Mathematics of Tsunamis

Computer modeling and simulations lead to a better understanding of natural disasters, such as the Indian Ocean Tsunami of 2004, and may prevent loss of life in the future. Using the system of partial differential equations known as the shallow water wave equations, this Demonstration provides a reasonable approximation of the behavior of real ocean waves during a tsunami.

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The SWE model makes the following assumptions: hydrostatic pressure distribution; incompressible, homogeneous fluid; well-mixed-in-depth flows: uniform vertical mixing; small vertical scale relative to horizontal. The last assumption is certainly violated when a tsunami nears land.
The US NOAA (National Oceanic and Atmospheric Administration) uses a model they refer to as MOST (Method of Splitting Tsunami) that uses different computations and models for the three phases: generation, propagation, and inundation. The propagation phase is computed by solving the SWE on the globe.
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