dimensional (3D) coupled-mode model is able to deal with the internal wave problem with satisfactory accuracy, but such a model is in general numerically inefficient. A numerically efficient 3D model is presented for sound propagation in a range-dependent waveguide in the presence of solitary internal waves in this work. The present model is a forward-marching model that neglects backscattering. In this 3D model, an efficient two-dimensional (2D) coupled-mode model, C-SNAP, is adopted to compute 2D acoustic field solutions excited by a line source. The C-SNAP is a 2D forward-marching model, which uses an energy-conserving matching condition to preserve accuracy. An appealing aspect of C-SNAP is that its efficiency is competitive with that of the existing parabolic equation model. The integral transform technique is used to extend C-SNAP to a 3D model, where a complex integration contour is used for evaluating the wavenumber integral. A brief review of C-SNAP and formulation of the present 3D model are given. The forward-marching models are primarily suitable for treating the range-dependent problems with weak backscattering, such as with a slowly varying bathymetry. Since in general the backscattering from internal wave is weak, which is also validated numerically in this work, the present model is able to address the problem of sound propagation through internal wave with satisfactory accuracy. At the same time, it achieves an efficiency gain of at least an order of magnitude over that of full two-way, 3D model. In addition to the internal wave, the present model is also suitable for solving the general range-dependent problems where backscattering is weak, such as in the presence of a bottom ridge of a small height. Numerical simulations are also provided to validate the present model, where a two-way, 3D model serves as the benchmark. The numerical results show that the effect of the internal wave on the acoustic field is negligible for the region between the source and the internal wave. However, the effect is significant on the other side of the internal wave. A more interesting observation is the angular dependence of the interference pattern induced by the internal wave.

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

通信作者: 骆文于, lwy@mail.ioa.ac.cn

基金项目: 国家自然科学基金(批准号: 11774374)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

Corresponding author: Luo Wen-Yu, lwy@mail.ioa.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11774374)

文章全文 : translate this paragraph

参考文献

[1]	王宁, 张海青, 王好忠, 高大治 2010 声学学报 35 38 Wang N, Zhang H Q, Wang H Z, Gao D Z 2010 Acta Acust. 35 38
[2]	马树青, 杨士莪, 朴胜春, 李婷婷 2009 振动与冲击 28 73 Google Scholar Ma S Q, Yang S E, Piao S C, Li T T 2009 J. Vib. Shock 28 73 Google Scholar
[3]	Badiey M, Katsnelson B G, Lynch J F, Pereselkov S, Siegmann W L 2005 J. Acoust. Soc. Am. 117 613 Google Scholar
[4]	Luo J, Badiey M, Karjadi E A, Katsnelson B, Tskhoidze A, Lynch J F, Moum J N 2008 J. Acoust. Soc. Am. 124 66 Google Scholar
[5]	Lin Y T, Duda T F, Lynch J F 2009 J. Acoust. Soc. Am. 126 1752 Google Scholar
[6]	Colosi J A 2008 J. Acoust. Soc. Am. 124 1452 Google Scholar
[7]	Yang T C 2014 J. Acoust. Soc. Am. 135 610 Google Scholar
[8]	Siegmann W L, Kriegsmann G A, Lee D 1985 J. Acoust. Soc. Am. 78 659 Google Scholar
[9]	Lee D, Botseas G, Siegmann W L 1992 J. Acoust. Soc. Am. 91 3192 Google Scholar
[10]	Collins M D, Chin-Bing S A 1990 J. Acoust. Soc. Am. 87 1104 Google Scholar
[11]	Ferla C M, Porter M B, Jensen F B 1993 C-SNAP: Coupled SACLANTCEN Normal Mode Propagation Loss Model (La Spezia: SACLANT Undersea Research Center) pp1–46
[12]	Luo W Y, Yang C M, Qin J X, Zhang R H 2012 Sci. Chin. Phys. Mech. Astron. 55 572 Google Scholar
[13]	杨春梅, 骆文于, 张仁和, 秦继兴 2014 声学学报 39 295 Yang C M, Luo W Y, Zhang R H, Qin J X 2014 Acta Acust. 39 295
[14]	Luo W Y, Zhang R H 2015 Sci. China-G: Phys. Mech. Astron. 58 1
[15]	Evans R B 1983 J. Acoust. Soc. Am. 74 188 Google Scholar
[16]	Collins M D, Westwood E K 1991 J. Acoust. Soc. Am. 89 1068 Google Scholar
[17]	Jensen F B, Kuperman W A, Porter M B, Schmidt H 2011 Computational Ocean Acoustics （2nd ed.） (New York: Springer) pp337–445
[18]	Buckingham M J 1989 J. Acoust. Soc. Am. 86 2273 Google Scholar
[19]	Luo W Y, Yu X L, Yang X F, Zhang Z Z, Zhang R H 2016 Chin. Phys. B 25 124309 Google Scholar
[20]	Jensen F B 1998 J. Acoust. Soc. Am. 104 1310 Google Scholar

