In the open ocean a tsunami is barely a ripple travelling at 700 km/h. Near shore it slows, steepens, and rears up — the physics of shallow-water waves.
Tsunami PropagationLive
shallow-water waves · shoaling
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A tsunami is a shallow-water wave even in the deep ocean, travelling at √(g·h). Over 4 km of water that is roughly 700 km/h — jet speed — yet only tens of centimeters high. As it reaches shallow coast it slows and its amplitude grows as h^(−1/4) (Green's law), piling into a destructive wall.
Reading this result: At 4000 m depth the pulse moves at ~713 km/h; Green law shoaling then amplifies its 0.5 m deep-water height as it nears the coast.
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How it works
A tsunami's wavelength dwarfs the ocean depth, so it behaves as a shallow-water wave with speed √(g·h). As it reaches shallower coast it slows, and conservation of energy forces its amplitude to grow as h^(−1/4), Green's law. This shoaling is why a low deep-ocean swell becomes a towering coastal wave. Educational model only.
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