waves move equatorward – negative phase speed – on a western boundary and poleward – positive phase speed – on an eastern boundary; the waves move cyclonically around an ocean basin). Equatorial Kelvin wave The equatorial zone essentially acts as a waveguide, causing disturbances to be trapped in the vicinity of the Equator, and the equatorial Kelvin wave illustrates this fact because the Equator acts analogously to a topographic boundary for both the Northern and Southern Hemispheres, making this wave very similar to the coastally-trapped Kelvin wave. The primitive equations are identical to those used to develop the coastal Kelvin wave phase speed solution (U-momentum, V-momentum, and continuity equations) and the motion is unidirectional and parallel to the Equator. Because these waves are equatorial, the Coriolis parameter vanishes at 0 degrees; therefore, it is necessary to use the equatorial beta plane approximation that states: where β is the variation of the Coriolis parameter with latitude. This equatorial beta plane assumption requires a geostrophic balance between the eastward velocity and the north–south pressure gradient. The phase speed is identical to that of coastal Kelvin waves, indicating that the equatorial Kelvin waves propagate toward the east without dispersion (as if the earth were a non-rotating planet). For the first baroclinic mode in the ocean, a typical phase speed would be about 2.8 m/s, causing an equatorial Kelvin wave to take 2 months to cross the Pacific Ocean between New Guinea and South America; for higher ocean and atmospheric modes, the phase speeds are comparable to fluid flow speeds. When the motion at the Equator is to the east, any deviation toward the north is brought back toward the Equator because the Coriolis force acts to the right of the direction of motion in the Northern Hemisphere, and any deviation to the south is brought back toward the Equator because the Coriolis force acts to the left of the direction of motion in the Southern Hemisphere. Note that for motion toward the west, the Coriolis force would not restore a northward or southward deviation back toward the Equator; thus, equatorial Kelvin waves are only possible for eastward motion (as noted above). Both atmospheric and oceanic equatorial Kelvin waves play an important role in the dynamics of El Nino-Southern Oscillation, by transmitting changes in conditions in the Western Pacific to the Eastern Pacific. There have been studies that connect equatorial Kelvin waves to coastal