Improvements on the normal mode decomposition method used in harbor resonance

In the article by Sobey (Rodney J. Sobey, 2006. Normal mode decomposition for identification of storm tide and tsunami hazard. Coastal Engineering 53, 289–301), the author proposed a normal mode decomposition method to calculate the eigenfrequencies, the eigenmodes and the response amplitudes of different resonant modes in natural harbors that are subjected to storm tides and tsunamis. However, the numerical method to address the no-flow boundary condition in that article is imprecise, which would lead to inexact eigenfrequencies and eigenmodes. In this article, the mirror-image method was proposed to improve this handling process. The accuracy of the improved normal mode decomposition method was verified using three verification tests. With a set of numerical experiments, it was determined that during the process of decomposing the response amplitudes of different resonant modes, the numerical fitting error between the simulated free surfaces and the corresponding fitted ones gradually increases with the wave nonlinearity inside the harbor. This article sought to identify the critical wave condition under which the normal mode decomposition method can accurately decompose the response amplitudes of different modes.

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