Baroclinic Rossby-wave group velocity ($c_{gx}=\frac{\partial \omega }{\partial k}$)

For fixed meridional wavenumber and deformation radius, differentiating $\omega =Uk-\beta k/(k^2+l^2+L_d^{-2})$ gives $c_{gx}=U+\beta (k^2-l^2-L_d^{-2})/(k^2+l^2+L_d^{-2}{)}^2$. A localized packet uses this velocity rather than $\omega /k$. For $l=0$ its intrinsic sign changes at $|k|L_d=1$.