大气科学基础课件 2-1-16

第2章大气动力学基础2.1大气运动基本方程2.2大气中的平衡运动2.3大气边界层中的风2.1大气运动基本方程

（1）作用于空气的力（2）标准坐标系中的动量方程（3）连续方程的推导及物理意义（1）作用于空气的力重力g（包括万有引力和惯性离心力）气压梯度力G地转偏向力C摩擦力Fr气压分布不均匀产生气压梯度力，气压梯度力是空气产生运动的直接原因。

当空气一开始运动，地转偏向力和摩擦力立即产生。在空气作曲线运动时也就产生了惯性离心力。气压梯度力G水平气压梯度力垂直气压梯度力其中，气压梯度力的大小决定于气压梯度和空气密度，它的方向为垂直于等压面从高压指向低压。地转偏向力C由于在转动的非惯性参照系下自由运动的物体受到的一种使运动方向发生偏转的力，称为地转偏向力。物理学上也称为科里奥利力，简称科氏力。

作用在单位质量物体上的地转偏向力的大小与物理运动速度和地球自转角速度成正比。CoriolisForce

Anapparentforcethatisduetotherotationoftheearth;Notarealforceinthesensethatitcannotcauseamotion;Asanearth-boundobserver,wearenotawareoftherotationoftheearth;Corioliseffectactsonlyonobjectsmovingwithrespecttotheearth’ssurface.Considerarocketfirednorthfromtheequator:Sincetheearthrotatesasasolidbody,theequatorwillmovefasterthanlandnearthepoles.Thegreenguywillhavetorunfasterthantheorangeguytokeepup.产生的原因物体为保持水平惯性运动，经纬网因随地球自转而产生相对加速度。地转偏向力向右是在北半球，在南半球则都向左；由于除南北两极外，各纬度的角速度都一样，从北向南飞的时候，南边的圈大，即越向南纬线越长，所以线速度大，所以在北边的时候具有的一个小的线速度与南边的线速度相比就显的慢了。，

在北半球，当物体从南向北飞行时，即由快的地方到慢的地方，速度‘超前’了，前进方向上也就向右偏了；同理，向南飞行。其结果都是使得物体出现向右偏转的效果，这个效果就是由地转偏向力造成的。

影响与应用科里奥利力不仅仅对风产生影响，任何一个环绕地表的远距离运动都会受到它的捉弄。在一战期间，德军用他们引以自豪的射程为113千米的大炮轰击巴黎时，懊恼地发现炮弹总是向右偏离目标。直到那时为止，他们从没担心过科里奥利力的影响，因为他们从没有这样远距离的开火；当然，对于近距离的运动，科里奥利力影响极小。从场地一边把篮球抛到另一边的运动员，考虑科里奥利力的影响而需要调整自己投球的偏移量为1.3厘米。当你拔掉盥洗池的橡皮塞时，会发现有时水流并不是逆时针旋转流走的，因为科里奥利力几乎没有足够的时间来影响水这样短距离的运动，水流的形态更多地受到水池形状或者水龙头喷射角度的影响；一个名叫古斯塔·加斯佩德·科里奥利的法国人在1835年最先用数学方法描述了这种效应，所以科学界用他的姓氏来命名此种力。我们通常也称它为地转偏向力。在北半球，科里奥利力使风向右偏离其原始的路线；在南半球，这种力使风向左偏离。风速越大，产生的偏离越大。于是，在北半球，当空气向低压中心辐合时会向右弯曲，形成了一个逆时针方向的旋转气流。从高压中心辐散出来的空气，则因为向右弯曲而形成了顺时针方向的旋风。我们把逆时针旋转的叫做气旋，把顺时针旋转的叫做反气旋。在南半球，上述的情形正好相反。车辆和行人靠右行左右鞋磨损程度不同跑道上逆时针跑行（2）标准坐标系中的动量方程NewtonsLawsThefundamentallawusedtotryanddeterminemotionintheatmosphereisNewtons2ndLawForce=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 whereisthelocallatitude

ItsmagnitudeisproportionaltothewindstrengthCoriolisForceItcanbeshownthattheCoriolisforceisgivenby2sinVTheterm2sinisknownastheCoriolisparameterandisoftenwrittenintextsasf.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.Theacceleration