The dispersion relation ω²=gk·tanh(kh) governs all water waves. Deep water (kh≫1): ω≈√(gk), dispersive — each frequency travels at its own speed, spreading wave packets.
Shallow water (kh≪1): ω≈k√(gh), non-dispersive — tsunamis behave this way.
The group velocity c_g=dω/dk carries energy; phase velocity c_p=ω/k carries wave crests.
The dispersion curve is shown below; click to set wavenumber.