Movatterモバイル変換

[0]ホーム
URL:

Jump to content
WikipediaThe Free Encyclopedia
Search

Rossby wave

From Wikipedia, the free encyclopedia
Inertial wave in rotating fluids
icon
This articleneeds additional citations forverification. Please helpimprove this article byadding citations to reliable sources. Unsourced material may be challenged and removed.
Find sources: "Rossby wave" – news ·newspapers ·books ·scholar ·JSTOR(July 2025) (Learn how and when to remove this message)

Meanders of the Northern Hemisphere'sjet stream developing around the northernpolar 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.

Rossby waves, also known asplanetary waves, are a type ofinertial wave naturally occurring in rotating fluids.[1] They were first identified by Sweden-born American meteorologistCarl-Gustaf Arvid Rossby in theEarth's atmosphere in 1939. They are observed in theatmospheres andoceans of Earth and other planets, owing to therotation of Earth or of the planet involved. Atmospheric Rossby waves on Earth are giantmeanders in high-altitudewinds that have a major influence onweather. These waves are associated withpressure systems and thejet stream (especially around thepolar vortices).[2] Oceanic Rossby waves move along thethermocline: the boundary between the warm upper layer and the cold deeper part of the ocean.

Rossby wave types

[edit]

Atmospheric waves

[edit]
Sketches of Rossby waves' fundamental principles.a andb The restoring force.c–e The waveform's velocity. Ina, an air parcel follows along latitudeφ0{\displaystyle \varphi _{0}} at an eastward velocityvE{\displaystyle v_{E}} with a meridional accelerationaN=0{\displaystyle a_{N}=0} when the pressure gradient force balances the Coriolis force. Inb, when the parcel encounters a small displacementδφ{\displaystyle \delta \varphi } in latitude, the Coriolis force's gradient imposes a meridional accelerationaN{\displaystyle a_{N}} that always points againstδφ{\displaystyle \delta \varphi } whenvE>0{\displaystyle v_{E}>0}. Here,Ω{\displaystyle \Omega } denotes the Earth's angular frequency andaN{\displaystyle a_{N}} is the northward Coriolis acceleration. While the parcel meanders along the blue arrowed linel{\displaystyle l} inb , its waveform travels westward as sketched inc. The absolute vorticity composes the planetary vorticityf{\displaystyle f} and the relative vorticityζ{\displaystyle \zeta }, reflecting the Earth's rotation and the parcel's rotation with respect to the Earth, respectively. The conservation of absolute vorticityη{\displaystyle \eta } determines a southward gradient ofζ{\displaystyle \zeta }, as denoted by the red shadow inc. The gradient's projection along the flow pathl{\displaystyle l} is typically not zero and would cause a tangential velocityvt{\displaystyle v_{t}}. As an example, the pathl{\displaystyle l} inc is zoomed in at two green crosses, displayed ind ande. These two crosses are associated with positive and negative gradients ofζ{\displaystyle \zeta } alongl{\displaystyle l}, respectively, as denoted by the red and pink arrows ind ande. The black arrowsvt{\displaystyle v_{t}} 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 inc and, visually, the pathl{\displaystyle l} drifts westward toward the dotted line.[3]

Atmospheric Rossby waves result from the conservation ofpotential vorticity and are influenced by theCoriolis 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 ofangular momentum in mechanics. In planetary atmospheres, including Earth, Rossby waves are due to the variation in the Coriolis effect withlatitude.

One can identify a terrestrial Rossby wave as itsphase velocity, marked by its wave crest, always has a westward component.[1][4] However, the collected set of Rossby waves may appear to move in either direction with what is known as itsgroup velocity. In general, shorter waves have an eastward group velocity and long waves a westward group velocity.

The terms "barotropic" and "baroclinic" are used to distinguish the vertical structure of Rossby waves. Barotropic Rossby waves do not vary in the vertical[clarification needed], and have the fastest propagation speeds. The baroclinic wave modes, on the other hand, do vary in the vertical. They are also slower, with speeds of only a few centimeters per second or less.[5]

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 thejet stream. When these deviations become very pronounced, masses of cold or warm air detach, and become low-strengthcyclones andanticyclones, 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 samelatitudes,[6] and why the Mediterranean is dry during summer (Rodwell–Hoskins mechanism).[7]

Poleward-propagating atmospheric waves

[edit]

Deepconvection (heat transfer) to thetroposphere is enhanced over very warm sea surfaces in the tropics, such as duringEl Niño events. This tropical forcing generates atmospheric Rossby waves that have a poleward and eastward migration.

