ABSTRACTABSTRACTWhen a tsunami attacks an island, heavy damage can be caused by a trapping effect. A theoretical solution was obtained for such trapping of long waves using a conical island model. The effects of both the finite radius of the island and the refraction over a sloping beach were taken into account. Characteristic distributions of water surface elevation, runup height, and their frequency responses were studied through the theoretical solution, and the conditions pertaining to strong trapping were examined. The heights recorded in Oki and Okushiri Islands can be explained satisfactorily using the theory as verified through hydraulic experiments.Keywords: tsunami trappingtsunami refractionHokkaido Nansei-Oki earthquake
We conducted a numerical simulation that takes into account the effect of wave frequency dispersion in the Indian Ocean Tsunami that occurred on December 26, 2004. A leapfrog-implicit numerical scheme based on Shigihara et al. [6] is applicable to practical simulation. Dispersion effect is negligible for the runup to the northwest coast of Sumatra Island. At the west side of tsunami source, if the aim of simulation is the reproduction of detailed propagation process, dispersion should be considered in Sri Lanka. If maximum runup height and tsunami arrival time are required, however, dispersion may be negligible.
Through the rapid progress of computer technology, direct wave simulation techniques using CFD (Computational Fluid Dynamics) have been applied to practical problems in coastal, port and harbor engineering. A numerical wave flume, which is one of the representative direct simulation techniques, has been expected to substitute for hydraulic model tests.In this paper, wave transformation of bore on a reef, sand spit and lagoon is computed by the numerical wave flume. The applicability of numerical wave flume is examined through comparisons of numerical results with experimental ones.
In tsunami research, dispersive wave theory is used to numerically simulate transoceanic and near-field propagation by soliton fission. Many numerical schemes have been proposed to solve the dispersive wave effect, but there has been no reliable criterion for selecting an adequate scheme. To address this, we derive exact numerical stability solutions to the linear finite difference equations of dispersive wave theory by using several numerical methods. Characteristics of the truncation error and the numerical stability of the methods are discussed, and the leap-frog implicit scheme appears to be applicable to practical problems due to its superior stability. A new numerical model that uses an implicit scheme is proposed based on the above results. The dispersive term in the equation of motion is solved by a Poisson-type differential equation and the model can be extended to the nonlinear physics. This model is validated by being compared to the conventional models, and it is applied to a Tonankai-Nankai tsunami as an example of a practical problem. The model shows excellent agreement with both the linear analytical solution and the laboratory experiments. Furthermore, the solutions to this model require less computing time than those of the conventional models.
Based on the linear long wave theory, a theoretical solution was obtained for the tsunami, which propagated from a tsunami source generated on the shelf with a straight coastline and a uniform slope. The solution shows that the behavior of a tsunami generated on the shelf is affected by the conditions of the tsunami source. The tsunami propagation is classified into three types by examining the generated edge waves. The limit of conditions providing each propagation type is determined mainly by the source distance to the coastline. The empirical relations are derived which evaluate the characteristics of induced tsunami by using the tsunami source parameters such as the lengths of the long-axis and short-axis, the location and the direction of the tsunami source and so on. The effect of the Coriolis force is also discussed.
This study aims to develop a tsunami numerical model which is capable to include several grid systems and facilitate the process of assembling domains of different resolutions. The assembly of structured domains (inner and outer) is achieved by constructing an intermediate unstructured grid between them. The present scheme is able to diminish short period waves reflected on the boundary of a coarse grid domain. A numerical simulation consisting of a Gaussian-hump shape is used for validation by determining the energy transferred/retained in a finer grid domain. In addition a practical application, the 2010 Chilean Tsunami, is provided as a case study to confirm the validity of proposed model.
The variation of the foreshore in Iwo-Jima is studied by analyzing a series of aerial photographs taken seasonally for the past 4 years since 1987, and data of various surveys obtained for the past 10 years since 1982. These observations are compared with results of numerical analysis of the effects of storm waves on the foreshore. the findings obtained through these analyses are: (1)The island is still rising at a yearly rate of more than 30 cm/year; (2)The foreshore is eroded in summer and fall when typhoons often hit the island, but is restored back in winter and spring of the following year. The seasonal variation of the foreshore area ranges from 300,000 m2 to 600,000 m2 depending on the magnitude and frequency of the typhoons hitting the island in a year; (3)The foreshore area is increasing at a rate of 50,000 m2/year which is caused by the upheaval of the island; (4)A one-line model can be applicable for the prediction of the short-term variation of the shoreline caused by storm waves.
We conducted an urgent field survey at the Sendai Plain to measure the run-up heights and inundation distances of the 2011 Tohoku-oki tsunami. We used GPS measurements because of the remarkably long inundation distances (ca. 5.4 km). We established an accurate measurement scheme using the far electric reference points (about 350 km). Using this method, we quickly measured 69 run-up heights within 3 days. The tsunami run-up heights and inundation distances varied mainly according to the local topography, ranging from 9.6 m at 0.4 km to 0.2 m at 5.4 km, respectively. Furthermore, artificial structures and topography played an important role in constraining the inundation limit. Our observations are important for future analyses using aerial and satellite imagery and numerical modeling in the area because the maximum inundation area might be underestimated in the images as a result of the subtle traces of the tsunami inundation, which were difficult to identify in the field. However, results show that numerical modeling might not reproduce minor inundation beyond the highway without sufficiently high-resolution topographic data because data for the modeling are usually rough, and the highway, small channels, and street gutters, which played an important role in local inundation, are too small a resolution to be recognized in the model.
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