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 parameterγis 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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