Poleward-propagating Rossby waves explain many of the observed statistical connections between low- and high-latitude climates.[8] One such phenomenon issudden 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 theAmundsen Sea region of Antarctica.[9] In 2011, aNature Geoscience study usinggeneral 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 ofEllsworth Land andMarie Byrd Land inWest Antarctica via an increase inadvection.[10]

Rossby waves on other planets

[edit]

Atmospheric Rossby waves, likeKelvin waves, can occur on any rotating planet with an atmosphere. The Y-shaped cloud feature onVenus is attributed to Kelvin and Rossby waves.[11]

Oceanic waves

[edit]

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 gainmomentum fromwind stress at the ocean surface layer and are thought to communicate climatic changes due to variability inforcing, due to both thewind andbuoyancy. Off-equatorial Rossby waves are believed to propagate through eastward-propagatingKelvin waves that upwell againstEastern Boundary Currents, while equatorial Kelvin waves are believed to derive some of their energy from the reflection of Rossby waves against Western Boundary Currents.[12]

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 ofsatellitealtimetry.Satellite observations have confirmed the existence of oceanic Rossby waves.[13]

Baroclinic waves also generate significant displacements of the oceanicthermocline, often of tens of meters. Satellite observations have revealed the stately progression of Rossby waves across all theocean basins, particularly at low- and mid-latitudes. Due to thebeta effect, transit times of Rossby waves increase with latitude. In a basin like thePacific, waves travelling at the equator may take months, while closer to the poles transit may take decades.[14]

Rossby waves have been suggested as an important mechanism to account for the heating ofthe ocean on Europa, a moon ofJupiter.[15]

Waves in astrophysical discs

[edit]

Rossby wave instabilities are also thought to be found in astrophysicaldiscs, for example, around newly forming stars.[16][17]

Amplification of Rossby waves

[edit]

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 byquasiresonant amplification of Rossby waves. Examples include the2013 European floods, the2012 China floods, the2010 Russian heat wave, the2010 Pakistan floods and the2003 European heat wave. Even takingglobal warming into account, the 2003 heat wave would have been highly unlikely without such a mechanism.

Normally freely travellingsynoptic-scale Rossby waves andquasistationary planetary-scale Rossby waves exist in themid-latitudes with only weak interactions. The hypothesis, proposed byVladimir Petoukhov,Stefan Rahmstorf,Stefan Petri, andHans Joachim Schellnhuber, is that under some circumstances these waves interact to produce the static pattern. For this to happen, they suggest, thezonal (east-west)wave number of both types of wave should be in the range 6–8, the synoptic waves should be arrested within thetroposphere (so that energy does not escape to thestratosphere) and mid-latitudewaveguides should trap the quasistationary components of the synoptic waves. In this case the planetary-scale waves may respond unusually strongly toorography and thermal sources and sinks because of "quasiresonance".[18]

A 2017 study byMann, Rahmstorf, et al. connected the phenomenon of anthropogenicArctic amplification to planetary wave resonance andextreme weather events.[19]

Mathematical definitions

[edit]

Free barotropic Rossby waves under a zonal flow with linearized vorticity equation

[edit]

To start with, a zonal mean flow,U, can be considered to be perturbed whereU is constant in time and space. Letu→=⟨u,v⟩{\displaystyle {\vec {u}}=\langle u,v\rangle } be the total horizontal wind field, whereu andv are the components of the wind in thex- andy- directions, respectively. The total wind field can be written as a mean flow,U, with a small superimposed perturbation,u′ andv′.u=U+u′(t,x,y){\displaystyle u=U+u'(t,x,y)\!}v=v′(t,x,y){\displaystyle v=v'(t,x,y)\!}

The perturbation is assumed to be much smaller than the mean zonal flow.U≫u′,v′{\displaystyle U\gg u',v'\!}

The relative vorticityη{\displaystyle \eta } and the perturbationsu′{\displaystyle u'} andv′{\displaystyle v'} can be written in terms of thestream functionψ{\displaystyle \psi } (assuming non-divergent flow, for which the stream function completely describes the flow):u′=∂ψ∂yv′=−∂ψ∂xη=∇×(u′ı^+v′ȷ^)=−∇2ψ{\displaystyle {\begin{aligned}u'&={\frac {\partial \psi }{\partial y}}\\[5pt]v'&=-{\frac {\partial \psi }{\partial x}}\\[5pt]\eta &=\nabla \times (u'\mathbf {\hat {\boldsymbol {\imath }}} +v'\mathbf {\hat {\boldsymbol {\jmath }}} )=-\nabla ^{2}\psi \end{aligned}}}

Considering a parcel of air that has no relative vorticity before perturbation (uniformU has no vorticity) but with planetary vorticityf 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 conservepotential vorticity. Also the above approximationU >>u' ensures that the perturbation flow does not advect relative vorticity.

