unit 7...from density current to bore to solitary waves during an ihop (internaonal h 2 o project)...
TRANSCRIPT
Unit 7 AtmosphericWavesand
Topographically-InducedFlowPhenomena
Reading Assignment
MR10Chap11:ThermallyForcedWindsinMountanousTerrain,pp.317-325Chap.12:MountainWavesandDownslopeWindstorms,pp.327-342Chap.13:BlockingoftheWindbyTerrain,pp.343-366
Atmospheric Waves Primer:
Ducted Gravity Waves, Solitary Waves, Density Currents, and Bores
h = A cos (kx – ωt) Oscillation in space and time. A = Amplitude ω = ct c = phase speed k = 2π / λx
= horizontal wavenumber λx = horizontal wavelength
Wave kinematics
h = 10 cos (kx – ωt)
h = 10 cos (ωt) At x=0, oscillation in time.
Wave kinematics
h = 10 cos (kx) At t=0, oscillation in space.
Wave kinematics
• GravitywaveisawavedisturbanceinwhichbuoyancyactsastherestoringforceonparcelsdisplacedfromhydrostaNcequilibrium.
• AlsoknownasbuoyancyoscillaNons.• This buoyancy oscillation has a frequency related to stability,
known as the Brunt-Vaisala frequency (N)
Gravity Waves
Buoyancy - Driven by gravity through Archimedes’ Principle
Buoyancy
Buoyancy - Driven by gravity through Archimedes’ Principle
Buoyancy
Buoyancy - Driven by gravity through Archimedes’ Principle
Buoyancy
Buoyancy - Driven by gravity through Archimedes’ Principle
Buoyancy
Buoyancy - Driven by gravity through Archimedes’ Principle
Buoyancy
• GravitywavegeneraNonmechanisms:• Topography
• Airflowovermountains• Changesinsurfaceroughness
• ConvecNon• ConvecNvepenetraNonintostablelayersaloQ• Densitycurrentsimpingingonstableboundarylayer.
• Shearinstability–Kelvin-Helmholtzinstability• GeostrophicAdjustment
Gravity Waves
• Also known as Kelvin-Helmholtz instability
• Occurs when Ri < 0.25
(RAM 2002)
2
2
⎟⎠
⎞⎜⎝
⎛=
dzduNRi
N g ddz
=θ
θ
Gravity wave generation mechanisms Shear instability
Shear Instability – KH Waves
(NOAA)
12/16/2011 - BHM
Gravity wave generation mechanisms Shear instability
• When stability is present above or below, internal gravity waves may radiate away from the shear layer
(Scinocca and Ford 2000)
(CIMSS)
Gravity wave generation mechanisms Convection
Gravity wave generation mechanisms Convection
(Bretherton and Smolarkiewicz 1989)
• Contours of mixing ratio and potential temperature around simulated cumulus cloud
Gravity wave generation mechanisms Convection
(Alexander 2002)
Gravity wave generation mechanisms Topography
• Flow over “two-dimensional” mountains
(NASA)
ATS454/554Mesoscale 22
Exampleof“MountainWaves”• PhototakenbyT.Lyzaduringthe
morninghoursof9June2012• LocaNon:About20milessouthof
MilesCity,MT• Viewingangle:towardtheNE• RockyMountainsdistantbehind
picture
Gravity wave generation mechanisms Shear instability
• Geostrophic adjustment (unbalanced jet)
(Koch and O’Handley 1997)
Ducted gravity waves • Superposition of two internal gravity waves
• One moving downward, one moving upward
• Reflected above by layer with decreasing m2 (vertical wavenumber) and below by the ground
• m2 (below), is taken from the Taylor-Goldstein Eqn, and is dependent on:
§ Stability determined by the Brunt-Vaisala freq (remember, these are buoyancy oscillations!)
§ Change in vertical shear – particularly due to curvature.
• Thus, ducts can be created by 1) thermal inversions and 2) significant change/curvature in the vertical wind shear.
• If duct depth is ¼ of a vertical wavelength of the internal gravity waves, the waves constructively interfere.
m Nc U
d Udzc U
k22
2
2
22=
−+
−−
( ) ( )
Ducted gravity waves • Superposition of two internal gravity waves
• Here, vertical wavelength is 8 km, ¼ of vertical wavelength is 2 km – this is the duct.
