Kelvin Wave - Coastal Kelvin Wave

Coastal Kelvin Wave

In a stratified ocean of mean depth H, free waves propagate along coastal boundaries (and hence become trapped in the vicinity of the coast itself) in the form of internal Kelvin waves on a scale of about 30 km. These waves are called coastal Kelvin waves, and have propagation speeds of approximately 2 m/s in the ocean. Using the assumption that the cross-shore velocity v is zero at the coast, v = 0, one may solve a frequency relation for the phase speed of coastal Kelvin waves, which are among the class of waves called boundary waves, edge waves, trapped waves, or surface waves (similar to the Lamb waves). The (linearised) primitive equations then become the following:

• the continuity equation (accounting for the effects of horizontal convergence and divergence):

• the u-momentum equation (zonal wind component):

• the v-momentum equation (meridional wind component):

If one assumes that the Coriolis coefficient f is constant along the right boundary conditions and the zonal wind speed is set equal to zero, then the primitive equations become the following:

• the continuity equation:

• the u-momentum equation:

• the v-momentum equation:

.

The solution to these equations yields the following phase speed: c2 = gH, which is the same speed as for shallow-water gravity waves without the effect of Earth’s rotation. It is important to note that for an observer traveling with the wave, the coastal boundary (maximum amplitude) is always to the right in the northern hemisphere and to the left in the southern hemisphere (i.e. these waves move equatorward/southward – negative phase speed – on a western boundary and poleward/northward – positive phase speed – on an eastern boundary; the waves move cyclonically around an ocean basin).