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Mode coupling and intensity fluctuation of sound propagation over continental slope in presence of internal waves

Gao Fei Xu Fang-Hua Li Zheng-Lin Qin Ji-Xing

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Mode coupling and intensity fluctuation of sound propagation over continental slope in presence of internal waves

Gao Fei, Xu Fang-Hua, Li Zheng-Lin, Qin Ji-Xing
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  • The topographic variation underwater of the continental slope is one of the main causes for triggering off the formation of internal waves, and the continental slope internal waves are ubiquitous in the ocean. The horizontal variation of waveguide environment, caused by the internal wave and the continental slope, can lead to acoustic normal mode coupling, and then generate sound field fluctuation. Most of the existing research work focused on studying the effect of single perturbation factor of either the internal waves or the continental slope on acoustic mode coupling and intensity fluctuation, while it is hard to find some research work that takes into account both the internal waves and the topographic variations as influencing factors. In this work, numerical simulations for the sound waves to propagate through the internal waves in the downhill direction are performed by using the acoustic coupled normal-mode model in four waveguide environments: thermocline, internal wave, continental slope and continental slope internal wave. And the mode coupling and intensity fluctuation characteristics and their physical mechanisms are studied by comparing and analyzing the simulation results of the four different waveguide environment constructed. Some conclusions are obtained as follows. The intra-mode conduction coefficients are symmetric with respect to the center of the internal wave, while the inter-mode coupling coefficients are antisymmetric around it. As the sound waves propagate toward or away from the center of the internal wave, the acoustic mode coupling becomes enhanced or weakened, and the coupling coefficients curves for large mode oscillate. The influence of internal wave perturbation makes the energy transfer from the smaller modes to the larger modes, which increases the attenuation of sound field intensity. The number of the waveguide modes increases and the mode intensity attenuation decreases, when the sound waves propagate downhill. The total intensity of all modes for the continental slope internal wave environment is greater than for the internal wave environment and less than for the continental environment, and the energy transfer between mode groups is stronger than for individual effect of internal wave or continental slope, which leads more energy to transfer from the smaller to larger mode groups and the energy of the sound field above the thermocline to increase.
      Corresponding author: Xu Fang-Hua, fxu@mails.tsinghua.edu.cn ; Qin Ji-Xing, qjx@mail.ioa.ac.cn
    • Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2020YFA0607900), the National Natural Science Foundation of China (Grant Nos. 42176019, 11874061), and the Youth Innovation Promotion Association, Chinese Academy of Sciences (Grant No. 2021023).
    [1]

    Whalen C B, Lavergne C D, Garabato N A C, Klymak J M, Mackinnon J A, Sheen 2020 Nature 1 606

    [2]

    Alford M H, Mackinnon J A, Simmons H L Nash J D 2016 Annu. Rev. Mar. Sci. 8 95Google Scholar

    [3]

    Zhao Z, Alford M H, Girton J B, Rainville L, Simmons H L 2016 J. Phys. Oceanogr. 46 1657Google Scholar

    [4]

    Grisouard N, Staquet C 2010 Nonlinear Processes Geophys. 17 575Google Scholar

    [5]

    张泽众, 骆文于, 庞哲, 周益清 2019 物理学报 68 204302Google Scholar

    Zhang Z Z, Luo W Y, Pan Z, Zhou Y Q 2019 Acta Phys. Sin. 68 204302Google Scholar

    [6]

    Preisig J C, Duda T F 1997 IEEE J. Oceanic Eng. 22 256Google Scholar

    [7]

    Zhou J X, Zhang X Z, Rogers P H 1991 J. Acoust. Soc. Am. 90 2042Google Scholar

    [8]

    Rouseff D, Turgut A, Wolf S N, Finette S, Orr M H, Pasewark B H, Apel J R, Badiey M, Chiu C S, Headrick R H, Lynch J F, Kemp J N, Newhall A E, von der Heydt K, Tielbuerger D 2002 J. Acoust. Soc. Am. 111 1655Google Scholar

    [9]

    Katsnelson B G, Pereselkov S A 2000 Acoust. Phys. 46 684Google Scholar

    [10]

    Lin Y T, Duda T F, Lynch J F 2009 J. Acoust. Soc. Am. 126 1752Google Scholar

    [11]

    Milone M A, DeCourcy B J, Lin Y T, Siegmann 2019 J. Acoust. Soc. Am. 146 1934Google Scholar

    [12]

    秦继兴, Katsnelson Boris, 彭朝晖, 李整林, 张仁和, 骆文于 2016 物理学报 65 034301Google Scholar

    Qin J X, Katsnelson B G, Peng Z H, Li Z L, Zhang R H, Luo W Y 2016 Acta Phys. Sin. 65 034301Google Scholar

