Presets
Playback
Sea floor
Deep ocean, shelf depth and slope shape.
Wave
Open-ocean height and wavelength of the initial pulse.
Model checks
The science
Long-wave equations
For wavelength much larger than depth, the linear shallow-water equations are ∂η/∂t + ∂(h u)/∂x = 0 and ∂u/∂t + g ∂η/∂x = 0, giving a wave speed c = √(g h). At 4000 m this is about 200 m/s (720 km/h); on a 100 m shelf only 31 m/s. The grid uses a staggered leapfrog scheme at 0.45 of the stability limit.
Shoaling
As depth falls the wave slows and its energy flux (∝ η² c) is conserved, so amplitude grows as Green's law η ∝ h-1/4; wavelength shrinks in proportion to c.
Honest simplifications: linear and one-dimensional: no run-up, breaking, bottom friction, Coriolis force, dispersion or spreading of a real source (a circular front loses amplitude like 1/√r). Heights shown on the shelf are therefore upper-trend values; they illustrate the physics and are not a hazard forecast.
What to try
- Choose Steep coast: the same wave grows more over a narrow slope, yet Green law still holds on gentle ones.
- Make the shelf as deep as the ocean (No shelf): no speed change and no growth.
- Watch the probes: the same wave arrives later and taller at P3.