[2] Their frequencies are much lower than that of gravity waves and represent motion that occurs as a result of the undisturbed potential vorticity varying (not constant) with latitude on the curved surface of the earth.
For very long waves (as the zonal wavenumber approaches zero), the non-dispersive phase speed is approximately:
To illustrate, suppose c = 2.8 m/s for the first baroclinic mode in the Pacific; then the Rossby wave speed would correspond to ~0.9 m/s, requiring a 6-month time frame to cross the Pacific basin from east to west.
[2] For very short waves (as the zonal wavenumber increases), the group velocity (energy packet) is eastward and opposite to the phase speed, both of which are given by the following relations: Thus, the phase and group speeds are equal in magnitude but opposite in direction (phase speed is westward and group velocity is eastward); note that is often useful to use potential vorticity as a tracer for these planetary waves, due to its invertibility (especially in the quasi-geostrophic framework).
Therefore, the physical mechanism responsible for the propagation of these equatorial Rossby waves is none other than the conservation of potential vorticity: Thus, as a fluid parcel moves equatorward (βy approaches zero), the relative vorticity must increase and become more cyclonic in nature.
Conversely, if the same fluid parcel moves poleward, (βy becomes larger), the relative vorticity must decrease and become more anticyclonic in nature.
As a side note, these equatorial Rossby waves can also be vertically-propagating waves when the Brunt–Vaisala frequency (buoyancy frequency) is held constant, ultimately resulting in solutions proportional to
The adjustment process tends to take place in two distinct stages where the first stage is a rapid change due to the fast propagation of gravity waves, the same as that on an f-plane (Coriolis parameter held constant), resulting in a flow that is close to geostrophic equilibrium.
The second stage is one where quasi-geostrophic adjustment takes place by means of planetary waves; this process can be comparable to the wave field adjusting to the mass field (due to the wavelengths being larger than the Rossby deformation radius.