Wave celerity

Wave celerity is the phase speed of a surface gravity wave, the rate at which a crest travels, c = L over T = omega over k. From the dispersion relation omega squared = g k times the hyperbolic tangent of k h, deep water (h above about L over 2) gives c = square root of g L over 2 pi, so longer waves run faster (dispersion), while shallow water (h below about L over 20) gives the nondispersive c = square root of g h. Energy and wave groups move at the group velocity, half of c in deep water. Celerity relative to ship speed sets the wave-encounter frequency and the broaching risk in following seas.