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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This research was financially supported by the National Natural Science Foundation of China (Grant Nos. 51579090 and 51425901), the Open Foundation of State Key Laboratory of Coastal and Offshore Engineering (Grant No. LP1405), the Open Foundation of the Key Laboratory of Water-Sediment Sciences and Water Disaster Prevention of Hunan Province (Grant No. 2014SS02), and the Fundamental Research Funds for the Central University (Hohai University, Grant No. 2014B04114).
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Zheng, Jh., Xiong, Mj. & Wang, G. Trapping mechanism of submerged ridge on trans-oceanic tsunami propagation. China Ocean Eng 30, 271–282 (2016). https://doi.org/10.1007/s13344-016-0017-7
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DOI: https://doi.org/10.1007/s13344-016-0017-7