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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

张士钊 朴胜春

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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

张士钊, 朴胜春

Coherent mode coupling in shallow water overlaying sloping elastic ocean bottom

Zhang Shi-Zhao, Piao Sheng-Chun
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  • 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.
    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.
      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.
      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).
    [1]

    Pekeris C L 1948 Mem. Geol. Soc. Amer. 27 48Google Scholar

    [2]

    Press F, Ewing M 1950 Geophysics 15 426Google Scholar

    [3]

    Porter M B, Reiss E L 1985 J. Acoust. Soc. Am. 77 1760Google Scholar

    [4]

    Ainslie M A 1995 J. Acoust. Soc. Am. 97 954Google Scholar

    [5]

    Schneiderwind J D, Collis J M, Simpson H J 2012 J. Acoust. Soc. Am. 132 EL182Google Scholar

    [6]

    Pierce A D 1965 J. Acoust. Soc. Am. 37 19Google Scholar

    [7]

    Chwieroth F S, Nagl A, Uberall H, Zarur G L 1978 J. Acoust. Soc. Am. 64 1105Google Scholar

    [8]

    Williams A O 1980 J. Acoust. Soc. Am. 67 177Google Scholar

    [9]

    Rutherford S R, Hawker K E 1981 J. Acoust. Soc. Am. 70 554Google Scholar

    [10]

    McDaniel S T 1982 J. Acoust. Soc. Am. 72 916Google Scholar

    [11]

    Evans R B 1983 J. Acoust. Soc. Am. 74 188Google Scholar

    [12]

    Porter M B, Jensen F B, Ferla C M 1991 J. Acoust. Soc. Am. 89 1058Google Scholar

    [13]

    Abawi A T, Kuperman W A 1997 J. Acoust. Soc. Am. 102 233Google Scholar

    [14]

    Knobles D P, Stotts S A, Koch R A 2003 J. Acoust. Soc. Am. 113 781Google Scholar

    [15]

    莫亚枭, 朴胜春, 张海刚, 李丽 2016 声学学报 41 154Google Scholar

    Mo Y X, Piao S C, Zhang H G, Li L 2016 Acta Acustica 41 154Google Scholar

    [16]

    Kennett B L N 1984 Geophys. J. R. Astron. Soc. 79 235Google Scholar

    [17]

    Odom R I 1986 Geophys J. R. Astron. Soc. 86 425Google Scholar

    [18]

    Hall M 1986 J. Acoust. Soc. Am. 79 332Google Scholar

    [19]

    Maupin V 1988 Geophys. J. 93 173Google Scholar

    [20]

    Collins M D 1993 J. Acoust. Soc. Am. 94 975Google Scholar

    [21]

    Collins M D, Siegmann W L 1999 J. Acoust. Soc. Am. 105 687Google Scholar

    [22]

    Jeroen T 1994 Geophys. J. Int. 117 153Google 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 2079Google Scholar

    [25]

    Abawi A T, Porter M B 2007 J. Acoust. Soc. Am. 121 1374Google Scholar

    [26]

    Xie Z, Matzen Rene, Cristini P, Komatitsch D, Martin R 2016 J. Acoust. Soc. Am. 140 165Google Scholar

    [27]

    骆文于, 于晓林, 张仁和 2016 声学学报 41 321Google Scholar

    Luo W Y, Yu X L, Zhang R H 2016 Acta Acustica 41 321Google Scholar

    [28]

    莫亚枭, 朴胜春, 张海刚, 李丽 2014 声学学报 39 428Google Scholar

    Mo Y X, Piao S C, Zhang H G, Li L 2014 Acta Acustica 39 428Google Scholar

    [29]

    Chapman D M F, Ward P D, Ellis D D 1989 J. Acoust. Soc. Am. 85 648Google Scholar

    [30]

    McCollom B A, Collis J M 2014 J. Acoust. Soc. Am. 136 1036Google Scholar

    [31]

    Zhang Z Y, Tindle C T 1993 J. Acoust. Soc. Am. 93 205Google Scholar

    [32]

    Stickler D C 1975 J. Acoust. Soc. Am. 57 856Google Scholar

    [33]

    Westwood E K, Koch R A 1999 J. Acoust. Soc. Am. 106 2513Google Scholar

    [34]

    Westwood E K, Tindle C T, Chapman N R 1996 J. Acoust. Soc. Am. 100 3631Google 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)

  • 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.

    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, cs = 2000 m/s, 不考虑; (f) f = 25 Hz, cs = 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, cs = 2000 m/s, without, (f) f = 25 Hz, cs = 2000 m/s, with considering the normalization of amplitude and phase processing, compared with the sound pressure obtained by RAMS and COMSOL.

    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.

    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.

    图 5  zr = 30 m, zs = (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Bmn

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

    图 6  (a) zs = 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 zs = (a) 50, (b) 70, (c) 100 m, compared with the sound pressure when the coupling coefficient is kept as a complex number.

    图 7  zs = 50 m, 各阶简正波的(a) |am|和(b) am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 zs = 50 m, (a) |am| and (b) the phases of am 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.

    图 8  zs = (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 zs = (a) 50 and (b) 100 m.

    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|Bmn(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 |Bmn(x)| considering the leaky mode when x = 1 km when the slope is (e) 0.0125 and (f) 0.025.