施引文献

图 1 水平变化波导(红色虚线)的阶梯近似

Fig. 1. Stair step approximation of a sloping bottom (red dashed line)

下载: 全尺寸图片幻灯片

图 2 反傅里叶变换的积分围线(圆圈代表简正波的本征值, 即水平波数)

Fig. 2. Complex integration contour for evaluation of the wavenumber integral. The dots indicate horizontal wavenumbers of the normal modes.

下载: 全尺寸图片幻灯片

图 3 二维声速剖面示意图　(a)无孤子内波的声速剖面; (b)孤子内波位于4 km处的声速剖面; (c)孤子内波位于4 km处, 海脊位于6 km处的声速剖面

Fig. 3. Sound speed fields considered in this paper: (a) The background sound speed field; (b) in the presence of an internal wave soliton, centered at range 4 km from the source; (c) in the presence of both an internal wave soliton centered at 4 km and a cosine-bell shaped bottom ridge centered at 6 km from the source.

下载: 全尺寸图片幻灯片

图 4 孤子内波环境下DGMCM2D和C-SNAP在70 m深度传播损失曲线　蓝色实线和红色虚线分别表示无孤子内波时DGMCM2D和C-SNAP的计算结果, 绿色和枚红色虚线分别表示孤子内波波包在4 km时DGMCM2D和C-SNAP的计算结果, 黑色虚线表示孤子内波波包位置

Fig. 4. Transmission loss results for the internal solitary wave problem computed by DGMCM2D and C-SNAP. The blue solid line and red dashed line are the results by DGMCM2D and C-SNAP for the case without internal waves, respectively, and the green and magenta dashed lines are the results by DGMCM2D and C-SNAP for the case with a soliton located at range 4 km, respectively. The black dashed line indicates the center of the soliton.

下载: 全尺寸图片幻灯片

图 5 70 m深度水平面上的三维传播损失结果　(a) DGMCM3D的结果; (b)本文提出的三维模型的结果, 黑色虚线代表孤子内波波包的位置

Fig. 5. Three-dimensional transmission loss results in the horizontal plane at depth 70 m computed by (a) DGMCM3D and (b) the present 3D model. The center location of the internal wave is indicated by dashed black lines.

下载: 全尺寸图片幻灯片

图 6 纵向距离$ y = 0 \;{\rm{km}}$, 深度z = 70 m, 随距离传播的损失曲线, 蓝色实线和红色虚线分别为DGMCM3D和本文提出的三维模型的结果

Fig. 6. Transmission loss lines versus range along the cross-range $ y = 0 \;{\rm{km}}$ at depth z = 70 m computed by DGMCM3D (the blue, solid curve) and the present 3D model (the red, dashed curve).

下载: 全尺寸图片幻灯片

图 7 海底存在海脊的水平变化波导示意图

Fig. 7. Geometry of a range-dependent waveguide with a bottom ridge.

