高等大气动力学Rossbywave

PhysicsofRossbyWaveYihuaLinAOPP,ClarendonLaboratoryUniversityofOxford,UK4th,June,2008WaveRossbywaveinatmosphere&oceanMechanismofRossbywavePropagation&dispersionofRossbywaveOutline2Whatiswave？Inphysics,awaveisadisturbancethattravelsthroughspaceandtime,usuallyaccompaniedbythetransferofenergy.Wavestravelandthewavemotiontransfersenergyfromonepointtoanother,oftenwithnopermanentdisplacementoftheparticlesofthemedium—thatis,withlittleornoassociatedmasstransport.Theyconsist,instead,ofoscillationsorvibrationsaroundalmostfixedlocations.Wave3Mechanicalwave,whichpropagatesthroughamediuminwhichthesubstanceofthismediumisdeformed.Thedeformationreversesitselfowingtorestoringforcesresultingfromitsdeformation.Forexample,soundwaves.Electromagneticradiation(includingvisiblelight,ultravioletradiation,infraredradiation,gammarays,X-rays,andradiowaves).Thistypewavecantravelthroughavacuumandconsistsofperiodicoscillationsinelectricalandmagneticfields.4Transverseandlongitudinalwaves.Transversewavesoccurwhenadisturbancesendswavesperpendicular(atrightangles)totheoriginalwave.Longitudinalwavesoccurwhenadisturbancesendswavesinthesamedirectionastheoriginalwave.5Wavesinfluidsresultfromtheactionofrestoringforcesonfluidparcelsthathavebeendisplacedfromtheirequilibriumpositions.Therestoringforcesmaybeduetocompressibility,gravity,rotation,orelectromagneticeffects.Acousticwave,shallowwatergravitywave,buoyancywaveorinternalgravitywave,inertialwave,Rossbywave(planetarywaves),mixedwave.6WavesinAtmosphere&Ocean7•usuallyare4-6ofthemaroundtheglobeatagiventime•wavelengthvariesbetween4000-8000km•aregenerallystationary-ormoveveryslowlyeastorwestAtmosphere8Heightofthe500hPaisobaricsurface(dam),03March200506Z.Surfacepressureanalysis;03March200512Z.910The2smallblackcirclesoffthecoastoftheAmericascorrespondtosealevelhighsonthetrailingedgeofKelvinwaves.Theleadingedgeofthiswavegrouphasbouncedoffthecoastline,creatingRossbywaveswhoserisingandfallingsealevelsaremarkedbysolidanddashedlines,respectively.IntheJulyimage,thecirclesaremovingwestwiththeRossbywaves.TheXmarksarelativesealevellowcausedbyaKelvinwavemovingeast.InDecember,theRossbywavescontinuetomovewestward.TheshapesofthesolidanddashedlinesindicatethattheRossbywavesaremovingawayfromtheAmericasfasterattheequatorthanathigherlatitudes.Whiteandredindicatedhigherthanaveragelevels;purpleandmagentaindicatelowerthanaveragelevels.Thesescenesshoweastward-movingKelvinwavesandwestward-movingRossbywaves.SuperimposedblackcirclesshowhowtheelevatedseasurfacemoveseastinApril,thenwestasRossbywavesduringJulyandDecember.OceanRossbyWavesThemostimportantclassoflarge-scaleatmosphericwavesarecalledplanetarywaves,orRossbywaves.Thesewavesarecharacterizedbyoscillationsintherotationalpartofthehorizontalwindthatareparalleltothehorizontalgradientinthepotentialvorticity.11MechanismofRossbyWaveRestoringforceisthenorth-southgradientofbackgroundpotentialvorticity(f/H).Thatgradientcanbeduetoeitherthevariationinfwithlatitude,ortoavariationinH(“topographicRossbywaves”andwhentrappednearthecoast“continentalshelfwaves”).NotethatRossbywavesaretranversewaves,thatistheparticlesmoveperpendiculartothedirectionofpropagation.ConservesPV=(f+ζ)/H.1213Sketch:northernhemisphereImaginethatsomethingpushesawatercolumnperpendiculartotheplanetaryvorticity.Whatwillhappen?Theparcelwillconservetotalpotentialvorticity─(f+ζ/H).Asitmovesintoaregionofhigherf,itwilltendtodecreaserelativevorticity─atendencytoclockwisemotion.Likewiseifitweredisplacedtowardslowerrelativevorticity,itwillincreaserelativevorticity─atendencytowardscounterclockwisemotion.1415Nowlet’slookattheCoriolisforcesontheinducedcirculationpattern.Sizeofrestoringforce(foragivendisplacement)isproportionaltoβ=df/dy.PVequation:Dζ/Dt+βv=0Thesamethingwillholdtrueonaslope─pushedtowardsshallowerwaterwillrequiredecreasedrelativevorticityandviceversa─soshallowerwateristheanalogofnorthwardoveraflatbottomandthereareanalogouswavesgeneratedonstrongtopographicslopescalledtopographicRossbywaves.H～f.16Inlastsection,wederivedthepropertiesofRossbywaves.OurkeyfindingswasthatRossbywavesrelyontheβ-effectfortheirexistence.WealsodiscussedthemechanismforRossbywavepropagationthroughpotentialvorticityconservation.17RossbywavepropagationPotentialvorticityequationConsidersmall-amplitudedisturbancestoauniformzonalbackgroundflow(U,0,0)forwhichthestreamfunctionisandthequasigeostrophicpotentialvorticityisThestreamfunctionforthetotalflow(backgroundplussmalldisturbance)isthusandthepotentialvorticity18WhereWenowsubstitutetheaboveinthequasigeostrophicpotentialvorticityequationandneglecttermsthatarequadraticinthedisturbancequantities:Thefirsttermrepresentstherateofchangeoftheperturbedpotentialvorticityfollowingthemeanflow,andthesecondtermrepresentstheadvectionofmeanpotentialvorticitybytheperturbedflow.19DispersionrelationWenowlookforplane-wavesolutions,Weshallalsoassumeconstantstratification,i.e.,N2=constant.ThisgivesthedispersionrelationforquasigeostrophicRossbywaves:Asinlastsection,theβ-effectiscrucialfortheseRossbywaves.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