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🌊 Tsunami

About this simulation

This simulation solves the 2D Shallow Water Equations to reproduce how a tsunami is born and travels across an ocean. A seafloor rupture displaces the whole water column, launching long-period gravity waves that race across deep water and then pile up dramatically at the coast. Tsunami warning centres run versions of these same equations to forecast arrival times and run-up heights after a submarine earthquake.

How it works

• Choose a bathymetry preset — continent, island, basin, or trench — which sets the water depth H across the grid.
• Click the ocean to trigger a Gaussian seafloor uplift; this seeds the initial surface elevation.
• A leapfrog finite-difference scheme steps the wave equation forward, using a variable wave speed c = √(gH) that depends on local depth.
• As waves reach the shallow shelf they slow, shorten, and grow taller (shoaling) before running up onto the land cells.

Key equations

η_next = 2η − η_prev + dt²·∇·(c²∇η) — η is surface elevation above rest, c² = gH is the squared wave speed, H the water depth, g gravity, and dt the time-step. Wave speed c = √(gH) gives ≈200 m/s in 4 km deep water and ≈10 m/s near shore.

Controls

• Bathymetry Preset — pick the seafloor shape.
• Uplift height — strength of the seafloor source (m).
• Source radius — width of the rupture zone (cells).
• Absorption — damping factor that bleeds off energy.
• Pause / Play — freeze or resume the time-stepping.
• Reset — rebuild the ocean and clear all waves.
• Click / drag — trigger an earthquake or add energy.

Did you know?

In the open ocean a tsunami may be only half a metre tall yet hundreds of kilometres long, so ships sail over it unnoticed — but Green's Law means that same energy compresses near shore, where the wave can rear up into a wall of water many metres high.