dynamicallydrivenflows-2017u0028395/classes/6250/lectures/dynamicallyd… · flow over (Ĥ< 1)...
TRANSCRIPT
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DynamicallyDrivenFlows
Atmos 6250:MountainMeteorologyJimSteenburgh
DepartmentofAtmosphericSciencesUniversityofUtah
Reading
Jackson,P.L.,G.Mayr,andS.Vosper,2013:Dynamically-drivenwinds.MountainWeatherResearchandForecasting:Recent
ProgressandCurrentChallenges.T.Chow,S.deWekker,andB.Snyder,Eds.,Springer,121–218.
Discussion
• Howandwhyisthebehavioroftheflowdifferentoverareasofcomplexterrain?
• Whatmechanismsdrivethisdifferingbehavior?
TypesofMountainWinds
• Dynamicallydrivenflows producedbytheinteractionofthelarge-scaleflowwithtopography
• Thermallydrivenflows (a.k.a.diurnalmountainwinds)producedbyhorizontalcontrastsinheatingandcoolingthatarisefromtopographicandland-surfacecontrasts
• Frequentlycombinedtosomeextent
TypesofMountainWinds
• Dynamicallydrivenflows producedbytheinteractionofthelarge-scaleflowwithtopography
• Thermallydrivenflows (a.k.a.diurnalmountainwinds)producedbyhorizontalcontrastsinheatingandcoolingthatarisefromtopographicandland-surfacecontrasts
• Frequentlycombinedtosomeextent
ThisLecture
Discussion
• Whatoptionsdoesairhavewhenitapproachesamountainbarrier?
• Whatcharacteristicsoftheincidentflowandthetopographyarelikelytodeterminetheoutcome?
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DynamicallyDrivenFlows• Asairapproachesabarrieritcanflow
– Over thebarrier• Mountainwavesanddownslopewinds
– Tthrough gapsorvalleysthatdissectthebarrier• Gapflows
– Around thebarrier• Ridges:Barrierjets,damming• Isolatedobstacles:Flowsplitting;leewardconvergence,vortices,andwakes
• Outcomedeterminedby– Strengthandstabilityoftheincidentflow– Shapeandsizeofthetopography
• Allthreecanoccursimultaneouslywithinagivenregion
Source:Jacksonetal.(2013)
BasicDynamicsofDynamicallyForcedFlows
Photo:http://www.pa.op.dlr.de/ostiv/Projects/mwavproj.htm
KeyParameters:Rossby Number(Ro)Ro =U/fL
U =Cross-barrierwindspeedf =Coriolis parameter
L =Mountainbarrierwidth
KeyParameters:Rossby Number(Ro)
Ro <<1Airtakes>>f-1 tocrossbarrier
Coriolis forcedominatesParcelsdisplacedhorizontally
Rossby wavesproduced
Ro >>1Coriolis effectsnegligibleBuoyancyforcedominatesParcelsdisplacedverticallyGravitywavesproduced
Images:Whiteman(2000)
Ro =U/fL
KeyParameters:Rossby Number(Ro)
Ro <<1Airtakes>>f-1 tocrossbarrier
Coriolis forcedominatesParcelsdisplacedhorizontally
Rossby wavesproduced
Ro >>1Coriolis effectsnegligibleBuoyancyforcedominatesParcelsdisplacedverticallyGravitywavesproduced
Images:Whiteman(2000)
Ro =U/fL ThisLecture
KeyParameters:Non-DimensionalMountainHeight(Ĥ)
Ĥ =NH/U
N =[(g/qo)(dqo/dz)]1/2 =Brunt–Väisälä FrequencyH =MountainHeight
U =CrossBarrierWindSpeed
Ĥ-1=U/NHissometimesreferredtoastheFroudeNumber
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KeyParameters:Non-DimensionalMountainHeight(Ĥ)
Ĥ =NH/U
Willtheairflowoverthebarrier?
