🌊 Shallow-Water Tsunami Simulation

About this simulation

Basin-crossing tsunamis are modelled with the shallow-water equations — valid whenever a wave's length is far greater than the water depth beneath it, which is exactly the case for a tsunami crossing an ocean basin. This scene solves a linearised form of those equations on a finite-difference grid: a leapfrog update advances the sea surface elevation η using a Laplacian weighted by local water depth H(x,y), the same core idea used in production codes like GeoClaw or MOST, just at a scale a browser can animate in real time.

How it works

• Wave speed — in shallow water, waves travel at c = √(g·H), so speed falls as depth falls. Offshore the wave crosses at hundreds of km/h; on the shelf it slows sharply.
• Shoaling — as the wave slows, energy flux conservation forces its amplitude to grow (roughly depth^-1/4), which is why a barely-noticeable open-ocean wave can become a devastating coastal wave.
• Run-up — once the wave reaches the shoreline it can push inland over "dry" cells; a steep coast produces a taller, shorter run-up while a gradual beach spreads the same energy over a longer inundation zone.
• Adaptive mesh refinement (AMR) — real forecasting codes only need fine resolution near the coast, where depth changes fast; the coarse open-ocean grid stays cheap. The wireframe overlay near the shore approximates that idea.

Controls

• Seafloor displacement — the initial vertical offset injected into the water column, standing in for the fault slip that generates a real tsunami.
• Ocean depth — the still-water depth of the open basin; deeper water means faster, longer waves.
• Coastal slope — switches between a narrow, steep shelf and a wide, gradual one.
• Adaptive mesh (AMR) — toggles the refined wireframe overlay near the coastline.
• 🌊 Trigger tsunami — resets the solver and injects a fresh wave. Drag to rotate, scroll to zoom.

Did you know?

Real-time tsunami forecasting systems such as NOAA's MOST/ComMIT and GeoClaw run thousands of scenario simulations offline, then interpolate a forecast within minutes of an earthquake — GPU acceleration and adaptive mesh refinement are what make it possible to resolve metre-scale coastal detail without simulating the whole Pacific at that resolution.