下载: 全尺寸图片幻灯片

图 8 孤子内波和海脊同时存在时深度70 m处的二维传播损失结果, 其中蓝色实线为DGMCM2D结果, 红色虚线为C-SNAP结果

Fig. 8. Two-dimensional transmission loss results at a depth of 70 m for the problem involving a solitary internal wave as well as a bottom ridge by DGMCM2D (the blue, solid curve) and C-SNAP (the red, dashed curve).

下载: 全尺寸图片幻灯片

图 9 同时存在孤子内波和海脊时深度70 m水平平面上的三维传播损失　(a) DGMCM3D结果; (b)本文提出的三维模型的结果. 黑色和红色虚线分别表示孤子内波波包和海脊中心的位置

Fig. 9. Three-dimensional transmission loss results in the horizontal plane at depth of 70 m in the presence of a solitary internal wave as well as a bottom ridge computed by (a) DGMCM3D and (b) the present 3D model. The center locations of the internal wave and the ridge are indicated by dashed black and red lines, respectively.

下载: 全尺寸图片幻灯片

[1]	王宁, 张海青, 王好忠, 高大治 2010 声学学报 35 38 Wang N, Zhang H Q, Wang H Z, Gao D Z 2010 Acta Acust. 35 38
[2]	马树青, 杨士莪, 朴胜春, 李婷婷 2009 振动与冲击 28 73 Google Scholar Ma S Q, Yang S E, Piao S C, Li T T 2009 J. Vib. Shock 28 73 Google Scholar
[3]	Badiey M, Katsnelson B G, Lynch J F, Pereselkov S, Siegmann W L 2005 J. Acoust. Soc. Am. 117 613 Google Scholar
[4]	Luo J, Badiey M, Karjadi E A, Katsnelson B, Tskhoidze A, Lynch J F, Moum J N 2008 J. Acoust. Soc. Am. 124 66 Google Scholar
[5]	Lin Y T, Duda T F, Lynch J F 2009 J. Acoust. Soc. Am. 126 1752 Google Scholar
[6]	Colosi J A 2008 J. Acoust. Soc. Am. 124 1452 Google Scholar
[7]	Yang T C 2014 J. Acoust. Soc. Am. 135 610 Google Scholar
[8]	Siegmann W L, Kriegsmann G A, Lee D 1985 J. Acoust. Soc. Am. 78 659 Google Scholar
[9]	Lee D, Botseas G, Siegmann W L 1992 J. Acoust. Soc. Am. 91 3192 Google Scholar
[10]	Collins M D, Chin-Bing S A 1990 J. Acoust. Soc. Am. 87 1104 Google Scholar
[11]	Ferla C M, Porter M B, Jensen F B 1993 C-SNAP: Coupled SACLANTCEN Normal Mode Propagation Loss Model (La Spezia: SACLANT Undersea Research Center) pp1–46
[12]	Luo W Y, Yang C M, Qin J X, Zhang R H 2012 Sci. Chin. Phys. Mech. Astron. 55 572 Google Scholar
[13]	杨春梅, 骆文于, 张仁和, 秦继兴 2014 声学学报 39 295 Yang C M, Luo W Y, Zhang R H, Qin J X 2014 Acta Acust. 39 295
[14]	Luo W Y, Zhang R H 2015 Sci. China-G: Phys. Mech. Astron. 58 1
[15]	Evans R B 1983 J. Acoust. Soc. Am. 74 188 Google Scholar
[16]	Collins M D, Westwood E K 1991 J. Acoust. Soc. Am. 89 1068 Google Scholar
[17]	Jensen F B, Kuperman W A, Porter M B, Schmidt H 2011 Computational Ocean Acoustics （2nd ed.） (New York: Springer) pp337–445
[18]	Buckingham M J 1989 J. Acoust. Soc. Am. 86 2273 Google Scholar
[19]	Luo W Y, Yu X L, Yang X F, Zhang Z Z, Zhang R H 2016 Chin. Phys. B 25 124309 Google Scholar
[20]	Jensen F B 1998 J. Acoust. Soc. Am. 104 1310 Google Scholar

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孤子内波环境下三维声传播建模