Shallow-water Rossby-wave dispersion relation
= Shallow-water Rossby-wave dispersion relation
{title2=$\omega=-\beta k/(k^2+l^2+a^2)$}
For a resting midlatitude layer, the slow <Rossby wave> equation is $(\nabla_h^2-a^2)\eta_t=-\beta\eta_x$, where $a=f_0/\sqrt{gH}$. With the <plane wave> convention $e^{i(kx+ly-\omega t)}$,
$$
\omega=-\frac{\beta k}{k^2+l^2+a^2}.
$$
The zonal <phase velocity> is westward for $\beta>0$, but the zonal <group velocity> changes sign at $k^2=l^2+a^2$.