倾斜弹性海底条件下浅海声场的简正波相干耦合特性分析

张士钊; 朴胜春

doi:10.7498/aps.70.20211013

摘要

建立了一种适用于复本征值情况下的弹性耦合简正波声场模型, 给出了包含泄漏模态时弹性简正波的归一化和耦合系数表达式, 耦合系数满足声能流守恒. 利用该模型分析了倾斜弹性海底条件下声场的简正波相干耦合特性, 发现考虑泄漏模态时, 简正波耦合不仅会导致简正波幅度变化, 而且也会带来附加相移. 仿真计算表明: 其一, 在倾斜弹性海底条件下, 考虑泄漏模态耦合附加相移影响后得到的声传播损失更接近有限元商用软件的计算结果; 其二, 耦合大大提升了界面波的幅度. 此外, 本文还分析了海洋环境参数变化对声传播损失的影响.

关键词:

Abstract

In this paper, a sound field model of elastically coupled normal mode suitable for complex eigenvalues is established. The normalization and coupling coefficient expression of elastic normal mode are given when the leaky mode is included. The coupling coefficients satisfy the conservation of sound energy flow. This model is used to analyze the coherent coupling characteristics of the normal mode of the sound field under the condition of the inclined elastic seabed. It is found that when the leaky mode is considered, the normal mode coupling will not only cause the amplitude of the normal mode to change, but also bring additional phase shift. The simulation calculation shows that under the condition of inclined elastic seabed, the acoustic propagation loss obtained by considering the effect of the additional phase shift of the leaky mode coupling is closer to the calculation result obtained by using the finite element commercial software, and that the mode coupling greatly enhances the amplitude of interface wave. In addition, this paper also analyzes the influence of changes in marine environmental parameters on sound transmission loss.

Keywords:

作者及机构信息

张士钊³,
朴胜春^1,2,3

1.
哈尔滨工程大学, 水声技术重点实验室, 哈尔滨　150001

2.
哈尔滨工程大学, 海洋信息获取与安全工信部重点实验室, 哈尔滨　150001

3.
哈尔滨工程大学水声工程学院, 哈尔滨　150001

通信作者: 朴胜春, piaoshengchun@hrbeu.edu.cn

基金项目: 国家自然科学基金(批准号: 11474073)和中央高校基本科研业务费专项资金(批准号: 3514497)资助的课题．

Authors and contacts

1.
Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China

2.
Key Laboratory of Marine Information Acquisition and Security, Ministry of Industry and Information Technology, Harbin Engineering University, Harbin 150001, China

3.
College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China

Corresponding author: Piao Sheng-Chun, piaoshengchun@hrbeu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11474073) and the Fundamental Research Funds for the Central Universities, China (Grant No. 3514497).

