Presets
Playback
Harbor and sea wave
Narrow mouth (r small): half-wave modes T = 2L/(n c). Wide mouth (r above 1): quarter-wave modes T = 4L/((2n-1) c).
Model checks
The science
Shallow-water waves in a basin
Long waves obey the linear shallow-water equations ∂η/∂t = -h ∂u/∂x and ∂u/∂t = -g ∂η/∂x, so they travel at c = √(g h) (about 10 m/s for 10 m of water). The quay at x = 0 is a wall (u = 0); at the mouth x = L the basin is joined to the open sea, where outgoing waves leave freely: u(L) = r (c/h)[η(L) - 2 ηin], with r the width of the mouth relative to the basin.
Frequency response
For a forced harmonic wave the quay amplitude is |η(0)| = 2 r a / √(r² cos²kL + sin²kL), k = ω/c. A narrow mouth makes the basin nearly closed and the peaks sit at kL = nπ (T = 2L/(n c)); a wide mouth releases the pressure at the mouth and the peaks sit at kL = (n - 1/2)π (T = 4L/((2n-1)c)). Real harbour disasters (seiches, tsunami "rissaga") happen when the sea's forcing period matches one of these modes.
Honest simplifications: one horizontal dimension (no 2D diffraction, no refraction or shoaling, constant depth and width), a lumped mouth model that radiates into a sea channel of fixed relative width, small amplitudes only (no breaking or run-up) and optional linear friction. Real harbours have a complicated shape and many coupled modes.
What to try
- Press Narrow mouth, half-wave and then Off resonance: the same wave, a few times less water motion at the quay.
- Press Uniform channel (r = 1): the response is flat, because the sea simply continues the basin.
- Add friction to see the resonant peak fall.