    [13]

    Chiu C S, Ramp S R, Miller C W, Lynch J F, Duda T F, Tang T Y 2004 IEEE J. Oceanic Eng. 29 1249Google Scholar

    [14]

    秦继兴, Katsnelson Boris, 李整林, 张仁和, 骆文于 2016 声学学报 41 145

    Qin J X, Katsnelson B G, Li Z L, Zhang R H, Luo W Y 2016 Acta Acustia 41 145

    [15]

    Badiey M, Katsnelson B G, Lynch J F, Pereselkov S, Siegmann W L 2005 J. Acoust. Soc. Am. 117 613Google Scholar

    [16]

    李沁然, 孙超, 谢磊 2022 物理学报 71 024302Google Scholar

    Li Q R, Sun C, Xie L 2022 Acta Phys. Sin. 71 024302Google Scholar

    [17]

    Chiu L Y S, Chang A Y Y, Reeder D B 2015 J. Acoust. Soc. Am. 138 515Google Scholar

    [18]

    刘代, 李整林, 刘若芸 2021 物理学报 70 034302Google Scholar

    Liu D, Li Z L, Liu R Y 2021 Acta Phys. Sin. 70 034302Google Scholar

    [19]

    莫亚枭, 朴胜春, 张海刚, 李丽 2014 物理学报 63 214302Google Scholar

    Mo Y X, Piao S C, Zhang H G Li L 2014 Acta Phys. Sin. 63 214302Google Scholar

    [20]

    Sagers J D, Ballard M S, Knobles D P 2014 J. Acoust. Soc. Am. 136 2453Google Scholar

    [21]

    Chiu L Y S, Reeder D B, Chang Y Y, Chen C F, Chiu C S, Lynch J F 2013 J. Acoust. Soc. Am. 133 1306Google Scholar

    [22]

    Porter M B 1991 The KRAKEN Normal Mode Program (La Spezia: SACLANT Undersea Research Centre) Technical Report SM-2

    [23]

    Jensen F B, Kuperman W A, Porter M B, Schmidt H 2011 Computational Ocean Acoustics (New York: Springer) pp403–408

    [24]

    Apel J R, Ostrovsky L A, Stepanyants Y A, Lynch J F 2007 J. Acoust. Soc. Am. 121 695Google Scholar

    [25]

    Yang T C 2014 J. Acoust. Soc. Am. 135 610Google Scholar

    [26]

    Dozier L B, Tappert F D 1978 J. Acoust. Soc. Am. 63 353Google Scholar

    [27]

    Yang T C 2017 IEEE J. Oceanic Eng. 42 663Google Scholar

  • 图 1  大陆坡内波波导环境参数示意图

    Figure 1.  Diagram of parameters for continental slope internal wave waveguide environment.

    图 2  仿真用四种典型海洋环境 (a) 环境1(跃层环境); (b) 环境2(内波环境); (c)环境3(大陆坡环境); (d) 环境4(大陆坡内波环境)

    Figure 2.  Four typical environments for simulation: (a) Environment 1 (thermocline); (b) environment 2 (internal wave); (c) environment 3 (continental slope); (d) environment 4 (continental slope internal wave).

    图 3  内波环境水平声速梯度分布

    Figure 3.  Distributions of horizontal sound speed gradient in internal wave environment.

    图 4  第1—4号简正波在不同波导环境中水平距离2—4 km处的模内传导系数$ C_{m, m}^{j + 1} $ (a) 1号模态; (b) 2号模态; (c) 3号模态; (d) 4号模态

    Figure 4.  The intra-mode conduction coefficients $ C_{m, m}^{j + 1} $ of mode 1, 2, 3 and 4 at range 2–4 km in different waveguide environments: (a) Mode 1; (b) mode 2; (c) mode 3; (d) mode 4.

    图 5  不同波导环境中水平距离2—4 km处的模间耦合系数$ C_{1, n}^{j{\text{ + }}1} $ (a) 1号与2号模态; (b) 1号与3号模态; (c) 1号与5号模态; (d) 1号与13号模态

    Figure 5.  The inter-mode coupling coefficients $ C_{1, n}^{j{\text{ + }}1} $ at range of 2–4 km in different waveguide environments: (a) Mode 1 with 2; (b) mode 1 with 3; (c) mode 1 with 5; (d) mode 1 with 13.

    图 6  不同波导环境中1号局地模态函数 (a) 内波环境; (b) 大陆坡环境; (c) 大陆坡内波环境

    Figure 6.  The local function of mode 1 in different waveguide environments: (a) Internal wave environment; (b) continental slope environment; (c) continental slope internal wave environment.

