251. Analytical and numerical investigation of trapped ocean waves along a submerged ridge
- Author
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Jinhai Zheng, Gang Wang, Qiuhua Liang, and Fengyan Shi
- Subjects
geography ,geography.geographical_feature_category ,010504 meteorology & atmospheric sciences ,Topographic profile ,Mechanical Engineering ,Mid-ocean ridge ,Mechanics ,010502 geochemistry & geophysics ,Condensed Matter Physics ,Ridge (differential geometry) ,01 natural sciences ,Legendre function ,Wave model ,Mechanics of Materials ,Free surface ,Wind wave ,Dispersion (water waves) ,Geology ,0105 earth and related environmental sciences - Abstract
Based on the linear shallow-water equations, new analytical solutions are derived for trapped waves over a ridge with a hyperbolic-cosine squared cross-sectional profile which may be used to idealize many real-world ocean ridges. In the new analytical formulation, the free surface of the trapped waves is described using the combination of the first and second kinds of the associated Legendre functions, which is further analysed to reveal the existence of both symmetrical and anti-symmetrical trapped waves on the ridge under consideration. New algebraic equations are also derived to depict the wave dispersion relationships, allowing explicit quantification of their sensitivity to the topographic profile. Furthermore, a ray-tracing method is applied to interpret the propagation paths of trapped waves over the ridge and better understand the excitation mechanisms. Finally, an extensively validated Boussinesq wave model is used to conduct numerical experiments for trapped waves induced by tsunamis. The numerical predictions are consistent with the new analytical solutions, which effectively confirms the validity of the new analytical framework for trapped waves over a more general type of oceanic ridges.
- Published
- 2021
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