Shorter Rossby-wave propagation inside a stationary long wave

For a stationary $n=2$, $l=0$ wave in a uniform zonal current, a perturbation $n>2$ has phase speed $U(1-4/n^2)$ and zonal group speed $U(1+4/n^2)$. Phase speed relative to the air is westward; packet propagation relative to the ground is faster downstream.

A wave packet can transfer energy downstream faster than individual phase features move, allowing successive downstream disturbances to develop while upstream ones weaken. In the simple uniform-current barotropic model with zero meridional wavenumber, the zonal group speed is $U+\beta /k^2$ while phase speed is $U-\beta /k^2$. Linear superposition and interference are not direct nonlinear eddy scattering. Real weather development also involves baroclinic energy conversion and wave–mean-flow feedback, which require additional dynamics.