2D Ocean Waves: Deep-Water Wave Cross-Section

Sea state

Wave parameters

Wave height H 1.5 m

Wave period T (≈ wind speed) 8.0 s

Live readouts

Wavelength L

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Phase speed c

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Energy density E

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Wave power P

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How it works

This is the flat, side-on companion to the 3D ocean simulator: instead of an orbitable open-water surface, it shows a vertical cross-section of deep-water swell moving past a small boat. The surface profile is a Stokes-corrected wave — a primary sinusoid plus a smaller second-harmonic term that sharpens the crests and flattens the troughs, matching how real ocean swell actually looks compared to a pure sine wave.

Everything is computed from the deep-water dispersion relation ω² = g·k (valid once depth exceeds roughly half a wavelength), so only wave height H and period T need to be set — wavelength, phase speed, energy density and power follow directly:

Wavelength L = g·T² / (2π)
Phase speed c = L / T = g·T / (2π)
Energy density E = (1/8)·ρ·g·H² (per unit sea-surface area, linear wave theory, seawater ρ ≈ 1025 kg/m³)
Wave power P = E·c_g, with group speed c_g = c/2 in deep water — the rate energy is carried toward shore, per metre of wave crest

Wave period is the closest single dial to wind speed: sustained stronger wind over a longer fetch builds longer-period, longer-wavelength, faster-travelling swell. The direction button reverses which way the wave train propagates.

Set wave height and period — the boat rides the surface