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Complete analytical solutions for guided waves along a parabolic symmetrical ridge
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Jianhao Liu1, 2, Gang Wang1, 2, *, Hai Guo3, Jinhai Zheng1, 2, Qilu Du4
Haiyang Xuebao | 2023, 45(6) : 36 - 43
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Haiyang Xuebao | 2023, 45(6): 36-43
• Article •
Complete analytical solutions for guided waves along a parabolic symmetrical ridge
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Jianhao Liu1, 2, Gang Wang1, 2, *, Hai Guo3, Jinhai Zheng1, 2, Qilu Du4
Affiliations
  • 1Key Laboratory of Coastal Disaster and Defence, Ministry of Education, Hohai University, Nanjing 210098, China
  • 2College of Harbour, Coastal and Offshore Engineering, Hohai University , Nanjing 210098, China
  • 3National Ocean Technology Center, Tianjin 300112, China
  • 4Nanjing Communications Institute of Technology, Nanjing 211188, China
Published: 2023-06-30 doi: 10.12284/hyxb2023095
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Transoceanic tsunamis can be guided by oceanic ridges and transferred large energy with slower velocity, hitting far-field regions and causing disaster effects. Therefore, the study on guided waves is crucial to improve the understanding of tsunami propagation characteristics. Based on the linear shallow water equation, the complete analytical solutions for guided waves over a parabolic symmetric ridge are derived. It is shown that both symmetric and anti-symmetric guided waves can exist along symmetric ridges and the free surface is described using the modified Bessel functions. Dispersion relationships, determining the relationship between the wave frequency and the wavenumber, are obtained from the continuity of water surface and velocity at the top of the ridge. The kinematic characteristics of guided waves, such as phase velocity, group velocity and surface spatial distribution are further revealed. This paper theoretically elaborates the guided waves over the ridge with its topographic slope generally increasing from the top to the bottom and provides the formulas to predicate the arrival time of the most threatening waves for the actual transoceanic tsunamis.

tsunamis  /  oceanic guided waves  /  trapped waves  /  analytical solutions  /  linear shallow water equations
Jianhao Liu, Gang Wang, Hai Guo, Jinhai Zheng, Qilu Du. Complete analytical solutions for guided waves along a parabolic symmetrical ridge[J]. Haiyang Xuebao, 2023 , 45 (6) : 36 -43 . DOI: 10.12284/hyxb2023095
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Year 2023 volume 45 Issue 6
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Article Info
doi: 10.12284/hyxb2023095
  • Receive Date：2022-10-08
  • Online Date：2025-12-26
  • Published：2023-06-30
Article Data
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History
  • Received：2022-10-08
  • Revised：2023-01-30
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Affiliations
    1Key Laboratory of Coastal Disaster and Defence, Ministry of Education, Hohai University, Nanjing 210098, China
    2College of Harbour, Coastal and Offshore Engineering, Hohai University , Nanjing 210098, China
    3National Ocean Technology Center, Tianjin 300112, China
    4Nanjing Communications Institute of Technology, Nanjing 211188, China
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表12种不同金属材料的力学参数
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小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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