d(η+f)dt=0=∂η∂t+U∂η∂x+βv′{\displaystyle {\frac {d(\eta +f)}{dt}}=0={\frac {\partial \eta }{\partial t}}+U{\frac {\partial \eta }{\partial x}}+\beta v'}withβ=∂f∂y{\displaystyle \beta ={\frac {\partial f}{\partial y}}}. Plug in the definition of stream function to obtain:0=∂∇2ψ∂t+U∂∇2ψ∂x+β∂ψ∂x{\displaystyle 0={\frac {\partial \nabla ^{2}\psi }{\partial t}}+U{\frac {\partial \nabla ^{2}\psi }{\partial x}}+\beta {\frac {\partial \psi }{\partial x}}}

Using themethod of undetermined coefficients one can consider a traveling wave solution withzonal and meridionalwavenumbersk andℓ, respectively, and frequencyω{\displaystyle \omega }:ψ=ψ0ei(kx+ℓy−ωt){\displaystyle \psi =\psi _{0}e^{i(kx+\ell y-\omega t)}\!}

This yields thedispersion relation:ω=Uk−βkk2+ℓ2{\displaystyle \omega =Uk-\beta {\frac {k}{k^{2}+\ell ^{2}}}}

The zonal (x-direction)phase speed andgroup velocity of the Rossby wave are then given byc≡ωk=U−βk2+ℓ2,cg≡∂ω∂k =U−β(ℓ2−k2)(k2+ℓ2)2,{\displaystyle {\begin{aligned}c&\equiv {\frac {\omega }{k}}=U-{\frac {\beta }{k^{2}+\ell ^{2}}},\\[5pt]c_{g}&\equiv {\frac {\partial \omega }{\partial k}}\ =U-{\frac {\beta (\ell ^{2}-k^{2})}{(k^{2}+\ell ^{2})^{2}}},\end{aligned}}}wherec is the phase speed,cg is the group speed,U is the mean westerly flow,β{\displaystyle \beta } is theRossby parameter,k is thezonal wavenumber, andℓ is themeridional wavenumber. It is noted that the zonal phase speed of Rossby waves is always westward (traveling east to west) relative to mean flowU, but the zonal group speed of Rossby waves can be eastward or westward depending on wavenumber.

Rossby parameter

[edit]

TheRossby parameter is defined as the rate of change of theCoriolis frequency along the meridional direction:β=∂f∂y=1addφ(2ωsin⁡φ)=2ωcos⁡φa,{\displaystyle \beta ={\frac {\partial f}{\partial y}}={\frac {1}{a}}{\frac {d}{d\varphi }}(2\omega \sin \varphi )={\frac {2\omega \cos \varphi }{a}},}whereφ{\displaystyle \varphi } is the latitude,ω is theangular speed of theEarth's rotation, anda is the meanradius of the Earth.

Ifβ=0{\displaystyle \beta =0}, 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 thatf=0{\displaystyle f=0}, becauseβ>0{\displaystyle \beta >0}. These are known asEquatorial Rossby waves.

See also

[edit]

