Mixed Rossby-gravity waves are the n=0 westward-propagating rotational mode on the sphere.
Mixed Rossby-gravity (MRG) wave is the equatorially-trapped mode which together with the Kelvin wave fills the frequency gap between the Rossby and gravity modes in the tropics. As its zonal wavenumber increases, the MRG wave becomes increasingly more rotational mode. In the case of linearized equations on the equatorial beta-plane, the mixed Rossby-gravity wave is denoted the westward-propagating MRG 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