= Rossby-gravity wave
{c}
{wiki=Rossby-gravity_waves}
= Yanai wave
{c}
{synonym}
= Mixed Rossby-gravity wave
{synonym}
The Yanai wave is the $n=0$ branch of the <equatorial shallow-water dispersion relation> with positive frequency:
$$
k=\frac\omega c-\frac\beta\omega,\qquad v\propto e^{-\beta y^2/(2c)}.
$$
Its <group velocity> is $d\omega/dk=c\omega^2/(\omega^2+\beta c)>0$. At low frequency it has westward <phase velocity> but transports energy eastward; at high frequency its phase and group velocities approach $c$.
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