Oceanography

Phase velocity

The phase velocity c is the speed at which a particular phase of the wave propagates, for  example, the speed of propagation of the wave crest. In one wave period T the crest advances one wave-length L and the phase speed is c=L/T= ?/k.

Thus,, the definition of phase speed is:

                   C= ω

                         K

The direction of propagation is perpendicular to the wave crest and toward the positive x direction. The deep-and shallow-water approximations for the dispersion relation give

                                      C=    g               g

                                              _     =        _       Deep –water phase velocity

 

                                              K              ω                                        

The approximations are accurate to about 5% for limits stated in deep-water dispersion relation and shallow-water dispersion relation. In deep water, the phase speed depends on wave-length or wave frequency. Longer waves travel faster. Thus, deep-water waves are said to be dispersive. In shallow water, the phase speed is independent of the wave; it depends only on the depth of the water. Shallow-water waves are non-dispersive.