MY SIMULATOR

Bay Wave Dynamics

Refraction, diffraction and harbour agitation.

INTERACTIVE 3D

Sim time 0:00Basin Kd 0.00FPS 0

WAVE HEIGHT H2.5 m

PERIOD / LENGTH AT MOUTH11 s / 90 m

HARBOUR HEIGHT0.00 m

SETTLE🌊⏱

Bay Wave Lab: Refraction, Diffraction & Harbour Agitation

Swell arrives from the open sea on the left. As the water gets shallower the waves slow down, bend towards the shore, grow, and finally break. Behind a breakwater they spread into the shadow. Watch the harbour on the right.

Preset

Swell and sea

Live numbers

Wave height along a section in the open bay, with Green’s law

Harbour basin Kd history

Missions

Independent numerical checks

Also run outside the browser: node src/check.js (dispersion limits, Eckart approximation, 1D shoaling vs Green’s law, half-plane diffraction at the shadow line, Snell’s law on a slope).

Educational model, not an engineering design tool and not a forecast. One regular wave (one period) is simulated with linear theory; real seas mix many periods and directions. Damping coefficients for breaking, beach and rubble mound are illustrative [assumption]. Water-surface heights are exaggerated 3x for readability; the terrain is schematic.

Controls

Drag / one finger: orbit; wheel / pinch: zoom; Hero, Section and Map buttons (or keys H, S, T) jump the camera.
Sliders change the swell and the sea level. The model keeps running and adapts; after you release a slider it fast-forwards 4 minutes so the pattern settles.
Wave-height map: red/yellow = higher than the incident wave (Kd > 1), blue = shelter (Kd < 1). White arrows show where the wave energy flows.
Keys: Space start/pause, R reset. Waves shorter than 8 s are not offered: at 10 m grid spacing they are under-resolved.

The science

Dispersion. A water wave of angular frequency ω = 2π/T obeys ω² = g k tanh(k h). In deep water the length is L₀ = gT²/2π; in shallow water the speed tends to √(gh). Phase speed C = ω/k, group speed C_g = nC with n = ½(1 + 2kh / sinh 2kh).

Mild-slope equation. For slowly varying depth the wave amplitude obeys ∇·(C C_g ∇η) + k² C C_g η = 0 (Berkhoff). The page integrates its time-dependent form η_tt = (C/C_g) ∇·(C C_g ∇η) on a 200×200 grid (10 m cells) with a leapfrog scheme. That single equation contains refraction (waves bend toward slower water, Snell), shoaling (amplitude grows as (C_g0/C_g)½, Green’s law), diffraction (energy spreads into the shadow of a breakwater tip; on the shadow line the amplitude is about half the incident one) and reflection from walls.

Breaking and beaches. Where the local height exceeds about 0.78 h [verify against a coastal-engineering text] extra damping removes energy and foam appears; very shallow cells damp strongly so the beach absorbs instead of reflecting. Breakwater type changes the wall damping: a vertical caisson reflects, a rubble mound absorbs [assumed coefficients].

Harbour agitation. Kd = local height / incident height. The basin number is the mean over a disc inside the harbour.

Not modelled: nonlinearity, wind, currents, irregular seas, wave overtopping and transmission, harbour resonance by long waves, sediment. The solver is non-dispersive around the chosen period, which is exact for one wave frequency only.