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抛物型对称海脊引导波完整解析理论

刘建豪 王岗 郭海 郑金海 杜齐鲁

刘建豪,王岗,郭海,等. 抛物型对称海脊引导波完整解析理论[J]. 海洋学报,2023,45(6):36–43 doi: 10.12284/hyxb2023095
引用本文: 刘建豪,王岗,郭海,等. 抛物型对称海脊引导波完整解析理论[J]. 海洋学报,2023,45(6):36–43 doi: 10.12284/hyxb2023095
Liu Jianhao,Wang Gang,Guo Hai, et al. Complete analytical solutions for guided waves along a parabolic symmetrical ridge[J]. Haiyang Xuebao,2023, 45(6):36–43 doi: 10.12284/hyxb2023095
Citation: Liu Jianhao,Wang Gang,Guo Hai, et al. Complete analytical solutions for guided waves along a parabolic symmetrical ridge[J]. Haiyang Xuebao,2023, 45(6):36–43 doi: 10.12284/hyxb2023095

抛物型对称海脊引导波完整解析理论

doi: 10.12284/hyxb2023095
基金项目: 国家自然科学基金委−山东联合基金(U1906230);国家自然科学基金面上项目(52071128);江苏省自然科学基金杰出青年基金(BK20220082);江苏省高职院校青年教师企业实践培训项目(2021QYSJ049)。
详细信息
    作者简介:

    刘建豪(1998-),女,湖南省娄底市人,主要从事海啸传播变形与数值模拟研究。E-mail:jianhao_liu@hhu.edu.cn

    通讯作者:

    王岗(1982-),男,河北省张家口市人,教授,主要从事波浪传播变形研究。E-mail:gangwang@hhu.edu.cn

  • 中图分类号: TV139.2

Complete analytical solutions for guided waves along a parabolic symmetrical ridge

  • 摘要: 越洋海啸能够被大洋海脊引导并沿海脊传播至远场地区,虽然传播速度较慢,但携带较大的能量,会对远场地区造成灾害影响,相关研究对于提高海啸传播特性本质的认识具有重要意义。本文基于线性长波方程,推导出了抛物型对称海脊引导波完整解析理论。研究表明对称型海脊同时存在对称与反对称引导波,其自由水面波动可以表示为虚宗量Bessel函数形式。利用海脊中心对称条件给出了描述其频率与波数的频散关系。基于所提理论进一步分析讨论了引导波的运动特性,包括频散关系、波速度、能量传播速度与波面空间分布等。本研究为揭示地形坡度由脊顶至两侧逐渐增加的海脊引导波运动特征,预测实际越洋海啸中最具威胁性海啸波的到达时间提供了理论依据。
  • 图  1  抛物型海脊剖面

    Fig.  1  Schematic of parabolic ridge profile

    图  2  抛物型海脊引导波的频散关系

    实线表示偶对称模式,虚线表示奇对称模式

    Fig.  2  Dispersion relationships for guided waves over a parabolic ridge

    The solid lines indicate the even-symmetric mode and the dashed lines represent the odd-symmetric mode

    图  3  引导波的相位速度、能量传播速度因子与能量传播速度随角频率ω和地形参数s、b变化示意图

    实线表示偶对称模式,虚线表示奇对称模式

    Fig.  3  Phase velocity, energy velocity factor and group velocity against angular frequency ω, and ridge shape parameters s, b for guided waves

    The solid lines indicate the even-symmetric mode and the dashed lines represent the odd-symmetric mode

    图  4  抛物型海脊引导波沿x方向的空间分布

    实线表示偶对称模式,虚线表示奇对称模式(s = 7.63×10−7 m−1b = 1.62×104 m,h0 = 200 m,T = 180 s)

    Fig.  4  Spatial distribution of guided waves over a parabolic ridge along the x-axis

    The solid lines indicate the even-symmetric mode and the dashed lines represent the odd-symmetric mode (s = 7.63×10−7 m−1, b = 1.62×104 m, h0 = 200 m, T = 180 s)

    图  5  引导波的三维空间分布(s = 7.63×10−7 m−1b = 1.62×104 m,h0 = 200 m,T = 180 s)

    a–d为偶对称模式,e–h为奇对称模式

    Fig.  5  Three-dimensional spatial distribution of guided waves (s = 7.63×10−7 m−1b = 1.62×104 m,h0 = 200 m,T = 180 s)

    a–d indicates the even-symmetric mode and the e–h represents the odd-symmetric mode

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出版历程
  • 收稿日期:  2022-10-08
  • 修回日期:  2023-01-30
  • 网络出版日期:  2023-04-27
  • 刊出日期:  2023-06-30

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