文章全文 : translate this paragraph

参考文献

[1]	Pekeris C L 1948 Mem. Geol. Soc. Amer. 27 48 Google Scholar
[2]	Press F, Ewing M 1950 Geophysics 15 426 Google Scholar
[3]	Porter M B, Reiss E L 1985 J. Acoust. Soc. Am. 77 1760 Google Scholar
[4]	Ainslie M A 1995 J. Acoust. Soc. Am. 97 954 Google Scholar
[5]	Schneiderwind J D, Collis J M, Simpson H J 2012 J. Acoust. Soc. Am. 132 EL182 Google Scholar
[6]	Pierce A D 1965 J. Acoust. Soc. Am. 37 19 Google Scholar
[7]	Chwieroth F S, Nagl A, Uberall H, Zarur G L 1978 J. Acoust. Soc. Am. 64 1105 Google Scholar
[8]	Williams A O 1980 J. Acoust. Soc. Am. 67 177 Google Scholar
[9]	Rutherford S R, Hawker K E 1981 J. Acoust. Soc. Am. 70 554 Google Scholar
[10]	McDaniel S T 1982 J. Acoust. Soc. Am. 72 916 Google Scholar
[11]	Evans R B 1983 J. Acoust. Soc. Am. 74 188 Google Scholar
[12]	Porter M B, Jensen F B, Ferla C M 1991 J. Acoust. Soc. Am. 89 1058 Google Scholar
[13]	Abawi A T, Kuperman W A 1997 J. Acoust. Soc. Am. 102 233 Google Scholar
[14]	Knobles D P, Stotts S A, Koch R A 2003 J. Acoust. Soc. Am. 113 781 Google Scholar
[15]	莫亚枭, 朴胜春, 张海刚, 李丽 2016 声学学报 41 154 Google Scholar Mo Y X, Piao S C, Zhang H G, Li L 2016 Acta Acustica 41 154 Google Scholar
[16]	Kennett B L N 1984 Geophys. J. R. Astron. Soc. 79 235 Google Scholar
[17]	Odom R I 1986 Geophys J. R. Astron. Soc. 86 425 Google Scholar
[18]	Hall M 1986 J. Acoust. Soc. Am. 79 332 Google Scholar
[19]	Maupin V 1988 Geophys. J. 93 173 Google Scholar
[20]	Collins M D 1993 J. Acoust. Soc. Am. 94 975 Google Scholar
[21]	Collins M D, Siegmann W L 1999 J. Acoust. Soc. Am. 105 687 Google Scholar
[22]	Jeroen T 1994 Geophys. J. Int. 117 153 Google Scholar
[23]	Abawi A T, Porter M B P 2008 https://apps.dtic.mil/dtic/tr/fulltext/u2/a541636.pdf
[24]	Odom R I, Park M, Mercer J A, Crosson R S, Paik P 1996 J. Acoust. Soc. Am. 100 2079 Google Scholar
[25]	Abawi A T, Porter M B 2007 J. Acoust. Soc. Am. 121 1374 Google Scholar
[26]	Xie Z, Matzen Rene, Cristini P, Komatitsch D, Martin R 2016 J. Acoust. Soc. Am. 140 165 Google Scholar
[27]	骆文于, 于晓林, 张仁和 2016 声学学报 41 321 Google Scholar Luo W Y, Yu X L, Zhang R H 2016 Acta Acustica 41 321 Google Scholar
[28]	莫亚枭, 朴胜春, 张海刚, 李丽 2014 声学学报 39 428 Google Scholar Mo Y X, Piao S C, Zhang H G, Li L 2014 Acta Acustica 39 428 Google Scholar
[29]	Chapman D M F, Ward P D, Ellis D D 1989 J. Acoust. Soc. Am. 85 648 Google Scholar
[30]	McCollom B A, Collis J M 2014 J. Acoust. Soc. Am. 136 1036 Google Scholar
[31]	Zhang Z Y, Tindle C T 1993 J. Acoust. Soc. Am. 93 205 Google Scholar
[32]	Stickler D C 1975 J. Acoust. Soc. Am. 57 856 Google Scholar
[33]	Westwood E K, Koch R A 1999 J. Acoust. Soc. Am. 106 2513 Google Scholar
[34]	Westwood E K, Tindle C T, Chapman N R 1996 J. Acoust. Soc. Am. 100 3631 Google Scholar
[35]	杨士莪 1994 水声传播原理 (哈尔滨: 哈尔滨工程大学出版社) 第16页 Yang S E 1994 Principle of Underwater Acoustic Propagation (Harbin: Haerbin Engineering University Press) p16 (in Chinese)

施引文献

图 1 水平变化弹性海底的分段阶梯近似

Fig. 1. Stepwise approximation of a horizontally varying elastic seabed.

下载: 全尺寸图片幻灯片

图 3 是否考虑幅度相位处理的$\left\langle {{{\boldsymbol{u}}_m}, {{\boldsymbol{u}}_n}} \right\rangle$归一化时本文方法所得声压, 及其和RAMS以及COMSOL所得声压对比　(a) f = 50 Hz, 不考虑; (b) f = 50 Hz, 考虑; (c) f = 25 Hz时, 不考虑; (d) f = 25 Hz, 考虑; (e) f = 25 Hz, c_s = 2000 m/s, 不考虑; (f) f = 25 Hz, c_s = 2000 m/s, 考虑

Fig. 3. Sound pressure obtained by the method in this paper when (a) f = 50 Hz, without, (b) f = 50 Hz, with, (c) f = 25 Hz, without, (d) f = 25 Hz, with, (e) f = 25 Hz, c_s = 2000 m/s, without, (f) f = 25 Hz, c_s = 2000 m/s, with considering the normalization of amplitude and phase processing, compared with the sound pressure obtained by RAMS and COMSOL.

下载: 全尺寸图片幻灯片

图 2 (a) 液态海底海洋环境模型; (b) 液态海底时的水中声压; (c) 弹性海底海洋环境模型; (d) 弹性海底时的水中声压

Fig. 2. (a) Marine environment model with liquid seabed; (b) sound pressure in water with liquid seabed; (c) marine environment model with elastic seabed; (d) sound pressure in water with elastic seabed.

