Yoshinori Shigihara

Wave Dispersion Study in the Indian Ocean-Tsunami of December 26, 2004

A numerical study which takes into account wave dispersion effects has been carried out in the Indian Ocean to reproduce the initial stage of wave propagation of the tsunami event that occurred on December 26, 2004. Three different numerical models have been used: the nonlinear shallow water (nondispersive), the nonlinear Boussinesq, and the full Navier-Stokes aided by the volume of fluid method to track the free surface. Numerical model results are compared against each other. General features of the wave propagation agreed very well in all numerical studies. However some important differences are observed in the wave patterns, i.e., the development in time of the wave front is shown to be strongly connected to the dispersion effects. Discussions and conclusions are made about the spatial and temporal distribution of the free surface reaffirming that the dispersion mechanism is important for tsunami hazard mitigation.

SURVEY RESULTS OF THE INDIAN OCEAN TSUNAMI IN THE MALDIVES

The Indian Ocean Tsunami occurred on 26 December 2004, causing serious damage in the Maldives, which is 2,000 km distant from the epicenter. A post-tsunami survey was carried out from 31 January to 4 February 2005. Tsunami height distribution, tsunami behavior in atoll and characteristics of tsunami disaster in atoll island were discussed through survey results. The height of tsunami traces in the Maldives ranged from 0.6 to 3.4 m. The trace height was not small even where there was a developed reef and even at island inside an atoll. The tsunami behavior appeared to be complex in an atoll. Several minutes were necessary for tsunami inflow to an atoll. Inertial force was small in the run-up process in some islands, but was not so in some islands. Because the Maldives consists of low-lying islands, a solid structure and artificial ground is required to improve the safety level of the Maldives.

Tsunami run-up heights of the 2004 off the Kii peninsula earthquakes

A tsunami height survey was conducted immediately after the 2004 off the Kii peninsula earthquakes. Results of the survey show that the largest tsunami height was about 4.6 m locally at Kiho-cho, Mie prefecture. Numerical simulation of the tsunami due to the earthquake was carried out using the model parameters estimated by NIED. The distribution pattern of the observed tsunami heights along the coast cannot be explained by the computed heights, because the model equation is linear long-wave theory and the run-up computations with a finer grid system are not included in this simulation. In order to explain tsunami run-up heights, it is necessary that the non-linear and run-up computation model should be used with a finer grid system.

AN ADEQUATE DISPERSIVE WAVE SCHEME FOR TSUNAMI SIMULATION

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.

EXPERIMENTAL STUDY ON TSUNAMI FORCES: ESTIMATION OF TSUNAMI FORCE ACTING ON STRUCTURES RELATED TO RUN UP DISTANCE, SCALE OF BUILDING AND PRESSURE DISTRIBUTION

The hydraulic experiments have been carried out for estimating tsunami wave force through water level, velocity, force and pressure measurements. Model of building was placed at several points with certain distance from shoreline. Wave force had been estimated by assuming as hydrostatic forces which only consider inundation depth while wave velocity data used as hydrodynamic forces assumption. Force estimation through integrating wave pressure had been conducted at almost all element on exposed area to ensure the effect of model’s breadth on magnitude of wave force (not only on the middle). However gap of time lag occurred certainly on each line of measurement points have been found. Therefore, precise estimation of wave force through wave pressure measurement seems very difficult. Present study data were compared to the past of available design guidelines for tsunami forces (Asakura et.al.2000) and some available data from past experiments (Yeom et.al.2007-2008) which had analyzed in order to check the validity of some tsunami wave force estimation methods. Some modification equations that refer to function of maximum inundation depth, maximum velocity and run up distance from shoreline are proposed for more considerable agreement of tsunami wave forces estimation

The Study on the Wave-Breaking Mechanism of Tsunami Against Flow

The ratio of water surface velocity to wave celerity is applied as the wave-breaking criteria, and the hydraulic experiment is carried out to clarify the relationship between Froude number and the wave-breaking criteria. The estimation method of wave-breaking criteria including flow effect is proposed and its validity is confirmed by comparing to the experimental result. In addition, we study the governing equation, space grid size and scheme of advective term in order to express the transformation of flow-ascending tsunami adequately in numerical simulation.