Basicallytheratiooftheenergyrequiredtogetoverbarrier(N2H2/2)tothekineticenergyofincomingflow(U2/2)
Ĥ =[(N2H2/2)/(U2/2)]1/2=NH/U
Ĥ >1:Inertiatooweakandtheflowisblocked
Ĥ <1:Inertiaovercomesstability,flowsurmountsbarrier
KeyParameters:Non-DimensionalMountainHeight(Ĥ)
Ĥ =NH/U
Blocking(Ĥ >1)favoredbyHighstability
LargemountainWeakcross-barrierflow
Flowover(Ĥ <1)favoredbyLowstability
SmallmountainStrongcross-barrierflow
Thecriticalmountainheight,Hc,iswhereĤ =1andtheflowtransitionsfromblockedtounblocked
Settting Ĥ =1andreplacingHwithHc yieldsHc =U/N
KeyParameters:CriticalMountainHeight(Hc)
• Hc =U/N
• H>Hc: Flowisblocked
• H<Hc:Flowsurmountsbarrier
H>Hc
H<Hc
Parcelsurmountsbarrier
Parcelblocked
WhichisMostLikelytoResultinaTransitionfromBlockingtoFlowOver?• Flowspeedandstabilityincreasing
• Flowspeedandstabilitydecreasing
• Flowspeedincreasingandstabilitydecreasing
• Flowspeeddecreasingandstabilityincreasing
WhichisMostLikelytoResultinaTransitionfromBlockingtoFlowOver?• Flowspeedandstabilityincreasing
• Flowspeedandstabilitydecreasing
• Flowspeedincreasingandstabilitydecreasing
• Flowspeeddecreasingandstabilityincreasing
LimitationsofĤ and Hc
• Usefulconcepts,butassumeuniformupstreamwind,U, andstratification,N– Novariationshorizontallyorvertically
• Assumenoparcelaccelerationsfromlarge-scalefloworflowadjustmenttoorography
• Difficulttoapplyinpracticeduetonon-uniformnatureofrealworldflowsandstratification
Reinecke andDurran (2008)
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MountainWaves
LenticularcloudsoverMt.Hotaka,Hida Mountains,NaganoPrefecture,JapanbyAlpsdake (WikipediaCommonsCCBY-SA3.0
MountainWaves
• Generictermforallgravitywavesforcedduringflowovermountains
• Gravitywave – Awaveproducedbybuoyancyforceswhentheatmosphereisstablystratified(i.e.,N >0)
MountainWaves• Externalgravitywaves– Occurinfluidswithanupperboundaryorinternaldensitydiscontinuity(e.g.,oceanwaves)andpropagatemainlyinthehorizontalplane
• Internalgravitywaves– Occurincontinuouslystratifiedfluids(e.g.,theatmosphere)andcanpropagateinthehorizontalandverticalplanes
• Shallowwaterthinkingcanonlytakeyousofar
TheBuoyancyOscillation
t=0 t=t/2 t=tt
Period,t =2p/NAnddecreaseswithincreasingstability
MountainWaveTheory
• Basedonlineartheory
• Wewillassumeabell-shapedridgewhereh(x) =H/2atx=±L(otherterrainconfigurationscanbeused)
• WewillalsoassumeuniformU andN
H
L
h(x) = H L2
L2 + x2
KeyParameters:InternalFroudeNumber(FL)
FL =U/NLRatioofthenatural“frequency”offlowoverthemountain,U/L,to
thebuoyancyfrequency,NFL >1(L<U/N)“NarrowMountain”
Flowmovessorapidlyovermountainitcan’treachpressureequilibriumwithsurroundings
Buoyancyoscillationsnegated
Evanescentwavesgenerated
FL <1(L>U/N)“WideMountain”
Flowisabletoadjust
Buoyancyoscillationscanoccur
Verticallypropagatingwavesgenerated
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EvanescentWaves
• “NarrowMountain”
• Patternissymmetricaboutmountain
• Wavedecaysexponentiallywithheight
Durran (1986)
LikelyEvanescentWaves
Photo:BrandonSmith Photo:GarethBerry
VerticallyPropagatingWaves• “WideMountain”
• Wavespropagatevertically
• Wavecrestsconfinedtooverterrain
• Trough/ridgelinestiltupstreamwithheight
• Verticaltiltresultsinpossibleleecloudformation
Durran (1986),Whiteman(2000)
VerticallyPropagatingWaves
Onlyonewavecrest
http://www.atmos.washington.edu/~durrand/
WhyDoLenticularsForminLayers?
