Water Wave Dispersion

Deep-water waves are dispersive: different wavelengths travel at different speeds, causing a wave packet to spread. Click the ocean to add disturbances.

Water depth: ∞

Wave packet width: 4

Peak wavenumber k: 3

Show phase velocity

Phase speed: - Group speed: - Vg/Vp: - Depth: ∞

Deep water: ω = √(gk), so vₚ = √(g/k) (long waves faster). Group velocity vg = ½vₚ — energy travels at half the phase speed. Shallow water: ω = k√(gh) — dispersionless. The dispersion relation ω² = gk·tanh(kh) smoothly connects both regimes.