    图 7  不同波导环境中1—20号简正波模态强度随距离变化 (a) 跃层环境; (b) 内波环境; (c) 大陆坡环境; (d) 大陆坡内波环境, 红色点划线为1—6号模态, 蓝色实线为7—13号模态, 黑色点线为14—20号模态

    Figure 7.  Modes 1–20 intensity variation with range in different waveguide environments: (a) Thermocline environment; (b) internal wave environment; (c) continental slope environment; (d) continental slope internal wave environment, the red dotted lines, blue solid lines and black dotted lines represent mode groups of 1–6, 7–13 and 14–20, respectively.

    图 8  内波波导环境中8号(a), 11号(b)简正波模态声场强度分布

    Figure 8.  The mode 8 (a) and mode 11 (b) intensity versus range and depth in the internal wave environment.

    图 9  大陆坡波导环境中不同水平距离前13号简正波模态特征值分布, 特征值实部大于横虚线为波导模态

    Figure 9.  Eigenvalues of the first 13 modes of different ranges in the continental slope environment.

    图 10  不同波导环境中各组模态强度之和随距离变化 (a) 所有模态$ {I_{{\text{1}}—{\max}}} $; (b) 1—6号模态$ {I_{{\text{1}}—{\text{6}}}} $; (c) 7—13号模态$ {I_{{\text{7}}—{\text{13}}}} $; (d) 14号以上模态$ {I_{{\text{14}}—{\max}}} $

    Figure 10.  The sum of intensity of each mode groups versus range in different environments: (a) $ {I_{{\text{1}}—{\max}}} $; (b) $ {I_{{\text{1}}—{\text{6}}}} $; (c) ${I_{{\text{7}}—{\text{13}}}}$; (d) $ {I_{{\text{14}}—{\max}}} $.

    图 11  大陆坡内波环境中2.7—3.3 km范围内第4—8号简正波模态强度

    Figure 11.  Intensity of modes 4–8 for at range 2.7–3.3 km in the continental slope internal wave environment.

    图 12  不同环境中参数变数时的模态强度之和$ {I_{{\text{1}}—{\text{6}}}} $随距离的变化 (a), (c), (e) 大陆坡内波环境; (b) 大陆坡环境; (d), (f) 内波环境

    Figure 12.  The sum of intensity$ {I_{{\text{1}}—{\text{6}}}} $versus range in different environments of various parameters: (a), (c), (e) Continental slope internal wave environment; (b) continental slope environment; (d), (f) internal wave environment.

    图 13  不同环境中的声场分布 (a), (c), (e) 大陆坡环境3中的所有模态、1—6号模态、7—max号模态声场; (b), (d), (f) 大陆坡内波环境4中的所有模态、1—6号模态、7—max号模态声场. 其中, 图中虚线方框标记了0—35 m深度、2—6 km水平距离的区域

    Figure 13.  The sound field in different environments: (a), (c), (e) The sound fields of the whole modes, models 1–6 and modes 7–max in continental slope environment, respectively; (b), (d), (f) the sound fields of the whole modes, models 1–6 and modes 7–max in continental slope internal wave environment, respectively. The white dashed boxes mark the area of 0–35 m and 2–6 km horizontal distance.

    表 1  仿真环境参数配置

    Table 1.  Configuration of environment parameters for simulations.

    参数类型参数值
    跃层上边界深度$ {z_{\text{u}}}/{\text{m}} $15
    跃层下边界深度$ {z_{\text{l}}} $/m35
    水体声速$ {c_{\text{u}}} $, $ {c_{\text{l}}} $/(m·s–1)1530, 1500
    内波的幅度$\varLambda$/m35
    内波的中心距离$ {r_0} $/km3
    内波的波宽$\varDelta$/m300
    大陆坡起点距离$ {r_{\text{s}}}/{\text{km}} $、水深$ {H_{\text{s}}}/{\text{m}} $2, 100
    大陆坡终点距离$ {r_{\text{e}}}/{\text{km}} $、水深$ {H_{\text{e}}}/{\text{m}} $4, 200
    大陆坡坡度/(°)2.86 (1/10)
    DownLoad: CSV
  • [1]

    Whalen C B, Lavergne C D, Garabato N A C, Klymak J M, Mackinnon J A, Sheen 2020 Nature 1 606

    [2]

    Alford M H, Mackinnon J A, Simmons H L Nash J D 2016 Annu. Rev. Mar. Sci. 8 95Google Scholar

    [3]

