Rossby wave

Rossby (or planetary) waves are large-scale motions in the ocean or atmosphere whose restoring force is the variation in Coriolis effect with latitude. The waves were first identified in the atmosphere in 1939 by Carl-Gustaf Arvid Rossby who went on to explain their motion. Rossby waves are a subset of inertial waves.

Terrestrial waves
The special identifying feature of the Rossby waves is its phase velocity (that of the wave crests) always has a westward component. However, the wave's group velocity (associated with the energy flux) can be in any direction. In general: shorter waves have an eastward group velocity and long waves a westward group velocity.

The terms "barotropic" and "baroclinic" Rossby waves are used to distinguish their vertical structure. Barotropic Rossby waves do not vary in the vertical, and have the fastest propagation speeds. The baroclinic wave modes are slower, with speeds of only a few centimetres per second or less.

Atmospheric waves
Rossby waves in the atmosphere are easy to observe as (usually 4-6) large-scale meanders of the jet stream. When these loops become very pronounced, they detach the masses of cold, or warm, air that become cyclones and anticyclones and are responsible for day-to-day weather patterns at mid-latitudes.

The wave speed is given by


 * $$ c = u - \frac{\beta}{k^2},$$

where c is the wave speed, u is the mean westerly flow, $$\beta$$ is the Rossby parameter, and k is the total wavenumber.

Furthermore, the Rossby parameter is defined:
 * $$\beta = \frac{1}{a} \frac{d}{d\phi}  (2 \omega sin\phi) = \frac{2\omega cos\phi}{a}$$

φ is the latitude, ω is the angular speed of the Earth's rotation, and a is the mean radius of the Earth.

Oceanic waves
Oceanic Rossby waves are thought to communicate climatic changes due to variability in forcing, due to both the wind and buoyancy. Both barotropic and baroclinic waves cause variations of the sea surface height, although the length of the waves made them difficult to detect until the advent of satellite altimetry. Baroclinic waves also generate significant displacements of the oceanic thermocline, often of tens of meters. Satellite observations have revealed the stately progression of Rossby waves across all the ocean basins, particularly at low- and mid-latitudes. These waves can take months or even years to cross a basin like the Pacific.