Numerical Simulation of East China Sea Tsunami by Boussinesq Equation Shanghai Jiao Tong University Department of Engineering Mechanics Xi ZHAO, Benlong WANG, Hua LIU

Contents 1. Research background 2. Linear theory and truncation error analysis for moving bottom boundary (1) transfer function (2) truncation (3) abrupt changing bottom 3. Fully Nonlinear and Highly Dispersive Boussinesq equations 4. Numerical results (1) influence of magnitude (2) influence of earthquake period (3) dispersive and nonlinear effects on the wave profile 5. Conclusions

The large earthquake in Indonesia Sumatra is the most serious disaster of recent years. The Pacific plate is more and more active.

The topography of the East China Sea The East China Sea is composed of continental shelf region and Okinawa Trench region. The continental shelf has mild slope and the water depth is small. The width of the continental shelf is about 600km,the depth of the edge is 150m. The depth of the trench is large. The bottom of the trench has possibility of earthquake.

Linear theory governing equations flow field Taylor operators

bottom boundary condition on beach of constant depth, reduced to transfer function between the moving bottom and free surface level

truncation Typical truncation forms of Taylor operators (T3) 5rd order truncation (T5) Padé approximation (P5) (better on linear dispersion characteristic)

Relative error analysis transfer function

considering both s and kh

accuracy analysis of the transfer function

exact solution T3 T5 P5

Abrupt changes of bathymetry

Boussinesq equations kinematic boundary condition of free surface dynamic boundary condition of free surface where bottom boundary condition

Velocities P5 velocity components

Simplified model of submarine earthquake Magnitude of 8.5

parameters Magnitude (Richter) L(km) C A Fault S (m) Period (s) 6.5 8 1 0.182 0.56 2.24 7.0 14 0.5 1.3 1.0 4 7.5 25 0.27 4.27 1.78 7.12 8.0 45 0.15 13.8 3.17 12.68 8.5 79 0.1 36.8 5.66 22.64 9 141 0.05 130 10 40 9.5 251 0.03 385 17.8 71.2 refers to Ward (2002)

Effects of the magnitude of earthquake 6.5 7.0 7.5 8.0 8.5 9.0 When the magnitude of earthquake increases, the wave height increases and the dispersion reduces.

The velocity of the submarine earthquake is difficult to be measured, the present measurement of earthquake can only obtain the final deformation.

Propagation of the tsunami waves motivated by earthquake of magnitude 6.5 t=1hours t=3hours

Propagation of the tsunami waves motivated by earthquake of magnitude 7.5

Conclusion The transfer function between free surface elevation and seabed deformation is deduced by a different approach. Three types of truncation have been analyzed. The relative errors have been compared. For abrupt changes of bathymetry, the magnitude of wave is much larger than the case that only a block moving horizontally. According to the topography of the Okinawa Trench, tsunamis motivated by different magnitudes of submarine earthquakes are simulated by fully nonlinear and highly dispersive Boussinesq equations. When the magnitude of earthquake increase, the wave height increase and the dispersion reduce.

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