    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.

    图 11  cs = (a) 1800, (b) 1900, (c) 2000 m/s时的水中声压; (d) 考虑泄漏模态条件下, cs = 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 cs = (a) 1800, (b) 1900, (c) 2000 m/s; (d) sound pressure comparison obtained by mode coupling method while condidering leaky modes when cs = 1800, 1900, 2000 m/s.

    图 12  cp = 1700 m/s, cs = (a) 600, (b) 700 和(c) 800 m/s时的水中声压; (d) cs = 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) cs = 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 cs = (a) 600, (b) 700, (c) 800 m/s; (d) sound pressure obtained by mode coupling method considering leaky modes and when cs = 600, 700, 800 m/s; (e) the attenuation coefficient of the 2nd normal mode varying with range when cs = 600, 700, 800 m/s.

    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RAMSCOMSOL
    平均耗时/s7.665.3727.33
    下载: 导出CSV
  • [1]

    Pekeris C L 1948 Mem. Geol. Soc. Amer. 27 48Google Scholar

    [2]

    Press F, Ewing M 1950 Geophysics 15 426Google Scholar

    [3]

    Porter M B, Reiss E L 1985 J. Acoust. Soc. Am. 77 1760Google Scholar

    [4]

    Ainslie M A 1995 J. Acoust. Soc. Am. 97 954Google Scholar

    [5]

    Schneiderwind J D, Collis J M, Simpson H J 2012 J. Acoust. Soc. Am. 132 EL182Google Scholar

    [6]

    Pierce A D 1965 J. Acoust. Soc. Am. 37 19Google Scholar

    [7]

    Chwieroth F S, Nagl A, Uberall H, Zarur G L 1978 J. Acoust. Soc. Am. 64 1105Google Scholar

    [8]

    Williams A O 1980 J. Acoust. Soc. Am. 67 177Google Scholar

    [9]

    Rutherford S R, Hawker K E 1981 J. Acoust. Soc. Am. 70 554Google Scholar

    [10]

    McDaniel S T 1982 J. Acoust. Soc. Am. 72 916Google Scholar

    [11]

    Evans R B 1983 J. Acoust. Soc. Am. 74 188Google Scholar

    [12]

    Porter M B, Jensen F B, Ferla C M 1991 J. Acoust. Soc. Am. 89 1058Google Scholar

    [13]

    Abawi A T, Kuperman W A 1997 J. Acoust. Soc. Am. 102 233Google Scholar

    [14]

    Knobles D P, Stotts S A, Koch R A 2003 J. Acoust. Soc. Am. 113 781Google Scholar

    [15]

    莫亚枭, 朴胜春, 张海刚, 李丽 2016 声学学报 41 154Google Scholar

    Mo Y X, Piao S C, Zhang H G, Li L 2016 Acta Acustica 41 154Google Scholar

    [16]

    Kennett B L N 1984 Geophys. J. R. Astron. Soc. 79 235Google Scholar

    [17]

    Odom R I 1986 Geophys J. R. Astron. Soc. 86 425Google Scholar

    [18]

    Hall M 1986 J. Acoust. Soc. Am. 79 332Google Scholar

    [19]

    Maupin V 1988 Geophys. J. 93 173Google Scholar

    [20]

    Collins M D 1993 J. Acoust. Soc. Am. 94 975Google Scholar

    [21]

    Collins M D, Siegmann W L 1999 J. Acoust. Soc. Am. 105 687Google Scholar

    [22]

    Jeroen T 1994 Geophys. J. Int. 117 153Google 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 2079Google Scholar

    [25]

    Abawi A T, Porter M B 2007 J. Acoust. Soc. Am. 121 1374Google Scholar

    [26]

    Xie Z, Matzen Rene, Cristini P, Komatitsch D, Martin R 2016 J. Acoust. Soc. Am. 140 165Google Scholar

    [27]

    骆文于, 于晓林, 张仁和 2016 声学学报 41 321Google Scholar

    Luo W Y, Yu X L, Zhang R H 2016 Acta Acustica 41 321Google Scholar

    [28]

    莫亚枭, 朴胜春, 张海刚, 李丽 2014 声学学报 39 428Google Scholar

    Mo Y X, Piao S C, Zhang H G, Li L 2014 Acta Acustica 39 428Google Scholar

    [29]

    Chapman D M F, Ward P D, Ellis D D 1989 J. Acoust. Soc. Am. 85 648Google Scholar

    [30]

    McCollom B A, Collis J M 2014 J. Acoust. Soc. Am. 136 1036Google Scholar

    [31]

    Zhang Z Y, Tindle C T 1993 J. Acoust. Soc. Am. 93 205Google Scholar

    [32]

    Stickler D C 1975 J. Acoust. Soc. Am. 57 856Google Scholar

    [33]

    Westwood E K, Koch R A 1999 J. Acoust. Soc. Am. 106 2513Google Scholar

    [34]

    Westwood E K, Tindle C T, Chapman N R 1996 J. Acoust. Soc. Am. 100 3631Google 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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出版历程
  • 收稿日期:  2021-05-28
  • 修回日期:  2021-06-22
  • 上网日期:  2021-08-15
  • 刊出日期:  2021-11-05

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