From AMS Glossary
(Also called mixed Rossby–gravity wave, Yanai wave.) An equatorial wave with a dispersion relation asymptotic to that for equatorial Kelvin waves for large positive (eastward) zonal wavenumbers and asymptotic to that for equatorial Rossby waves for large negative (westward) zonal wavenumbers.
In the shallow water approximation, the dispersion relationship is given by frequency
in which k is the zonal wavenumber, β is the meridional gradient of the Coriolis parameter at the equator, and
for which g is the acceleration of gravity and H is the mean fluid depth.