On the 1 lth of March, 2011, a subduction earthquake of magnitude Mw9.0 happened at the northeast of Japan, generating a tsunami which resulted in huge damage in Japan. Okada＇s elastic fault model is used to generate the deformation of the sea bottom based on USGS sources and UCSB sources respectively. The shallow water equations are solved by the adaptively refined finite volume methods so that it can compute the propagation of tsunami in the Pacific Ocean efficiently. The computed time series of the surface elevation are compared with the measured data from NOAA real-time tsunami monitoring systems for model validation, and UCSB sources derive better results than USGS sources. Furthermore, one nested domain with fine grid and higher topography reso- lution is combined to compute numerically this tsunami spreading in the Bohai Sea, Yellow Sea, East China Sea, and North of South China Sea. The impacts on China Coast and seas are analyzed and discussed. The results show that the tsunami has almost no impact in the Bohai Sea and Yellow Sea. It has some kind impact on the East China Sea and South China Sea. However, maximum wave height on China Coast is smaller than 0.5 m. It is thus concluded that the 2011 Tohoku tsunami did not generate a significant in- fluence on China Coast.
The evolution and run-up of double solitary waves on a plane beach were studied numerically using the nonlinear shallow water equations（NSWEs） and the Godunov scheme. The numerical model was validated through comparing the present numerical results with analytical solutions and laboratory measurements available for propagation and run-up of single solitary wave. Two successive solitary waves with equal wave heights and variable separation distance of two crests were used as the incoming wave on the open boundary at the toe of a slope beach. The run-ups of the first wave and the second wave with different separation distances were investigated. It is found that the run-up of the first wave does not change with the separation distance and the run-up of the second wave is affected slightly by the separation distance when the separation distance is gradually shortening. The ratio of the maximum run-up of the second wave to one of the first wave is related to the separation distance as well as wave height and slope. The run-ups of double solitary waves were compared with the linearly superposed results of two individual solitary-wave run-ups. The comparison reveals that linear superposition gives reasonable prediction when the separation distance is large, but it may overestimate the actual run-up when two waves are close.
Experiments of the runup of two solitary waves on a plane beach are carded out in a wave flume. The two solitary waves with the same amplitude and the crest separating distances are generated by using an improved wave generation method. It is found that, with regard to the two solitary waves with same wave amplitude, the runup amplification of the second wave is less than that of the first wave if the relative crest separating distance is reduced to a certain threshold value. The rundown of the first solitary wave depresses the maximtlm runup of the second wave, If the leading solitary wave is of relatively smaller amplitude for the two solitary waves, the runup amplification is affected by the overtaking process of two solitary waves. It turns out that the runup amplification of the second wave is larger than that of the first wave if the similarity factor is approximately larger than 15, which means the larger wave overtakes the smaller one before the waves runup on a beach.
Based on the filtered Navier-Stokes equations and Smagorinsky turbulence model, a numerical wave flume is developed to investigate the overtopping process of irregular waves over smooth sea dikes. Simulations of fully nonlinear standing wave and regular wave＇s run-up on a sea dike are carried out to validate the implementation of the numerical wave flume with wave generation and absorbing modules. To model stationary ergodic stochastic processes, several cases with different random seeds are computed for each specified irregular wave spectrum. It turns out that the statistical mean overtopping discharge shows good agreement with empirical formulas, other numerical results and experimental data.
