基于势流理论的海脊俘获波产生条件与运动特性研究

许洋; 王岗; 胡见

基于势流理论的海脊俘获波产生条件与运动特性研究

许洋^1,,
王岗^{2, 3, ,},
胡见⁴

1.
山东省交通规划设计院集团有限公司，山东济南 250101
2.
河海大学海岸灾害及防护教育部重点实验室，江苏南京 210024
3.
河海大学港口海岸与近海工程学院，江苏南京 210024
4.
长江航运发展研究中心，湖北武汉 430014

基金项目: 国家自然科学基金面上项目(51579090)。

详细信息

作者简介:
许洋（1994—），男，山东省日照市人，主要从事海啸传播变形研究。E-mail：653326021@qq.com

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

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出版历程
- 收稿日期: 2026-02-28
- 修回日期: 2026-05-15
- 网络出版日期: 2026-05-25

Occurrence Conditions and Propagation Characteristics of Trapped Waves over the Submerged Ridge Based on Potential Flow Theory

Xu Yang^1
,,
Wang Gang^{2, 3
, ,},
Hu Jian⁴

1.
Shandong Provincial Communications Planning and Design Institute Group Co., Ltd, Jinan 250101, China
2.
Key Laboratory of Ministry of Education for Coastal Disaster and Protection, Hohai University, Nanjing, 210024, China
3.
College of Harbour, Coastal and Offshore Engineering, Hohai University , Nanjing 210098, China
4.
Yangtze River Shipping Development Research Center, Wuhan 430014, China

摘要

摘要: 大洋海脊能将海啸能量以俘获波的形式引导传播逾万公里，并因其独特的运动机制携带大量能量影响到远海地区，严重威胁沿岸工程及居民生命财产安全。本研究基于势流理论，推导了表征台阶地形上俘获波的解析理论，从数学上证实了台阶型海脊俘获波是由波浪在突变地形处的反射所诱发，并进一步给出了波浪发生全反射时临界入射条件的具体表达式。结果表明，低频波浪成分更易被台阶地形所俘获，且随着入射角的增大，俘获效应也愈发显著。本研究采用全水深势流理论框架，突破了已有理论仅适用于浅水波海域的局限，为分析实际陡峭海脊地形上的俘获波提供了可靠的理论依据。
- 俘获波 /
- 台阶型海脊 /
- 解析解 /
- 势流理论 /
- 海啸
Abstract: Oceanic ridges can channel tsunami energy as trapped waves that propagate over distances exceeding ten thousand kilometers. Owing to their distinct propagation characteristics, these waves carry substantial energy to remote oceanic regions, posing serious threats to coastal engineering structures and to human life and property. Using potential flow theory, this study derives an analytical solution for trapped waves over a stepped ridge. It is mathematically demonstrated that trapped waves over a step-type ridge arise from wave reflection at the abrupt topographic change, and an explicit expression is provided for the critical condition required for total internal reflection to occur—thereby enabling wave trapping. The results show that lower-frequency wave components are more readily trapped by the stepped topography, and that the trapping effect becomes increasingly pronounced as the incident wave angle increases. By adopting the full-depth potential flow theory, this study overcomes the limitation of previous theories that are applicable only to shallow-water waves, thus offering reliable theoretical formulations for investigating trapped waves over realistic, steep ridge topographies.
- Trapped Waves /
- Stepped Ridges /
- Analytical Solution /
- Potential Flow Theory /
- Tsunami

HTML全文

图 1 台阶型海脊水深分布示意图

Fig. 1 Schematic representation of the bathymetry of the stepped ridge

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图 2 不同周期波浪以相同角度在台阶地形上传播示意

Fig. 2 Schematic diagram of waves with different periods propagating on a stepped ridge at the same incident angle

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图 3 波幅沿海脊垂向分布

Fig. 3 Wave amplitude varying across the stepped ridge

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图 4 不同入射角度下反射系数随无量纲参数k₀d₁的变化

Fig. 4 Variation of reflection coefficient with dimensionless parameter k₀d₁ under different incident angles

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图 5 不同水深比d₂/d₁条件下反射系数随k₀d₁的变化

Fig. 5 Variation of reflection coefficient with d₂/d₁ under different water depth ratios d₂/d₁

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图 6 全反射条件下入射角与k₀d₁和d₂/d₁的关系

Fig. 6 Relationship between incident angle, k₀d₁ and d₂/d₁ under total reflection conditions

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