?大氣科學(xué)根底?課件第2章大氣動(dòng)力學(xué)根底2.1大氣運(yùn)動(dòng)根本方程

〔1〕作用于空氣的力〔2〕標(biāo)準(zhǔn)坐標(biāo)系中的動(dòng)量方程〔3〕連續(xù)方程的推導(dǎo)及物理意義氣壓梯度力G水平氣壓梯度力垂直氣壓梯度力其中，氣壓梯度力的大小決定于氣壓梯度和空氣密度，它的方向?yàn)榇怪庇诘葔好鎻母邏褐赶虻蛪?。地轉(zhuǎn)偏向力C由于在轉(zhuǎn)動(dòng)的非慣性參照系下自由運(yùn)動(dòng)的物體受到的一種使運(yùn)動(dòng)方向發(fā)生偏轉(zhuǎn)的力，稱(chēng)為地轉(zhuǎn)偏向力。物理學(xué)上也稱(chēng)為科里奧利力，簡(jiǎn)稱(chēng)科氏力。

作用在單位質(zhì)量物體上的地轉(zhuǎn)偏向力的大小與物理運(yùn)動(dòng)速度和地球自轉(zhuǎn)角速度成正比。CoriolisForce

Anapparentforcethatisduetotherotationoftheearth;Notarealforceinthesensethatitcannotcauseamotion;Asanearth-boundobserver,wearenotawareoftherotationoftheearth;Corioliseffectactsonlyonobjectsmovingwithrespecttotheearth’ssurface.Considerarocketfirednorthfromtheequator:Sincetheearthrotatesasasolidbody,theequatorwillmovefasterthanlandnearthepoles.Thegreenguywillhavetorunfasterthantheorangeguytokeepup.產(chǎn)生的原因物體為保持水平慣性運(yùn)動(dòng)，經(jīng)緯網(wǎng)因隨地球自轉(zhuǎn)而產(chǎn)生相對(duì)加速度。地轉(zhuǎn)偏向力向右是在北半球，在南半球那么都向左；由于除南北兩極外，各緯度的角速度都一樣，從北向南飛的時(shí)候，南邊的圈大，即越向南緯線越長(zhǎng)，所以線速度大，所以在北邊的時(shí)候具有的一個(gè)小的線速度與南邊的線速度相比就顯的慢了。，

在北半球，當(dāng)物體從南向北飛行時(shí)，即由快的地方到慢的地方，速度‘超前’了，前進(jìn)方向上也就向右偏了；同理，向南飛行。其結(jié)果都是使得物體出現(xiàn)向右偏轉(zhuǎn)的效果，這個(gè)效果就是由地轉(zhuǎn)偏向力造成的。影響與應(yīng)用科里奧利力不僅僅對(duì)風(fēng)產(chǎn)生影響，任何一個(gè)環(huán)繞地表的遠(yuǎn)距離運(yùn)動(dòng)都會(huì)受到它的捉弄。在一戰(zhàn)期間，德軍用他們引以自豪的射程為113千米的大炮轟擊巴黎時(shí)，懊惱地發(fā)現(xiàn)炮彈總是向右偏離目標(biāo)。直到那時(shí)為止，他們從沒(méi)擔(dān)憂過(guò)科里奧利力的影響，因?yàn)樗麄儚臎](méi)有這樣遠(yuǎn)距離的開(kāi)火；當(dāng)然，對(duì)于近距離的運(yùn)動(dòng)，科里奧利力影響極小。從場(chǎng)地一邊把籃球拋到另一邊的運(yùn)發(fā)動(dòng)，考慮科里奧利力的影響而需要調(diào)整自己投球的偏移量為厘米。當(dāng)你拔掉盥洗池的橡皮塞時(shí)，會(huì)發(fā)現(xiàn)有時(shí)水流并不是逆時(shí)針旋轉(zhuǎn)流走的，因?yàn)榭评飱W利力幾乎沒(méi)有足夠的時(shí)間來(lái)影響水這樣短距離的運(yùn)動(dòng)，水流的形態(tài)更多地受到水池形狀或者水龍頭噴射角度的影響；一個(gè)名叫古斯塔·加斯佩德·科里奧利的法國(guó)人在1835年最先用數(shù)學(xué)方法描述了這種效應(yīng)，所以科學(xué)界用他的姓氏來(lái)命名此種力。我們通常也稱(chēng)它為地轉(zhuǎn)偏向力。在北半球，科里奧利力使風(fēng)向右偏離其原始的路線；在南半球，這種力使風(fēng)向左偏離。風(fēng)速越大，產(chǎn)生的偏離越大。于是，在北半球，當(dāng)空氣向低壓中心輻合時(shí)會(huì)向右彎曲，形成了一個(gè)逆時(shí)針?lè)较虻男D(zhuǎn)氣流。從高壓中心輻散出來(lái)的空氣，那么因?yàn)橄蛴覐澢纬闪隧槙r(shí)針?lè)较虻男L(fēng)。我們把逆時(shí)針旋轉(zhuǎn)的叫做氣旋，把順時(shí)針旋轉(zhuǎn)的叫做反氣旋。在南半球，上述的情形正好相反。車(chē)輛和行人靠右行左右鞋磨損程度不同跑道上逆時(shí)針跑行〔2〕標(biāo)準(zhǔn)坐標(biāo)系中的動(dòng)量方程N(yùn)ewtonsLawsThefundamentallawusedtotryanddeterminemotionintheatmosphereisNewtons2ndLawForce=MassxAccelerationMeteorologyisasciencethatlikestheKISSprinciple,andtofurthersimplifymattersweshallconsideronlyaunitmass.i.e.Force=AccelerationFrameofReferenceIfweweretoconsiderabsoluteaccelerationrelativeto“fixed〞stars(i.e.anon-rotatingEarth) Thenourequationwouldreadsomethinglikethis;“Therateofchangeofvelocitywithtimeisequaltothesumoftheforcesactingontheparcel〞FrameofReferenceForanon-rotatingEarth,theseforcesare:Pressuregradientforce(Pgf)Gravitationalforce(ga)andFrictionforce(F)FrameofReferenceHowever,wedon’tliveonanon-rotatingEarth,andwehavetoconsidertheadditionalforceswhichariseduetothisrotation,andtheseare:CentrifugalForce(Ce)andCoriolisForce(Cof)EquationofMotionWenowhaveanewequationwhichstatesthat:i.e.TherelativeaccelerationrelativetotheEarthisequaltotherealforces(Pressuregradient,GravityandFriction)plusthe“apparentforces〞CentrifugalforceandCoriolisforceAUseableformIfwenowconsiderthecentrifugalforcewecancombineitwiththegravitationalforce(ga)toproduceasinglegravitationalforce(g),sincethecentrifugalforcedependsonlyonpositionrelativetotheEarth.Hence,g=ga+CeAUseableformWecannowwriteourequationas:Wenowlookattheequationinitscomponentforms,sinceweareconsideringtheatmosphereasa3-DimensionalentityConventionsInMeteorology,theconventionsforthecomponentsinthehorizontalandverticalare;x=E-Wflowy=N-SflowZ=VerticalmotionAlso,theconventionsforvelocityareu=velocityE-Wv=velocityN-Sw=VerticalvelocityPressureGradientForce“Forceactingonairbyvirtueofspatialvariationsofpressure〞Thesechangesinpressure(orPressureGradient)aregivenby;PressureGradientForceIfwenowconsiderthispressuregradientactingonaunitcubicmassofairwithvolumegivenbyxyzwecansaythatthePressuregradient(Pg)onthiscubeisgivenby:(Pg)=Force/Volume.PressureGradientForceWecanalsosaythatthevolumeofthisunitmassisthespecificvolumewhichisgivenby1/,whereisdensity.ThishasthedimensionsofVolume/Mass.ThedimensionsofthePressuregradientareForce/VolumePressureGradientForcePressureGradientForceThereforewehavethePressureGradientForce(Pgf)givenby;

