= Stationary stratified Rossby-wave group velocity
{title2=$c_{g,x}=2\beta k^2/(k^2+\alpha^2)^2$}
For <dispersion relation> $\omega=Uk-\beta k/(k^2+\alpha^2)$ with fixed $\alpha^2\geq0$, nonzero zonal <wavenumber> and stationary phase imply $U=\beta/(k^2+\alpha^2)$. Differentiating at fixed $\alpha$ yields $c_{g,x}=U+\beta(k^2-\alpha^2)/(k^2+\alpha^2)^2$, which reduces to the displayed positive value for $\beta>0$. Thus a stationary <Rossby wave> can transport <energy> eastward even though its crests stay fixed.
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