下载: 全尺寸图片幻灯片

图 4 (a)不考虑和(b)考虑泄漏模态时的耦合矩阵法所得声压, 及其和RAMS, COMSOL程序所得声压的对比; (c) RAMS所得声压的FK变换结果

Fig. 4. Sound pressure obtained by the coupling matrix method when the leaky mode is (a) not considered or (b) considered, compared with the sound pressure obtained by the RAMS and COMSOL program; (c) the FK transformation result of the sound pressure obtained by RAMS.

下载: 全尺寸图片幻灯片

图 5 z_r = 30 m, z_s = (a) 50, (b) 70和(c) 100 m时的水中声压; m = (d) 1, (e) 5和(f) 9 时, x = 0 m处的耦合系数B_mn

Fig. 5. Sound pressure in water when z_r = 30 m, z_s = (a) 50, (b) 70, and (c) 100 m; the coupling coefficient B_mn at x = 0 m when m = (d) 1, (e) 5和(f) 9.

下载: 全尺寸图片幻灯片

图 6 (a) z_s = 50, (b) 70和(c) 100 m时, 不含波数差的耦合系数取实部和保持为复数时的声压对比

Fig. 6. Acoustic pressure when the real part of the coupling coefficient without wavenumber difference is taken when z_s = (a) 50, (b) 70, (c) 100 m, compared with the sound pressure when the coupling coefficient is kept as a complex number.

下载: 全尺寸图片幻灯片

图 7 z_s = 50 m, 各阶简正波的(a) |a_m|和(b) a_m的相位随距离的变化; (c) f = 50 Hz, 海洋环境如图2(c)时, 各阶简正波本征值的实部随距离的变化

Fig. 7. When z_s = 50 m, (a) |a_m| and (b) the phases of a_m of each order of normal mode varying with distance. (c) When f = 50 Hz and the marine environment is shown in Fig. 2(c), the real part of the normal mode eigenvalues of each order varying with distance.

下载: 全尺寸图片幻灯片

图 8 z_s = (a) 50和(b) 100 m时, 各阶简正波声压的FK变换结果图

Fig. 8. FK transformation results of normal mode sound pressure of each order when z_s = (a) 50 and (b) 100 m.

下载: 全尺寸图片幻灯片

图 9 上坡弹性海底的坡度为(a) 0.0125, (b) 0.025, (c) 0.05和(d) 0.075时的水中声压; 考虑泄漏模态, 坡度为(e) 0.0125和(f) 0.025, x = 1 km时的|B_mn(x)|

Fig. 9. Sound pressure in water when the seabed slope is (a) 0.0125, (b) 0.025, (c) 0.05 and (d) 0.075 on the upslope elastic seabed. The |B_mn(x)| considering the leaky mode when x = 1 km when the slope is (e) 0.0125 and (f) 0.025.

下载: 全尺寸图片幻灯片

图 10 (a)下坡海底海洋环境; (b)下坡和(c)上坡的坡度为0.05时的弹性海底声场

Fig. 10. (a) Downslope seabed marine environment; sound field in water with (b) downslope and (c) upslope elastic seabed with a slope of 0.05.

下载: 全尺寸图片幻灯片

图 11 c_s = (a) 1800, (b) 1900, (c) 2000 m/s时的水中声压; (d) 考虑泄漏模态条件下, c_s = 1800, 1900, 2000 m/s时采用耦合简正波法得到的声压对比

Fig. 11. Sound pressure in water when c_s = (a) 1800, (b) 1900, (c) 2000 m/s; (d) sound pressure comparison obtained by mode coupling method while condidering leaky modes when c_s = 1800, 1900, 2000 m/s.

下载: 全尺寸图片幻灯片

图 12 c_p = 1700 m/s, c_s = (a) 600, (b) 700 和(c) 800 m/s时的水中声压; (d) c_s = 600, 700, 800 m/s时, 考虑泄漏模态情况下, 采用耦合简正波方法所得声压对比; (e) c_s = 600, 700, 800 m/s时第2阶简正波衰减系数随距离的变化

Fig. 12. Sound pressure in water when c_s = (a) 600, (b) 700, (c) 800 m/s; (d) sound pressure obtained by mode coupling method considering leaky modes and when c_s = 600, 700, 800 m/s; (e) the attenuation coefficient of the 2^nd normal mode varying with range when c_s = 600, 700, 800 m/s.

