¹Division of Engineering & Applied Sciences Harvard University, Cambridge, Massachusetts, USA

　

²Department of Civil & Environmental Engineering University of Washington, Seattle, Washington, USA

harryeh@u.washington.edu

　

Tsunami runup and drawdown motions on a uniformly sloping beach are evaluated based on the fully nonlinear shallow-water wave theory. The nonlinear equations of mass conservation and linear momentum are first transformed to single linear hyperbolic equation using the hodograph transform technique. To solve the problem with arbitrary initial conditions, we apply the Fourier-Bessel transform, and then the inversion of the transform leads to the Green function representation. The solutions in the physical time and space domains are then obtained by numerical integration. With this solution technique, several examples of tsunami runup and drawdown motions are presented. In particular, detailed shoreline motions, velocity fields, and inundation depths on the shore are closely examined. This semi-analytical solutions of the fully nonlinear shallow-water-wave theory are useful for evaluating the accuracy of numerical algorithms. This method also provides a convenient means to evaluate the critical flow-velocity, as well as the fluid force, associated with tsunami runup and drawdown processes. It was found that the maximum fluid force occurs in the vicinity of the extreme drawdown location. The direction of the maximum force depends on the initial waveform: it is in the inshore direction when the initial waveform is predominantly depression, while the maximum force occurs in the offshore direction when the initial wave have a dominant elevation characteristic.

　

　

Nihon University Funabashi, Chiba, Japan

k21003@ocean.cst.nihon-u.ac.jp

　

In recent years, the wave data observed by NOWPHAS (Nationwide Ocean Wave information network for Ports and harbours) etc. is accumulated and the many researches on the Infra-gravity waves used these data are reported. However, characteristics of the Infra-gravity waves have much difficult elucidation. And, there is the damage report of a mooring cable fracture of a mooring vessel. Therefore, the immediate countermeasure against the damage by the Infra-gravity waves is required. There are a lot of researches argued about only heights of Infra-gravity waves, though there are few researches argued about its periods. In terms of a vessel moored to the quay and a work vessel to construct marine structure, it is important to clarify heights of Infra-gravity waves and to argue about periods considered main cause of the long period motion of vessel. Therefore, in this study, the analysis about heights and periods of Infra-gravity waves in the observation sea area with passage of a typhoon is performed, and the characteristic is considered.

　

The result obtained by the abovementioned analysis is as follows. The development and the decay of the Infra-gravity waves are greatly dependent on the course of a typhoon, and specifically, the characteristic of it changes greatly when a typhoon moves away from the observation point. The relation between the bound wave by verification to the theory, the free wave and the advance course of a typhoon, the central pressure of a typhoon, the distance from observation point to a typhoon was considered.

　

　

Institute of Computational Mathematics and Mathematical Geophysics Siberian Division of the Russian Academy of Sciences, Novosibirsk, RUSSIA

mag@omzg.sscc.ru

　

The most important question in the prognostic tsunami modeling is estimation of tsunami run-up heights at different points along the coastline. Also it is of great importance to know the water flow velocity in submerging areas, because a high-speed flow during tsunami run-up is the main destructive factor of a tsunami attack. Methods for the numerical simulation of tsunami waves propagation in deep and shallow sea are developed and widely used many scientists. In order to find possible submerged areas some of them use the simplifying assumptions about the ratio between the tsunami wave height near the shore and the wave run-up height. However this ratio strongly depends on the shore profile above the mean sea level.

　

In this paper the new algorithm for numerical simulation of the wave run-up process is proposed. It is based on the energy and the mass conservation laws and makes it possible to monitor the flow velocity in a submerged area. A few series of the one-dimensional computations of wave run-up on the model shore were carried out. Some results of modeling of real cases of historical tsunamis are presented. This method can also be used in the inverse tsunami problem: definition tsunami wave height in the deep ocean according to run-up records.

　

　

Department of Environmental and Ocean Engineering University of Tokyo, Tokyo, JAPAN

park@triton.naoe.t.u-tokyo.ac.jp

　

The objective of this paper is to develop a fully nonlinear numerical modeling of Nearshore Tsunami, which can cope with large amplitude waves and wave breaking motions.

　

The developed model uses a finite-difference algorithm based on a modified marker-and-cell method to solve the fully three-dimensional Navier-Stokes equation. The Navier-Stokes equation is solved for two fluid layers and the boundary values are updated at each time step by a finite difference time marching scheme in the framework of rectangular co-ordinate system. The pressure can be determined by iteratively solving the following Poisson equation in each layer using the Richardson method. The fully non-linear kinematic free-surface condition is satisfied by the marker-density function method developed for two layers.

　

In the present paper, first some numerical techniques for generating a solitary wave by numerical wavemaker are tested. And next, two benchmark problems mentioned in "International workshop on Long-wave runup models" (H. Yeh et al., 1995) are simulated, i.e., two-dimensional wave runup on a vertical wall with beach slop and three-dimensional simulation of Hokkaido southwest earthquake tsunami.

　

　

¹River and Coastal Engineering Department, NEWJEC Inc. Coastal Engineering Division Osaka, JAPAN

satohr@osaka.newjec.co.jp

　

²Department of Ecosystem Engineering, University of Tokushima Tokushima, Tokushima, JAPAN

　

The tsunami breakwater size mast be designed as meet the condition; the calculated tsunami height in the bay is under allowable height. The calculated tsunami is selected into the historical tsunamis. If the tsunami occurs some other different place, tsunami height in the bay may be over allowable height. It is important to consider the various locations and magnitudes of seabed displacement.

　

In this study, the Monte Carlo method was used for prediction of tsunami height in the bay. The tsunami calculation was considered random tidal height, latitude, longitude, vertical fault deformation and calculative accuracy. They were defined as the Normal or Weibull distribution. Ten cases of the different tsunami breakwater length were set. The repeating calculations were carried out at 1,000 times for one case. The number of tsunami over allowable was counted, and was defined as "suffer probability".

　

The suffer probabilities were compared with the tsunami breakwater length. When the tsunami breakwater is half-length, the suffer probability is more low. The tsunami attack at the under construction will have no effect for decay of the tsunami. When the allowable suffer probability is fixed, the best length against the various tsunamis is decided simply by using suffer probabilities.