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The science
Long waves in shallow water
A tsunami wavelength (tens to hundreds of km) is far longer than the ocean depth h, so the linear shallow-water equations apply: ηt + (h u)x = 0 and ut + g ηx = 0. They give a wave speed c = √(g h): about 700 km/h over a 4 km deep ocean and only about 60 km/h in 30 m of water. The travel time to the coast is T = ∫ dx / √(g h(x)).
Shoaling and Green's law
As the depth falls the wave slows, its energy flux stays almost constant and it grows: for a gentle slope A ∝ h-1/4 (Green's law). A wide, gently rising shelf therefore raises the height gradually, while the vertical wall at the coast here reflects the wave and doubles the elevation at the last cell.
Honest simplifications: linear equations (no breaking, run-up, bottom friction or dispersion), a one-dimensional section (no refraction, spreading or bay resonance), a vertical wall instead of a beach, and a Gaussian uplift as the source. The coast height printed is therefore a sketch, not a hazard forecast.
What to try
- Open Pacific: compare the simulated arrival time with the predicted one.
- Wide shelf vs Steep coast: how does the shelf change the peak height?
- Shallow sea: the same uplift travels roughly three times slower.
- Increase the source width: longer waves obey Green's law more closely.