Rossby wave
Rossby waves, also known as planetary waves, are a type of
Rossby wave types
Atmospheric waves
Atmospheric Rossby waves result from the conservation of potential vorticity and are influenced by the Coriolis force and pressure gradient.[3] The image on the left sketches fundamental principles of the wave, e.g., its restoring force and westward phase velocity. The rotation causes fluids to turn to the right as they move in the northern hemisphere and to the left in the southern hemisphere. For example, a fluid that moves from the equator toward the north pole will deviate toward the east; a fluid moving toward the equator from the north will deviate toward the west. These deviations are caused by the Coriolis force and conservation of potential vorticity which leads to changes of relative vorticity. This is analogous to conservation of angular momentum in mechanics. In planetary atmospheres, including Earth, Rossby waves are due to the variation in the Coriolis effect with latitude.
One can identify a terrestrial Rossby wave as its phase velocity, marked by its wave crest, always has a westward component.[citation needed] However, the collected set of Rossby waves may appear to move in either direction with what is known as its group velocity. In general, shorter waves have an eastward group velocity and long waves a westward group velocity.
The terms "
Most investigations of Rossby waves have been done on those in Earth's atmosphere. Rossby waves in the Earth's atmosphere are easy to observe as (usually 4–6) large-scale meanders of the jet stream. When these deviations become very pronounced, masses of cold or warm air detach, and become low-strength cyclones and anticyclones, respectively, and are responsible for day-to-day weather patterns at mid-latitudes. The action of Rossby waves partially explains why eastern continental edges in the Northern Hemisphere, such as the Northeast United States and Eastern Canada, are colder than Western Europe at the same latitudes,[5] and why the Mediterranean is dry during summer (Rodwell–Hoskins mechanism).[6]
Poleward-propagating atmospheric waves
Deep
Poleward-propagating Rossby waves explain many of the observed statistical connections between low- and high-latitude climates.[7] One such phenomenon is sudden stratospheric warming. Poleward-propagating Rossby waves are an important and unambiguous part of the variability in the Northern Hemisphere, as expressed in the Pacific North America pattern. Similar mechanisms apply in the Southern Hemisphere and partly explain the strong variability in the Amundsen Sea region of Antarctica.[8] In 2011, a Nature Geoscience study using general circulation models linked Pacific Rossby waves generated by increasing central tropical Pacific temperatures to warming of the Amundsen Sea region, leading to winter and spring continental warming of Ellsworth Land and Marie Byrd Land in West Antarctica via an increase in advection.[9]
Rossby waves on other planets
Atmospheric Rossby waves, like Kelvin waves, can occur on any rotating planet with an atmosphere. The Y-shaped cloud feature on Venus is attributed to Kelvin and Rossby waves.[10]
Oceanic waves
Oceanic Rossby waves are large-scale waves within an ocean basin. They have a low amplitude, in the order of centimetres (at the surface) to metres (at the thermocline), compared with atmospheric Rossby waves which are in the order of hundreds of kilometres. They may take months to cross an ocean basin. They gain momentum from wind stress at the ocean surface layer and are thought to communicate climatic changes due to variability in forcing, due to both the wind and buoyancy. Off-equatorial Rossby waves are believed to propagate through eastward-propagating Kelvin waves that upwell against Eastern Boundary Currents, while equatorial Kelvin waves are believed to derive some of their energy from the reflection of Rossby waves against Western Boundary Currents.[11]
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
Baroclinic waves also generate significant displacements of the oceanic
Rossby waves have been suggested as an important mechanism to account for the heating of the ocean on Europa, a moon of Jupiter.[14]
Waves in astrophysical discs
Rossby wave instabilities are also thought to be found in astrophysical discs, for example, around newly forming stars.[15][16]
Amplification of Rossby waves
It has been proposed that a number of regional weather extremes in the Northern Hemisphere associated with blocked atmospheric circulation patterns may have been caused by quasiresonant amplification of Rossby waves. Examples include the
Normally freely travelling
A 2017 study by
Mathematical definitions
Free barotropic Rossby waves under a zonal flow with linearized vorticity equation
To start with, a zonal mean flow, U, can be considered to be perturbed where U is constant in time and space. Let be the total horizontal wind field, where u and v are the components of the wind in the x- and y- directions, respectively. The total wind field can be written as a mean flow, U, with a small superimposed perturbation, u′ and v′.
The perturbation is assumed to be much smaller than the mean zonal flow.
The relative vorticity and the perturbations and can be written in terms of the stream function (assuming non-divergent flow, for which the stream function completely describes the flow):
Considering a parcel of air that has no relative vorticity before perturbation (uniform U has no vorticity) but with planetary vorticity f as a function of the latitude, perturbation will lead to a slight change of latitude, so the perturbed relative vorticity must change in order to conserve potential vorticity. Also the above approximation U >> u' ensures that the perturbation flow does not advect relative vorticity.
with . Plug in the definition of stream function to obtain:
Using the
This yields the dispersion relation:
The zonal (x-direction)
where c is the phase speed, cg is the group speed, U is the mean westerly flow, is the
Rossby parameter
The Rossby parameter is defined as the rate of change of the Coriolis frequency along the meridional direction:
where is the latitude, ω is the
If , there will be no Rossby waves; Rossby waves owe their origin to the gradient of the tangential speed of the planetary rotation (planetary vorticity). A "cylinder" planet has no Rossby waves. It also means that at the equator of any rotating, sphere-like planet, including Earth, one will still have Rossby waves, despite the fact that , because . These are known as Equatorial Rossby waves.
See also
- Atmospheric wave
- Equatorial wave
- Equatorial Rossby wave – mathematical treatment
- Harmonic
- Kelvin wave
- Polar vortex
- Rossby whistle
References
- ^ "What is a Rossby wave?". National Oceanic and Atmospheric Administration.
- ISBN 978-0-12-354015-7.
- ^ license.
- S2CID 9289503.
- S2CID 4388818.
- ISSN 1477-870X.
- .
- .
- doi:10.1038/ngeo1129.
- .
- ^ Battisti, David S. (April 1989). "On the Role of Off-Equatorial Oceanic Rossby Waves during ENSO". Journal of Physical Oceanography. 19.4: 551–560.
- S2CID 126953559.
- ^ Chelton, Dudley B.; Schlax, Michael B. (1996). "Global Observations of Oceanic Rossby Waves" (PDF). Science. 272 (5259): 234–238.
- S2CID 205215528.
- S2CID 8914218.
- S2CID 119382697.
- PMID 23457264.
- PMID 28345645.
Bibliography
- Rossby, C.-G. (21 June 1939). "Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action". Journal of Marine Research. 2 (1): 38–55. S2CID 27148455.
- Platzman, G. W. (July 1968). "The Rossby wave". Quarterly Journal of the Royal Meteorological Society. 94 (401): 225–248. .
- Dickinson, R. E. (January 1978). "Rossby Waves—Long-Period Oscillations of Oceans and Atmospheres". Annual Review of Fluid Mechanics. 10 (1): 159–195. .