Abstract
Near the equator, free-wave solutions are found under the assumption that the Coriolis parameter is given by \(f=\beta y\) (the equatorial \(\beta \)-plane approximation), which allows them to be represented as expansions in Hermite functions \(\phi _{j}\), \(j=0,1,2,\ldots \). Consequently, equatorial Rossby and gravity waves form a discrete set, with each wave corresponding to a specific j value. The \(j=0\) wave is a new type of wave, the mixed Rossby/gravity (Yanai) wave, which, depending on its zonal wavenumber, has properties similar to a Rossby or gravity wave. An equatorial Kelvin wave also exists. Solutions for the structures of these waves and their dispersion relations are obtained. Similarities between midlatitude and equatorial Rossby/gravity waves are noted: The two sets describe the same waves, differing only because of the approximation of f used to obtain them.
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Notes
- 1.
When the basin has northern and southern boundaries, however, this root is realistic. It corresponds to an antisymmetric pair of the zonal Kelvin waves discussed in Sect. 7.2.1, one located on each boundary (Philander 1977; Cane and Sarachik 1979).
- 2.
With northern and southern basin boundaries, however, the discarded root (the “anti-Kelvin wave”) is realistic, corresponding to a symmetric pair of the zonal Kelvin waves (Sect. 7.2.1) on each boundary (Cane and Sarachik 1979). Note that a combination of both discarded waves with the same amplitude gives a coastal Kelvin wave along only one of the boundaries.
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McCreary, J.P., Shetye, S.R. (2023). Equatorial Waves. In: Observations and Dynamics of Circulations in the North Indian Ocean. Atmosphere, Earth, Ocean & Space. Springer, Singapore. https://doi.org/10.1007/978-981-19-5864-9_8
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DOI: https://doi.org/10.1007/978-981-19-5864-9_8
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