Equatorial wave
[1] Wave trapping is the result of the Earth's rotation and its spherical shape which combine to cause the magnitude of the Coriolis force to increase rapidly away from the equator.
Equatorial waves are present in both the tropical atmosphere and ocean and play an important role in the evolution of many climate phenomena such as El Niño.
Many physical processes may excite equatorial waves including, in the case of the atmosphere, diabatic heat release associated with cloud formation, and in the case of the ocean, anomalous changes in the strength or direction of the trade winds.
[1] Equatorial waves may be separated into a series of subclasses depending on their fundamental dynamics (which also influences their typical periods and speeds and directions of propagation).
The latter two share the characteristics that they can have any period and also that they may carry energy only in an eastward (never westward) direction.
The remainder of this article discusses the relationship between the period of these waves, their wavelength in the zonal (east-west) direction and their speeds for a simplified ocean.
Rossby-gravity waves, first observed in the stratosphere by M. Yanai,[2] always carry energy eastward.
The eastward speed of propagation of these waves can be derived for an inviscid slowly moving layer of fluid of uniform depth H.[3][unreliable source?]
Because the Coriolis parameter (ƒ = 2Ω sin(θ) where Ω is the angular velocity of the earth, 7.2921
The remaining pair of roots correspond to the Yanai or mixed Rossby-gravity mode whose group velocity is always to the east [1] and interpolates between two types of
The Yanai modes, together with the Kelvin waves described in the next section, are rather special in that they are topologically protected.
Their existence is guaranteed by the fact that the band of positive frequency Poincaré modes in the f-plane form a non-trivial bundle over the two-sphere
Through the bulk-boundary connection[5] this necessitates the existence of two modes (Kelvin and Yanai) that cross the frequency gaps between the Poincaré and Rossby bands and are localized near the equator where
[1] The governing equations for these equatorial waves are similar to those presented above, except that there is no meridional velocity component
; this result is the same speed as for shallow-water gravity waves without the effect of Earth's rotation.
Kelvin waves have been connected to El Niño (beginning in the Northern Hemisphere winter months) in recent years in terms of precursors to this atmospheric and oceanic phenomenon.
Many scientists have utilized coupled atmosphere–ocean models to simulate an El Niño Southern Oscillation (ENSO) event and have stated that the Madden–Julian oscillation (MJO) can trigger oceanic Kelvin waves throughout its 30- to 60-day cycle or the latent heat of condensation can be released (from intense convection) resulting in Kelvin waves as well; this process can then signal the onset of an El Niño event.
[8] These easterly winds can force West Pacific warm surface water eastwards, and also excite Kelvin waves, which in this sense can be thought of as warm-water anomalies that affect the top few hundred metres of the ocean.
Changes associated with the waves and currents can be tracked using an array of 70 moorings which cover the equatorial Pacific Ocean from Papua New Guinea to the Ecuador coast.
[8] Sensors on the moorings measure the sea temperature at different depths and this is then sent by satellite to ground stations where the data can be analysed and used to predict the possible development of the next El Niño.
During the strongest El Niños the strength of the cold Equatorial Undercurrent drops as does the trade wind in the eastern Pacific.
As a result cold water is no longer upwelled along the Equator in the eastern Pacific, resulting in a large increase of sea surface temperatures and a corresponding sharp rise in sea surface height near the Galapagos Islands.
The resulting increase in sea surface temperatures also affects the waters off the South American coast (specifically Ecuador), and can also influence temperatures southward along the coast of Peru and north towards Central America and Mexico, and may reach parts of Northern California.
[9] After approximately 3 to 4 months of propagation across the Pacific (along the equatorial region), the Kelvin waves reach the western coast of South America and interact (merge/mix) with the cooler Peru current system.
[9] Rossby waves then enter the equation and, as previously stated, move at lower velocities than the Kelvin waves and can take anywhere from nine months to four years to fully cross the Pacific Ocean basin (from boundary to boundary).
[9] In terms of climate modeling and upon coupling the atmosphere and the ocean, an ENSO model typically contains the following dynamical equations: Note that h is the depth of the fluid (similar to the equivalent depth and analogous to H in the primitive equations listed above for Rossby-gravity and Kelvin waves), KT is temperature diffusion, KE is eddy diffusivity, and τ is the wind stress in either the x or y directions.
