A finite difference numerical model, which can correctly consider dispersion effect of waves over a slowly varying water depth, is developed for the simulation of tsunami propagation. The present model employs a linear Boussinesq-type wave equation that can be solved more easily than typical Boussinesq equations. In the present model numerical dispersion is minimized by controlling the dispersion-correction parameter determined by the time step, grid size and local water depth. In order to examine the applicability of the present model to dispersive waves, the propagation of tsunamis is simulated for an initial water surface displacement of Gaussian shape for the cases of several constant water depths and a submerged circular shoal. The numerical results are compared with analytical solutions or numerical solutions of linearized Boussinesq equations. The comparisons show that satisfactory agreement is obtained.
A rip-current warning index function, which is estimated from the likelihood of rip current quantified based on numerical simulations under various sea environments and is varied according to real-time buoy-observations, was studied to help protect against rip current accidents at Haeundae beach. For the quantification, the definition of likelihood of rip current, which proposed by Choi et al. (2011Choi et al. ( , 2012b, was employed and estimated based on Boussinesq modelling. The distribution of likelihood of rip current was evaluated by using various simulations according to scenarios established based on physical quantities(i.e., wave parameters) of buoy-observations. To index the likelihood of rip current, empirical functions were derived based on the distribution and adjusted to observational environments. In this study, the observations from June to September in 2011 at Haeundae beach were applied to the rip-current index functions, and its applications into the real events found based on CCTV images were presented and investigated. In addition, limitations and improvements of the rip-current index function were discussed.
In this study, a numerical modeling system based on the dispersion-correction finite difference scheme equipped with a grid-nesting scheme is constructed. The model is applied to simulate the propagation of three historical tsunami events that attacked the east coast of Korea. The calculated free-surface displacements for the cases of the 1983 Akita and the 1993 Okushiri tsunamis are compared with the observations at four tidal stations along the east coast of Korea. The comparison shows that the results agree well with the observations. The analyses of the simulated results show that underwater topography, such as submerged rises and ridges, plays an important role in the propagation of tsunamis in this region.
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