References

[edit]
  1. ^ab"What is a Rossby wave?".National Oceanic and Atmospheric Administration.
  2. ^Holton, James R. (2004).Dynamic Meteorology. Elsevier. p. 347.ISBN 978-0-12-354015-7.
  3. ^abHe, Maosheng; Forbes, Jeffrey M. (7 December 2022)."Rossby wave second harmonic generation observed in the middle atmosphere".Nature Communications.13 (1): 7544.Bibcode:2022NatCo..13.7544H.doi:10.1038/s41467-022-35142-3.ISSN 2041-1723.PMC 9729661.PMID 36476614. This article incorporates text from this source, which is available under theCC BY 4.0 license.
  4. ^Rossby, C. G.; Willett, H. C.; Holmboe, Messrs. J.; Namias, J.; Page, L.; Allen, R. (1939)."Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the permanent centers of action atmosphere and the displacements of the permanent centers of action".Journal of Marine Research.2 (1):38–55. Retrieved4 July 2024.
  5. ^Shepherd, Theodore G. (October 1987)."Rossby waves and two-dimensional turbulence in a large-scale zonal jet".Journal of Fluid Mechanics.183:467–509.Bibcode:1987JFM...183..467S.doi:10.1017/S0022112087002738.S2CID 9289503.
  6. ^Kaspi, Yohai; Schneider, Tapio (March 2011)."Winter cold of eastern continental boundaries induced by warm ocean waters"(PDF).Nature.471 (7340):621–624.Bibcode:2011Natur.471..621K.doi:10.1038/nature09924.PMID 21455177.S2CID 4388818.
  7. ^Rodwell, Mark J.; Hoskins, Brian J. (1996). "Monsoons and the dynamics of deserts".Quarterly Journal of the Royal Meteorological Society.122 (534):1385–1404.Bibcode:1996QJRMS.122.1385R.doi:10.1002/qj.49712253408.ISSN 1477-870X.
  8. ^Hoskins, Brian J.; Karoly, David J. (June 1981)."The Steady Linear Response of a Spherical Atmosphere to Thermal and Orographic Forcing".Journal of the Atmospheric Sciences.38 (6):1179–1196.Bibcode:1981JAtS...38.1179H.doi:10.1175/1520-0469(1981)038<1179:TSLROA>2.0.CO;2.
  9. ^Lachlan-Cope, Tom; Connolley, William (16 December 2006)."Teleconnections between the tropical Pacific and the Amundsen-Bellinghausens Sea: Role of the El Niño/Southern Oscillation".Journal of Geophysical Research: Atmospheres.111 (D23).Bibcode:2006JGRD..11123101L.doi:10.1029/2005JD006386.
  10. ^Ding, Qinghua; Steig, Eric J.; Battisti, David S.; Küttel, Marcel (June 2011). "Winter warming in West Antarctica caused by central tropical Pacific warming".Nature Geoscience.4 (6):398–403.Bibcode:2011NatGe...4..398D.CiteSeerX 10.1.1.459.8689.doi:10.1038/ngeo1129.
  11. ^Covey, Curt; Schubert, Gerald (November 1982)."Planetary-Scale Waves in the Venus Atmosphere".Journal of the Atmospheric Sciences.39 (11):2397–2413.Bibcode:1982JAtS...39.2397C.doi:10.1175/1520-0469(1982)039<2397:PSWITV>2.0.CO;2.
  12. ^Battisti, David S. (April 1989)."On the Role of Off-Equatorial Oceanic Rossby Waves during ENSO".Journal of Physical Oceanography.19.4:551–560.
  13. ^Chelton, D. B.; Schlax, M. G. (1996). "Global Observations of Oceanic Rossby Waves".Science.272 (5259): 234.Bibcode:1996Sci...272..234C.doi:10.1126/science.272.5259.234.S2CID 126953559.
  14. ^Chelton, Dudley B.; Schlax, Michael B. (1996)."Global Observations of Oceanic Rossby Waves"(PDF).Science.272 (5259):234–238.
  15. ^Tyler, Robert H. (2008). "Strong ocean tidal flow and heating on moons of the outer planets".Nature.456 (7223):770–2.Bibcode:2008Natur.456..770T.doi:10.1038/nature07571.PMID 19079055.S2CID 205215528.
  16. ^Lovelace, R. V. E.; Li, H.; Colgate, S. A.; Nelson, A. F. (10 March 1999). "Rossby Wave Instability of Keplerian Accretion Disks".The Astrophysical Journal.513 (2):805–810.arXiv:astro-ph/9809321.Bibcode:1999ApJ...513..805L.doi:10.1086/306900.S2CID 8914218.
  17. ^Li, H.; Finn, J. M.; Lovelace, R. V. E.; Colgate, S. A. (20 April 2000). "Rossby Wave Instability of Thin Accretion Disks. II. Detailed Linear Theory".The Astrophysical Journal.533 (2):1023–1034.arXiv:astro-ph/9907279.Bibcode:2000ApJ...533.1023L.doi:10.1086/308693.S2CID 119382697.
  18. ^Petoukhov, Vladimir; Rahmstorf, Stefan; Petri, Stefan; Schellnhuber, Hans Joachim (2 April 2013)."Quasiresonant amplification of planetary waves and recent Northern Hemisphere weather extremes".Proceedings of the National Academy of Sciences of the United States of America.110 (14):5336–5341.Bibcode:2013PNAS..110.5336P.doi:10.1073/pnas.1222000110.PMC 3619331.PMID 23457264.
  19. ^Mann, Michael E.; Rahmstorf, Stefan; Kornhuber, Kai; Steinman, Byron A.; Miller, Sonya K.; Coumou, Dim (30 May 2017)."Influence of Anthropogenic Climate Change on Planetary Wave Resonance and Extreme Weather Events".Scientific Reports.7 (1) 45242.Bibcode:2017NatSR...745242M.doi:10.1038/srep45242.PMC 5366916.PMID 28345645.

Bibliography

[edit]

External links

[edit]
Waves
Upwelling





Antarctic bottom water
Circulation
Tides
Landforms
Plate
tectonics
Ocean zones
Sea level
Acoustics
Satellites
Related
International
National
Other
Retrieved from "https://en.wikipedia.org/w/index.php?title=Rossby_wave&oldid=1319598599"
Categories:
Hidden categories:
[8]ページ先頭
©2009-2025 Movatter.jp