Trapping mechanism of submerged ridge on trans-oceanic tsunami propagation |
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| Authors: | Jin-hai Zheng Meng-jie Xiong Gang Wang |
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| Institution: | 1.State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering,Hohai University,Nanjing,China;2.College of Harbor, Coastal and Offshore Engineering,Hohai University,Nanjing,China;3.Nanjing Hydraulic Research Institute,Nanjing,China;4.State Key Laboratory of Coastal and Offshore Engineering,Dalian University of Technology,Dalian,China;5.The Key Laboratory of Water-Sediment Sciences and Water Disaster Prevention of Hunan Province,Changsha University of Science and Technology,Changsha,China |
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| Abstract: | Based on the linear shallow water equations, an analytic solution of trapped waves over a symmetric parabolic-profile submerged ridge is derived. The trapped waves act as propagating waves along the ridge and as standing waves across the ridge. The amplitude gets the maximum at the ridge top and decays gradually towards both sides. The decaying rate gets more gently with higher modes. Besides, an explicit first-order approximate dispersion relation is derived to simplify transcendental functions in the exact solution, which is useful to describe trapped waves over shallowly submerged ridges in reality. Furthermore, the trapping mechanism of the submerged ridge waveguides on the trans-oceanic tsunami propagation can be explained by the ray theory. A critical incident angle exists as a criterion to determine whether the wave is trapped. Besides, a trapped parameter γ is proposed to estimate the ratio of the energy trapped by the oceanic ridge if a tsunami is generated at its top. |
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