In my PhD, I studied three different types of atmospheric wave in the presence of a background flow like that observed in the atmosphere. I used the rotating shallow water equations on the sphere as a model.
The movies below plot the perturbation of the east-west wind velocity from the background flow where blue represents easterly and red represents westerly perturbation. The prevailing background flow is indicated by the blue arrows. The dotted horizontal lines are the latitudes where the background wind reverses direction. The dots that follow the wave packets are their characteristic curves.
Global long waves are waves that oscillate on the scale of the planet and travel both in the tropics and the midlatutides. These waves are observed in statistical analysis of the atmosphere (Madden 2007) and show up in classic computations (Kasahara 1980).
Midlatitude continuous spectrum waves are prevented from entering the tropics at "critical latitudes" (indicated in red) where the wave speed matches the speed of the background flow (Case 1960, Farrel 1982).
These waves have very short wavelength in the tropics and long wavelength in the midlatitudes. One of the key results of my thesis is that these waves complete the spectrum in the tropics where the continuous spectrum waves are prevented from propagating.