This chapter theoretically investigates tsunami generation. When an earthquake occurs in an offshore region, seismic waves, ocean acoustic waves, and tsunami are excited. Although the compressibility and elasticity of the sea layer are important for the propagation of ocean acoustic waves and high-frequency seismic waves, we may assume that the sea layer is incompressible for tsunami. This chapter is based on incompressible fluid dynamics. The theory gives the analytical solutions for tsunami generation and propagation, by which we would be able to understand the mechanism behind these phenomena in addition to describing the motion. Section 5.1 explains the difference between ocean acoustic waves and tsunami. In Sect. 5.2, a linear potential theory is formulated for the tsunami generation process in a water with uniform depth. Analytical solutions for the sea-surface displacement, velocity, and pressure field in the seawater are derived. In Sect. 5.3, we examine the analytical solutions for tsunami generation and propagation. The mathematical equations can directly provide us with a clear perspective on the tsunami mechanism. In Sect. 5.4, we bridge the gap between the analytical solutions derived under a constant sea-depth assumption and tsunami simulations with realistic bathymetry. The theoretical background of the initial conditions in the numerical simulations is explained.
Linear potential theory Incompressible fluid Initial tsunami height distribution Dynamic pressure change Static pressure change
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