Tsunami Shallow-Water Cross-Section (2D)

Ocean & Coast

Deep-ocean depth 4000 m

Beach slope angle 4.0°

Wave Source

Open-ocean wave height 1.0 m

Wave period 10 min

Playback speed 10×

Set the ocean and coast, then launch a wave.

Live Readout

Local depth

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Wave speed c=√(gh)

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Wave height (Green's Law)

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Elapsed time

00:00

Estimated runup height

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How it works

A tsunami in open water behaves as a shallow-water wave because its wavelength (tens to hundreds of km) is always far larger than the ocean depth. Its speed depends only on local depth: c = √(g·h). As the wave crosses the shown cross-section — deep ocean, optional continental shelf, then the beach slope — its speed drops continuously as h drops.

Shoaling (Green's Law): with no energy loss, wave-height × speed¹ᐟ² stays constant, so H(x) = H₀·(h₀/h(x))^¼ — height grows as the wave slows down.
Breaking: once the height-to-depth ratio H/h reaches about 0.78 (the breaker index), the wave can no longer keep shoaling smoothly and collapses into a turbulent bore. Past that point its front speed switches to the bore relation c ≈ √(g·(h+H)).
Runup: the final climb up the beach face is estimated from the surf-similarity (Iribarren) number ξ = tanβ / √(H_b/L₀), a standard coastal-engineering scaling — not a full nonlinear solve, so treat the number as an order-of-magnitude estimate. Real runup depends heavily on 3D coastline shape, channelling and reflections.

The vertical axis is exaggerated relative to the horizontal one (a few km deep vs. tens of km wide) — standard practice in bathymetric cross-sections, otherwise the ocean floor would look like a flat line.