“VerticallylayeredRHpertubations assmallas±0.25%canproducelenticularcloudswith
alayeredstructure”- HillsandDurran (2014,QJRMS)
TrappedLeeWaves• PreviousdiscussionassumesuniformU andN
• SituationswheretheScorerParameter,l,decreaseswithheightcanproduceintrappedleewaves
• Firsttermusuallydominates
• Possibleculprits– DecreasingNwithheight– IncreasingUwithheight– Rapidchangeinverticalshearsuchasbeneathastrongjet(2nd term
2
2
2
22 1
dzUd
UUNl -=
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TrappedLeeWaves
Durran (1986)
Smalll2
Largel2
TrappedLeeWaves
Durran (1986)
LinearTheoryStrengthsandWeaknesses
• Strengths(predictionsconfirmedbyobservations)– Gravitywavepenetrationtogreatheightsabovebarrier– Upstreamphasetilt– Upwardenergypropagation– Trappedwaves
• Weaknesses– Assumessmallverticalparceldisplacements
• Validonlyforsmall(H<500–1000m)mountainswithgradualslopes– Can’taccountforhigh-amplitudemountainwavesthatproducedownslopewinds,wavebreaking,androtors
– Solutionssensitivetoupper-boundarycondition
HighAmplitudeMountainWaves
• Associatedwith– Downslopewinds– Hydraulicjumps– Rotors–Wavebreaking/CAT
Whiteman(2000)
BoulderJan1972
Klemp andLilly(1975)
BoulderNov1972
Meteogram:Whiteman,Photo:BoulderDailyCamera
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SierraWavePhoto
View is toward south from 11 km height. Airflow is from right to left. The cloud mass on the right is plunging down the lee slope
of the Sierra Nevada; the near-vertical ascending cloud wall of the mountain wave is on the left. The turbulent lower part of the
cloud wall is a "rotor”; the smooth upper part is the "lenticular" or "wave cloud". The
cloud mass to the right is a "cap cloud" (Föhn-Mauer); the cloud-free gap (middle)
is the "Foehn gap" (= Föhn-Lücke).
Photo:JoachimKuettner andHalKlieforth,1952
RotorSimulation
Streamlines from glider measurements (from Doyle and Durran 2002, after Holmboe and
Klieforth 1957)
Simulation from Jim Doyle, NRL(Color Horizontal Vorticity)
Rotor
Sub-Rotor
DownslopeWindstormsoftheWesternUS
• Chinook(Alberta,Montana,Colorado)
• Canyonwinds(Utah)
• SantaAna(California)
• CascadeBora(Washington)
• Chinook:Descendingwarmairreplacescoldairmass
• Bora:Sourceairmass sufficientlycoldthatdownslopewindsarerelativelycolddespitecompressionalwarming
Whiteman2000
MountainWaveSummary
• Broadspectrumofwavesproducedbymountains– TopographicRossby waves(lowRossby number)– Inertio-gravitywaves(Rossby number~1)– Gravitywaves(a.k.a.mountainwaves;highRossbynumber)• Evanescentwaves(“narrowmountain”,L<U/N)• Verticallypropagatingwaves(“widemountain”,L>U/N)• Trappedleewaves(Scorerparameterdecreasingwithheight)
• Highamplitudemountainwaves(forthcomingtalkbyHorel)
FlowAroundIsolatedObstacles
NASA
Introduction• Isolatedobstacle– Abarrierwithcomparablelength
andwidthscales
• Wewillfocusonmesoscale barriers,ratherthansmall-scaleobjectslikebuildingsandtowers
• Examples– HawaiianIslands– GuadalupeIsland– OlympicMountains– Mt.Rainier
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Discussion
• Whatfactorsarelikelytocontributetoflowsplittingaroundanisolatedbarrierandtheformationofleesidevortices?