ThisPgfactsfromHighpressuretoLowpressure,andsowehaveafinalequationwhichreads;PressureGradientForceBecausewearedealingin3-D,therearecomponentstothisPgfandthesearegivenasfollows;PressureGradientForceCombiningthecomponentswegetatotalPgfofThecomponentsiandjarethePgfforhorizontalmotionandthekcomponentisthePgfforverticalmotion.HorizontalPgfWecansimplifymattersstillfurtherifwetakethexaxisoryaxisnormaltotheisobars,hedirectionofthegradient.Wethenonlyhavetoconsideroneofthecomponentsastheotheronewillbezero.yPgf=102010181016xVerticalPgfInthesynopticscale(largescalemotionssuchashighsandlows),theVerticalPgfisalmostexactlybalancedbygravity.SowecansaythatThisisknownastheHydrostaticequation,andbasicallystatesthatforsynopticscalemotionthereisnoverticalaccelerationCoriolisForceThisisan“apparent〞forcecausedbytherotationoftheEarth.ItcausesachangeofdirectionofairparcelsinmotionIntheSouthernHemispherethisdeflectionistotheLEFT.Isproportionalto whereisthelocallatitudeItsmagnitudeisproportionaltothewindstrengthCoriolisForceItcanbeshownthattheCoriolisforceisgivenby2sinVTheterm2sinisknownastheCoriolisparameterandisoftenwrittenintextsasf.BecauseoftherelationshipwiththesineofthelatitudeCofhasamaximumatthePolesandiszeroattheequator(Sin0°=0)ThestrengthofCoriolisforceisinfluencedbylatitudeandthespeedofthemovingobjectCoriolisparameterf=2sinComponentsofCofItcanbeshownthatthehorizontalandverticalcomponentsoftheCofareasfollows;ThecompleteequationWecannowwritetheequationofmotionwhichdescribesthemotionofparticlesonarotatingEarth.Rememberingthattheequationstatesthat;Acceleration=Pgf+Cof+g+F,Wecanwritetheequationasfollows;Thecompleteequation(Ignoringfrictionaleffects)Scaleanalysis尺度分析EventhoughtheequationhasbeensimplifiedbyexcludingFrictionaleffectsandcombiningtheCentrifugalforcewiththeGravitationalforce,itisstillacomplicatedequation.Tofurthersimplify,aprocessknownasScaleanalysisisemployed.WesimplyassigntypicalscalevaluestoeachelementandtheneliminatethosevalueswhichareSIGNIFICANTLYsmallerthantherestScaleAnalysisScaleAnalysisScaleAnalysis(HorizontalMotion)Fromthepreviousslidewecanseethatforthehorizontalequationsofmotiondu/dtanddv/dt,thelargesttermsarethePgfandtheCoriolisterminvolvinguandv.Theaccelerationisanorderofmagn