下载: 全尺寸图片幻灯片

表 1 图2(c)环境下声场计算的平均耗时

Table 1. Average time consumption for acoustic field computation under the environment shown in Fig. 2(c)

计算方法耦合矩阵法 RAMS COMSOL

平均耗时/s 7.66 5.37 27.33

下载: 导出CSV

map

[1]	Pekeris C L 1948 Mem. Geol. Soc. Amer. 27 48 Google Scholar
[2]	Press F, Ewing M 1950 Geophysics 15 426 Google Scholar
[3]	Porter M B, Reiss E L 1985 J. Acoust. Soc. Am. 77 1760 Google Scholar
[4]	Ainslie M A 1995 J. Acoust. Soc. Am. 97 954 Google Scholar
[5]	Schneiderwind J D, Collis J M, Simpson H J 2012 J. Acoust. Soc. Am. 132 EL182 Google Scholar
[6]	Pierce A D 1965 J. Acoust. Soc. Am. 37 19 Google Scholar
[7]	Chwieroth F S, Nagl A, Uberall H, Zarur G L 1978 J. Acoust. Soc. Am. 64 1105 Google Scholar
[8]	Williams A O 1980 J. Acoust. Soc. Am. 67 177 Google Scholar
[9]	Rutherford S R, Hawker K E 1981 J. Acoust. Soc. Am. 70 554 Google Scholar
[10]	McDaniel S T 1982 J. Acoust. Soc. Am. 72 916 Google Scholar
[11]	Evans R B 1983 J. Acoust. Soc. Am. 74 188 Google Scholar
[12]	Porter M B, Jensen F B, Ferla C M 1991 J. Acoust. Soc. Am. 89 1058 Google Scholar
[13]	Abawi A T, Kuperman W A 1997 J. Acoust. Soc. Am. 102 233 Google Scholar
[14]	Knobles D P, Stotts S A, Koch R A 2003 J. Acoust. Soc. Am. 113 781 Google Scholar
[15]	莫亚枭, 朴胜春, 张海刚, 李丽 2016 声学学报 41 154 Google Scholar Mo Y X, Piao S C, Zhang H G, Li L 2016 Acta Acustica 41 154 Google Scholar
[16]	Kennett B L N 1984 Geophys. J. R. Astron. Soc. 79 235 Google Scholar
[17]	Odom R I 1986 Geophys J. R. Astron. Soc. 86 425 Google Scholar
[18]	Hall M 1986 J. Acoust. Soc. Am. 79 332 Google Scholar
[19]	Maupin V 1988 Geophys. J. 93 173 Google Scholar
[20]	Collins M D 1993 J. Acoust. Soc. Am. 94 975 Google Scholar
[21]	Collins M D, Siegmann W L 1999 J. Acoust. Soc. Am. 105 687 Google Scholar
[22]	Jeroen T 1994 Geophys. J. Int. 117 153 Google Scholar
[23]	Abawi A T, Porter M B P 2008 https://apps.dtic.mil/dtic/tr/fulltext/u2/a541636.pdf
[24]	Odom R I, Park M, Mercer J A, Crosson R S, Paik P 1996 J. Acoust. Soc. Am. 100 2079 Google Scholar
[25]	Abawi A T, Porter M B 2007 J. Acoust. Soc. Am. 121 1374 Google Scholar
[26]	Xie Z, Matzen Rene, Cristini P, Komatitsch D, Martin R 2016 J. Acoust. Soc. Am. 140 165 Google Scholar
[27]	骆文于, 于晓林, 张仁和 2016 声学学报 41 321 Google Scholar Luo W Y, Yu X L, Zhang R H 2016 Acta Acustica 41 321 Google Scholar
[28]	莫亚枭, 朴胜春, 张海刚, 李丽 2014 声学学报 39 428 Google Scholar Mo Y X, Piao S C, Zhang H G, Li L 2014 Acta Acustica 39 428 Google Scholar
[29]	Chapman D M F, Ward P D, Ellis D D 1989 J. Acoust. Soc. Am. 85 648 Google Scholar
[30]	McCollom B A, Collis J M 2014 J. Acoust. Soc. Am. 136 1036 Google Scholar
[31]	Zhang Z Y, Tindle C T 1993 J. Acoust. Soc. Am. 93 205 Google Scholar
[32]	Stickler D C 1975 J. Acoust. Soc. Am. 57 856 Google Scholar
[33]	Westwood E K, Koch R A 1999 J. Acoust. Soc. Am. 106 2513 Google Scholar
[34]	Westwood E K, Tindle C T, Chapman N R 1996 J. Acoust. Soc. Am. 100 3631 Google Scholar
[35]	杨士莪 1994 水声传播原理 (哈尔滨: 哈尔滨工程大学出版社) 第16页 Yang S E 1994 Principle of Underwater Acoustic Propagation (Harbin: Haerbin Engineering University Press) p16 (in Chinese)

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倾斜弹性海底条件下浅海声场的简正波相干耦合特性分析