LowFroudeNumberFlow
FroudeNumber=Ĥ-1=U/NH
CharacteristicsoflowFroudeNumberflowaroundisolatedobstacleWindwardflowsplittingandreversal
Leewardconvergence,counterrotatingvortices,andflowreversal
Fr=2.2 Fr=0.66 Fr=.22
Smolarkiewicz andRotunno (1989)
WindwardFlowReversal
FroudeNumber=Ĥ-1=U/NH
CharacteristicsoflowFroudeNumberflowaroundisolatedobstacleWindwardflowsplittingandreversal
Leewardconvergence,counterrotatingvortices,andflowreversal
Smolarkiewicz andRotunno (1990)
Fr=.33
Example:HawaiianCloudBands
• FormaseasterlytradewindsinteractwithHawaii
• Narrowcloudbandlocatedoverorwindwardoftheisland
Smolarkiewicz etal.(1988)
Example:PugetSoundConvergenceZone
FlowaroundOlympicMountainsgeneratesleesideconvergence,clouds,andprecipitation
Mass(2008),http://charliesweatherforecasts.blogspot.com/2013_04_01_archive.html
Example:PugetSoundConvergenceZone
OlympicsdeflectlowFroudenumberflow(Fr=0.4)intotwobranchesLeesideconvergenceandcounter-rotatingvortices
BlockingbyCacscades alsocontributestoconvergenceChien andMass(1997)
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NASA
VortexShedding
Cesareo deLaRosaSiqueira
Oscillatorysheddingofvorticesfromthegeneratingobstacle
KnownasavonKármán vortexstreetorsheet
BannerClouds
Zacharie Grossen,Wikipedia
Formdownstreamofsteep,sharp-edgedpeaks(e.g.,Matterhorn)
Discussion
• Howdoyouthinkbannercloudsform?
BannerClouds
http://science-edu.larc.nasa.gov/SCOOL/banner.html
Accelerationalongstreamlinenearmountaintopproduces:Lowpressureimmediatelytolee(Bernoulli)
LeesiderotorandupslopeflowBannercloudifairnearsaturation
BannerCloudSimulations
Voight andWirth(2013),Schappert andWirth(2015)
NeutralstratificationtomountaintopthenstablystratifiedSpecifichumiditydecreaseswithheight(i.e.,PBLnotwellmixed,which
modelingandobservationssuggestisessentialforbannercloudformation)
BannerCloudSimulations
Schappert andWirth(2015)
Timeaveragedflow
Timeaveragedverticaldisplacement(m)
Selectedtrajectories
Ifatmospherewaswellmixed,noneofthesewouldreachsaturation
ExistenceofhigherqneargroundallowsforbannercloudtoformasnearsurfacetrajectoriesreachLCL
belowmountaintopinlee
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GapWinds
http://www.mileslight.com/travels/hoodriver/
GapWinds• Gapwinds– Windthatareacceleratedbyanalong-gappressuregradient(WalterandOverland1981)
• Examples:– ShelikofStrait,AK– ColumbiaGorge,WA– StraitofJuandeFuca,WA&BC– StraightofGibraltar– Vestfjoden,Norway– CookStrait,NZ
ColumbiaRiverGorge
Photo:KelvinKay,Wikipedia;SharpandMass2002;SharpandMass2004
ColumbiaRiverGorge
http://www.surfertoday.com/kiteboarding/5649-hood-river-gets-the-cabrinha-race-series
PressureDrivenChanneling
Whiteman(2000)
OtherFactors:
Diurnalmodulationofcross-barrierpressuregradient
MarineorArcticinversion(limitsmomentummixing)
Bendsandconstrictions
ForceBalanceinLong&WideGaps
VFH LE PGF
Along-GapDirectionBalancebetweenPGF,Friction,andEntrainment
Flowbelowinversionmuchweakerthanaloft
Lackmann andOverland(1989)
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ForceBalanceinLong&WideGaps
Cross-GapDirectionApproximategeostrophicbalance
Lackmann andOverland(1989)
V
PG
Cor
Cold/HighPress Warm/LowPress
GapOutflowoverGulfofTehuantepec
• Uniqueinthatwindsmoveintoaregionwithveryweaklarge-scaleforcing
• StrongestwindsdirectlyinleeofChivela Pass
• Counter-rotatingeddiesflankoutlfow jet
• Outflowjetturnsanticyclonically
Steenburghetal.(1998)
InertialBalance?
