Equatorial Waves - Equatorial Kelvin Waves

Equatorial Kelvin Waves

Discovered by Lord Kelvin, coastal Kelvin waves are trapped close to coasts and propagate along coasts in the Northern Hemisphere such that the coast is to the right of the alongshore direction of propagation (and to the left in the Southern Hemisphere). Equatorial Kelvin waves behave somewhat as if there were a wall at the equator – so that the equator is to the right of the direction of along-equator propagation in the Northern Hemisphere and to the left of the direction of propagation in the Southern Hemisphere, both of which are consistent with eastward propagation along the equator. The governing equations for these equatorial waves are similar to those presented above, except that there is no meridional velocity component (that is, no flow in the north–south direction).

• 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):

The solution to these equations yields the following phase speed: c2 = gH; this result is the same speed as for shallow-water gravity waves without the effect of Earth’s rotation. Therefore, these waves are non-dispersive (because the phase speed is not a function of the zonal wavenumber). Also, these Kelvin waves only propagate towards the east (because as Φ approaches zero, y approaches infinity).