Numerical Simulation Of Generation, Propagation And Runup Of Tsunamis

As one of the most destructive ocean disasters, tsunami is induced by submarine landslides and oceanic earthquakes. When tsunami waves propagate into nearshore region, the wave energy will focus and therefore wave amplitude increases significantly due to the decrease of water depth. Predictions of the arriving time and the maximum runup by numerical models are primary missions of the tsunami research, which can be accomplished by numerical studies on the hydrodynamic characteristics of tsunami's generation, propagating, shoaling and runup.Based on the fully nonlinear highly dispersive Boussinesq model, the whole life span of tsunami from its generation to runup process is investigated.How to setup the initial profile of tsunami wave is an open question. Imposing finial seabed rupture profile as initial surface water profile is taken as a general approach in most tsunami simulation models, which neglects the influence of temporal bottom varying effects. In this study, the Boussinesq model is extended to include the time varying beach terms in the bottom boundary condition. Therefore the seabed movement process could be exactly simulated.A simplified seabed deformation model is proposed based on the earthquake energy estimation and rupture parameters of different magnitudes. The tsunami waveforms caused by earthquakes of different magnitudes in both deep ocean and shallow water region are calculated. The results indicate that the small earthquakes lead to wave train with dispersion dominated property while large earthquakes result in N-shape waves. The relative wave heights of all kinds of tsunamis at initial stage are usually less than O (1 0?3), no matter it happens in deep ocean or shallow water region.To evaluate the accuracy on simulating the time varying beach, the transfer function describing the relationship between bottom displacement and surface elevation is investigated based on the linearized Boussinesq model. Various truncation forms of infinite series operator in the Boussinesq model are investigated for tsunami waves. The 3rd order Padéapproximation is selected to reconstructing the velocity field after the accuracy analysis of linear dispersion, shoaling gradient and transfer function.With the Boussinesq model, the shoaling process of various N-waves induced by submarine faults over mild slope beach is computed. Comparing with the results obtained by the Boussinesq model, it is found that the linear shoaling formula usually underestimates the wave height of the leading-depression N-wave and overestimates that of the leading-elevation N-wave.The destruction of coastal area in the tsunami events is caused by the wave runup. Great effort has been made on the study of solitary wave runup in the last decades. Many useful results have been obtained by both analytical methods and numerical methods, as well as physical experiments. With the detailed investigation of the runup speed and energy transformation of solitary wave and N-wave, the illusion of the shoreline delay before solitary wave advancing and the phenomenon of N-wave shoreline retreat are explained.The budget between kinetic energy and potential energy during the runup and rundown processes of solitary waves and N-waves is investigated. The proportion of potential energy in the total energy reduces when the beach slope decreases and wave height increases. The potential energy reaches the maximum near the maximum runup for leading-depression N-wave while near the maximum rundown for leading-elevation N-wave.The Indian Ocean tsunami 2004 has been simulated with the horizontal two dimensional Boussinesq model using a least squared-based finite difference method. Comparisons between numerical results and measured data of field survey validate the numerical model. The Okinawa trench in the East China Sea and the Manila trench in the South China Sea are identified as being most susceptible to future major earthquakes around China coast. In this paper, potential tsunamis waves in these two sites are studied. The arriving time of tsunami waves and water surface elevation near the coastal line are predicted for the first time.