• ParceldeflectedtorightbyCoriolis (NorthernHemisphere)
• Coriolis andcentrifugalforcedbalance
• RadiusofcurvaturegivenbyR=-V/f (minussignindicatesanticyclonic curvature)
Cent
Cor
V
InertialBalance?• Trajectoriesalongaxis
ofoutflowjetfollowinertialpath(dashed)
• Trajectoriestorightofjetcore(relativetoflow)havestrongercurvature
• Trajectoriestolefthaveweakerorcycloniccurvature
Steenburghetal.(1998)
InertialBalance?
• TrajectoriesalongaxisofoutflowjetdeflectedrightwardbyCoriolis andareinertially balanced
• Fanningofwindscausedbycross-trajectorypressuregradient
Steenburghetal.(1998)
C=Coriolis accelerationR=Totalacceleration
BarrierJets
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BarrierJets
• Mesoscale,along-barrierwindsthatdevelopadjacenttosteepterrainintheextratropics
• Associatedwithlow-levelblocking,althoughotherfactorscancontribute
• Impacts:Cold-airdamming,moisturetransport,orographicprecipitation,hazardouswinds
Discussion
• Asflowapproachesamountainbarrier,whatfactorsarelikelytoleadtoalong-barrierflowandtheformationofabarrierjet?
BasicDynamics
Intheabsenceoftopographyandfriction,theflowexhibitsgeostrophicbalance
996mb
100mb
V
COR
PG
BasicDynamics
996mb
100mb
V
COR
PG
IfflowischaracterizedbyalowFroudenumber(U/NH<1),thethelow-levelflowwillbeblockedanddecelerateas
itapproachesmountains
BasicDynamics
996mb
100mb
V
COR
PG
Astheflowdecelerates,theCoriolis forceweakens,andtheflowisdeflectedtowardlowerpressure
V
PG
Cor
BasicDynamics
996mb
100mb
V
COR
PG
V
PG
Cor
Flowdecelerationresultsinapilingupofmassanddevelopmentofamesoscale pressureridgenearthe
mountains(mutualadjustmentofmassandmomentum)
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BasicDynamics
996mb
100mb
V
COR
PG
Cor
V
PG
Friction
Thefinalnear-barrierforcebalance
MatureForceBalance
• Along-barrierantitriptic– Pressuregradientbalancesfriction
• Cross-barriergeostrophic
V Cor
V
PG
Friction
SierraBarrierJet
OldSchool(Marwitz 1987)
NewSchool(Kingsmill etal.2013)
WasatchRange
Coxetal.(2005)
Types(It’sNotAllBlocking)
Classic – Producedbyblockingasupstreamflowimpingesonbarrier
Hybrid – Gapoutflowturnsterrainparallelmergeswithterrainparallelsynopticflow
Loescher etal.(2006)
Types(It’sNotAllBlocking)
Shock – Classicbarrierjetwithsharpboundaryonsynopticupwindside
Variable – Terrainparallelflowissegmented
Loescher etal.(2006)
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Summary• Widerangeofdynamicallyforcedflowsincomplex
terrain
• Controlledbycharacteristicsofincidentflowandshapeofterrain
• Keyphenomena– Mountainwavesanddownslopewinds– Flowsplitting,vortices,vonKármán vortexstreet– Gapflow– Blocking,barrierjets
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