Complete analytical solutions for guided waves along a parabolic symmetrical ridge

Liu Jianhao; Wang Gang; Guo Hai; Zheng Jinhai; Du Qilu

doi:10.12284/hyxb2023095

Volume 45 Issue 6

Jun. 2023

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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

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

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Complete analytical solutions for guided waves along a parabolic symmetrical ridge

doi: 10.12284/hyxb2023095

Liu Jianhao^{1, 2
,},
Wang Gang^{1, 2
,
,},
Guo Hai³,
Zheng Jinhai^{1, 2},
Du Qilu⁴

1.
Key Laboratory of Coastal Disaster and Defence, Ministry of Education, Hohai University, Nanjing 210098, China
2.
College of Harbour, Coastal and Offshore Engineering, Hohai University , Nanjing 210098, China
3.
National Ocean Technology Center, Tianjin 300112, China
4.
Nanjing Communications Institute of Technology, Nanjing 211188, China

Received Date: 2022-10-08
Rev Recd Date: 2023-01-30

Available Online: 2023-04-27

Publish Date: 2023-06-30

Abstract

Abstract

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

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References(26)

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