Ocean Gravity Waves — Dispersion, Group vs Phase Velocity
Surface gravity waves satisfy ω²=gk·tanh(kh). Phase velocity c_p=ω/k and group velocity c_g=∂ω/∂k differ: wave packets travel at c_g while individual crests travel at c_p. This lab shows wavepackets, dispersion curves, and particle orbits.
Wave Parameters
Velocities (deep / shallow)
Phase velocity c_p — m/s
Group velocity c_g — m/s
c_g/c_p ratio —
Angular freq ω — rad/s
Wavelength λ — m
Period T — s
Dispersion relation: ω² = g·k·tanh(kh)
Deep water (kh≫1): ω=√(gk), c_p=√(g/k), c_g=c_p/2 Shallow water (kh≪1): ω=k√(gh), c_p=c_g=√(gh) (non-dispersive)
Wave energy travels at c_g, not c_p. Individual crests appear to move through the packet envelope — visible in the animation above.