dynamicallydrivenflows-2017u0028395/classes/6250/lectures/dynamicallyd… · flow over (Ĥ< 1)...

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DynamicallyDrivenFlows

Atmos 6250:MountainMeteorologyJimSteenburgh

DepartmentofAtmosphericSciencesUniversityofUtah

jim.steenburgh@utah.edu

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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Cox,J.A.W.,W.J.Steenburgh,D.E.Kingsmill,J.C.Shafer,B.A.Colle,O.Bousquet,B.F.Smull,andH.Cai,2005:ThekinematicstructureofaWasatchMountainwinterstormduringIPEXIOP3.Mon.Wea.Rev.,133,521-542.

Doyle,J.D.,andD.R.Durran,2002:Thedynamicsofmountain-wave-inducedrotors.J.Atmos.Sci.,59,186-201.

Durran,D.R.,1986:Mountainwaves.Mesoscale MeteorologyandForecasting.P.S.Ray,Ed.,Amer.Meteor.Soc.,472-492.

Holmboe,J.,andH.Klieforth,1957:InvestigationsofmountainleewavesandairflowovertheSierraNevada.FinalRep.ContractAF19(604)-728,UniversityofCaliforniaADNo.133606,DepartmentofMeteorology,UniversityofCalifornia,LosAngeles,290pp.

Jackson,P.L.,G.Mayr,andS.Vosper,2013:Dynamically-drivenwinds.MountainWeatherResearchandForecasting:RecentProgressandCurrentChallenges.T.Chow,S.deWekker,andB.Snyder,Eds.,Springer,121–218.

Kingsmill,D.E.,P.J.Neiman,B.J.Moore,M.Hughes,S.E.Yuter,andF.M.Ralph,2013:KinematicandthermodynamicstructuresofSierrabarrierjetsandoverrunningatmosphericriversduringalandfalling winterstorminnorthernCalifornia.Mon.Wea.Rev.,141,2015-2036.

Klemp,J.B.andD.K.Lilly,1975:Thedynamicsofwave-induceddownslopewinds.J.Atmos.Sci.,32,320-339.

Lackmann,G.M.,andJ.E.Overland,1989:Atmosphericstructureandmomentumbalanceduringagap-windeventinShelikofStrait,Alaska.Mon.Wea.Rev.,117,1817-1833.

Loescher,K.A.,G.S.Young,B.A.Colle,andN.S.Winstead,2006:ClimatologyofbarrierjetsalongtheAlaskancoast.PartI:Spatialandtemporaldistributions.Mon.Wea.Rev.,134,437-453.

Marwitz,J.,1987:DeeporographicstormsovertheSierraNevada.PartI:Thermodynamicandkinematicstructure.J.Atmos.Sci.,44,159–173.

Mass,C.,2008:TheWeatherofthePacificNorthwest. UniversityofWashingtonPress,281pp.

ReferencesReinecke,P.A.,andD.R.Durran,2008:EstimatingtopographicblockingusingaFroudenumberwhenthestaticstabilityisnonuniform.J.Atmos.Sci.,65,1035-1048.

Sharp,J.,andC.Mass,2002:ColumbiaGorgegapflow.Bull.Amer.Meteor.Soc.,83,1757-1762.

Sharp,J.,andC.F.Mass,2004:ColumbiaGorgegapwinds:Theirclimatologicalinfluenceandsynopticevolution.Wea.Forecasting,19,970-992.

Smolarkiewicz,P.K.,andR.Rotunno,1989:LowFroudenumberflowpastthree-dimensionalobstacles.PartI:Baroclinically generatedleevortices.J.Atmos.Sci.,46,1154–1164.

Smolarkiewicz,P.K.,andR.Rotunno,1990:LowFroudenumberflowpastthree-dimensionalobstacles.PartII:Upwindflowreversalzone.J.Atmos.Sci.,47,1498–1511.

Smolarkiewicz,P.K.,R.M.Rasmussen,andT.L.Clark,1988:OnthedynamicsofHawaiiancloudbands:Islandforcing.J.Atmos.Sci.,45,1872-1905.

Steenburgh,W.J.,D.M.Schultz,andB.A.Colle,1998:ThestructureandevolutionofgapoutflowovertheGulfofTehuantepec,Mexico.Mon.Wea.Rev.,126,2673-2691.

Whiteman,C.D.,2000:MountainMeteorology:FundamentalsandApplications.OxfordUniversityPress,355pp.