Rossby wave

Atmospheric Rossby waves on Earth are giant meanders in high-altitude winds that have a major influence on weather.

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.

In planetary atmospheres, including Earth, Rossby waves are due to the variation in the Coriolis effect with latitude.

Barotropic Rossby waves do not vary in the vertical[clarification needed], and have the fastest propagation speeds.

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.

[7] Deep convection (heat transfer) to the troposphere is enhanced over very warm sea surfaces in the tropics, such as during El Niño events.

Poleward-propagating Rossby waves explain many of the observed statistical connections between low- and high-latitude climates.

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.

[9] 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.

Satellite observations have revealed the stately progression of Rossby waves across all the ocean basins, particularly at low- and mid-latitudes.

[14] Rossby waves have been suggested as an important mechanism to account for the heating of the ocean on Europa, a moon of Jupiter.

[15] Rossby wave instabilities are also thought to be found in astrophysical discs, for example, around newly forming stars.

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.

In this case the planetary-scale waves may respond unusually strongly to orography and thermal sources and sinks because of "quasiresonance".

[18] A 2017 study by Mann, Rahmstorf, et al. connected the phenomenon of anthropogenic Arctic amplification to planetary wave resonance and extreme weather events.

Plug in the definition of stream function to obtain: Using the method of undetermined coefficients one can consider a traveling wave solution with zonal and meridional wavenumbers k and ℓ, respectively, and frequency

It is noted that the zonal phase speed of Rossby waves is always westward (traveling east to west) relative to mean flow U, but the zonal group speed of Rossby waves can be eastward or westward depending on wavenumber.

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

Meanders of the Northern Hemisphere's jet stream developing around the northern polar vortex (a, b) and finally detaching a "drop" of cold air (c). Orange: warmer masses of air; pink: jet stream; blue: colder masses of air.
Sketches of Rossby waves’ fundamental principles. a and b The restoring force. c – e The waveform’s velocity. In a , an air parcel follows along latitude at an eastward velocity with a meridional acceleration when the pressure gradient force balances the Coriolis force. In b , when the parcel encounters a small displacement in latitude, the Coriolis force’s gradient imposes a meridional acceleration that always points against when . Here, denotes the Earth’s angular frequency and is the northward Coriolis acceleration. While the parcel meanders along the blue arrowed line in b , its waveform travels westward as sketched in c . The absolute vorticity composes the planetary vorticity and the relative vorticity , reflecting the Earth’s rotation and the parcel’s rotation with respect to the Earth, respectively. The conservation of absolute vorticity determines a southward gradient of , as denoted by the red shadow in c . The gradient’s projection along the flow path is typically not zero and would cause a tangential velocity . As an example, the path in c is zoomed in at two green crosses, displayed in d and e . These two crosses are associated with positive and negative gradients of along , respectively, as denoted by the red and pink arrows in d and e . The black arrows denote the vector sums of the red and pink arrows bordering the crosses, both of which project zonally westward. The parcels at these crosses drift toward the green points in c and, visually, the path drifts westward toward the dotted line. [ 3 ]