    Zhao Z, Alford M H, Girton J B, Rainville L, Simmons H L 2016 J. Phys. Oceanogr. 46 1657Google Scholar

    [4]

    Grisouard N, Staquet C 2010 Nonlinear Processes Geophys. 17 575Google Scholar

    [5]

    张泽众, 骆文于, 庞哲, 周益清 2019 物理学报 68 204302Google Scholar

    Zhang Z Z, Luo W Y, Pan Z, Zhou Y Q 2019 Acta Phys. Sin. 68 204302Google Scholar

    [6]

    Preisig J C, Duda T F 1997 IEEE J. Oceanic Eng. 22 256Google Scholar

    [7]

    Zhou J X, Zhang X Z, Rogers P H 1991 J. Acoust. Soc. Am. 90 2042Google Scholar

    [8]

    Rouseff D, Turgut A, Wolf S N, Finette S, Orr M H, Pasewark B H, Apel J R, Badiey M, Chiu C S, Headrick R H, Lynch J F, Kemp J N, Newhall A E, von der Heydt K, Tielbuerger D 2002 J. Acoust. Soc. Am. 111 1655Google Scholar

    [9]

    Katsnelson B G, Pereselkov S A 2000 Acoust. Phys. 46 684Google Scholar

    [10]

    Lin Y T, Duda T F, Lynch J F 2009 J. Acoust. Soc. Am. 126 1752Google Scholar

    [11]

    Milone M A, DeCourcy B J, Lin Y T, Siegmann 2019 J. Acoust. Soc. Am. 146 1934Google Scholar

    [12]

    秦继兴, Katsnelson Boris, 彭朝晖, 李整林, 张仁和, 骆文于 2016 物理学报 65 034301Google Scholar

    Qin J X, Katsnelson B G, Peng Z H, Li Z L, Zhang R H, Luo W Y 2016 Acta Phys. Sin. 65 034301Google Scholar

    [13]

    Chiu C S, Ramp S R, Miller C W, Lynch J F, Duda T F, Tang T Y 2004 IEEE J. Oceanic Eng. 29 1249Google Scholar

    [14]

    秦继兴, Katsnelson Boris, 李整林, 张仁和, 骆文于 2016 声学学报 41 145

    Qin J X, Katsnelson B G, Li Z L, Zhang R H, Luo W Y 2016 Acta Acustia 41 145

    [15]

    Badiey M, Katsnelson B G, Lynch J F, Pereselkov S, Siegmann W L 2005 J. Acoust. Soc. Am. 117 613Google Scholar

    [16]

    李沁然, 孙超, 谢磊 2022 物理学报 71 024302Google Scholar

    Li Q R, Sun C, Xie L 2022 Acta Phys. Sin. 71 024302Google Scholar

    [17]

    Chiu L Y S, Chang A Y Y, Reeder D B 2015 J. Acoust. Soc. Am. 138 515Google Scholar

    [18]

    刘代, 李整林, 刘若芸 2021 物理学报 70 034302Google Scholar

    Liu D, Li Z L, Liu R Y 2021 Acta Phys. Sin. 70 034302Google Scholar

    [19]

    莫亚枭, 朴胜春, 张海刚, 李丽 2014 物理学报 63 214302Google Scholar

    Mo Y X, Piao S C, Zhang H G Li L 2014 Acta Phys. Sin. 63 214302Google Scholar

    [20]

    Sagers J D, Ballard M S, Knobles D P 2014 J. Acoust. Soc. Am. 136 2453Google Scholar

    [21]

    Chiu L Y S, Reeder D B, Chang Y Y, Chen C F, Chiu C S, Lynch J F 2013 J. Acoust. Soc. Am. 133 1306Google Scholar

    [22]

    Porter M B 1991 The KRAKEN Normal Mode Program (La Spezia: SACLANT Undersea Research Centre) Technical Report SM-2

    [23]

    Jensen F B, Kuperman W A, Porter M B, Schmidt H 2011 Computational Ocean Acoustics (New York: Springer) pp403–408

    [24]

    Apel J R, Ostrovsky L A, Stepanyants Y A, Lynch J F 2007 J. Acoust. Soc. Am. 121 695Google Scholar

    [25]

    Yang T C 2014 J. Acoust. Soc. Am. 135 610Google Scholar

    [26]

    Dozier L B, Tappert F D 1978 J. Acoust. Soc. Am. 63 353Google Scholar

    [27]

    Yang T C 2017 IEEE J. Oceanic Eng. 42 663Google Scholar

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  • Received Date:  07 April 2022
  • Accepted Date:  24 June 2022
  • Available Online:  10 October 2022
  • Published Online:  20 October 2022

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