Kelvin waves are the n=0 eastward-propagating inertia-gravity mode on the sphere.
Kelvin wave is the slowest eastward-propagating eigensolution of the linearized primitive equations on the sphere, associated with a large part of atmosphere and ocean variability in the tropics. Together with the MRG wave, Kelvin wave fills the frequency gap between the Rossby and inertia-gravity modes in the tropics. In the case of linearized equations on the equatorial beta-plane, the Kelvin wave is sometimes denoted n=-1 eastward-propagating inertia-gravity mode.
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Sielmann, Frank; Zagar, Nedjeljka; Lunkeit, Frank (2023). CLICCS-MODES - Modal wave filtering of ERA5 reanalyses with MODES (Version 2.0). World Data Center for Climate (WDCC) at DKRZ. https://doi.org/10.26050/WDCC/CLICCS-A2-M