Duct
Ducted gravity waves • Superposition of two internal gravity waves
• Here, vertical wavelength is 8 km, ¼ of vertical wavelength is 2 km – this is the duct.
Duct
Ducted gravity waves • Flow in ducted gravity wave, u’ = A cos (kx – ωt) cos (mz)
• u’ (and w’) sinusoidal in x and t
• u’ maximized at surface, decreases with height
• w’ maximized at top of duct, increases with height
Ducted gravity waves • p’ and u’ correlated
• Convergence and upward motion ahead of wave ridge
• Divergence and downward motion ahead of wave trough
Ducted gravity waves • Positive perturbation shear (du’/dz) in wave trough
• Negative perturbation shear (du’/dz) in wave ridge
Ducted gravity waves
(Koch and O’Handley 1997)
• Thermal ducts
Ducted gravity waves • Wind ducts (speed and direction)
ATS454/554Mesoscale 32
The Role of Gravity Waves in IniEaEng and Intensifying an EF5-Producing Supercell: 25 May 2008, Parkersburg, IA
(FromNWSDesMoinesServiceAssessment,2008)
ATS454/554Mesoscale 33
The Role of Gravity Waves in IniEaEng and Intensifying an EF5-Producing Supercell: 25 May 2008, Parkersburg, IA
(FromNWSDesMoinesServiceAssessment,2008)
ATS454/554Mesoscale 34
The Role of Gravity Waves in IniEaEng and Intensifying an EF5-Producing Supercell: 25 May 2008, Parkersburg, IA
(FromNWSDesMoinesServiceAssessment,2008)
The Role of Gravity Waves in IniEaEng and Intensifying an EF5-Producing Supercell: 25 May 2008, Parkersburg, IA
• TheParkersburgtornadowasadevastaNngEF5tornadothatoccurredduringthelateaQernoonhoursof25May2008
• FirstgravitywavemayhaveplayedaroleinCI,althoughexistenceofprefrontaltroughlowersconfidenceinhowmuchofaroleitplayed
• SecondgravitywavecoincidedwithrapidintensificaNonofsupercellandmesocyclongenesis
• Wewillcoverthelinkbetweengravitywavesandmesocyclones,QLCSmesovorNces,andtornadoesinUnit6
ATS454/554Mesoscale 35
• Layer of cooler, dense air overhead produces pressure rise, temperature drop and dewpoint rise at station as density current passes by.
• Wind shift in direction of current motion
Density Currents
• Often produced by cool thunderstorm downdrafts • Typically have rear-to-front relative flow near surface • Raised head near edge • Vertical motion often produces condensation and lifts insects, dust. • May produce CI
Density Currents
Seitter 1986
Density Currents
• Often detected on radar due to condensation, insects, dust, etc.
ATS454/554Mesoscale 39
Motion of a Density Current
• Density current motion is tied to the depth of the cold pool and the negative buoyancy of the cold pool
• The forward speed of a density current can be derived from forms of the hydrostatic equation and the x-equation of motion
• Derivation time!
• Flow suddenly changes from fast and shallow to slow and deep, maintaining constant flow rate.
• Produces jump in height of flow
Hydraulic Jumps
• A bore is a moving hydraulic jump in the atmosphere • Depth of stable BL suddenly increases, flow in direction
opposite of bore motion decreases • A wave phenomenon • Often produced when density current impinges on stable BL,
often at night.
Atmospheric bores
(Simpson 2007)
• Since wave phenomenon, often move faster than density current that produced it.
• When a bore passes, result is steady or increasing temperature (due to mixing of BL), drop in dewpoint (due to mixing), abrupt “permanent” rise in pressure.
Atmospheric bores
Atmospheric bores • Initial pressure rise often followed by smaller oscillations in pressure • Result in destabilization of atmosphere due to mixing of stable BL.
In combo with lift along leading edge of bore, may cause CI.
Atmospheric bores
• Bore strength determines whether bore is smooth, undular, or turbulent (energy imbalance at bore must be dissipated by waves/turbc)
Atmospheric bores
• A single wave of elevation or depression in a stable layer of fluid (stable BL near surface)
• A nonlinear form of wave between two fluids of different densities (similar to water waves)
• Two types of dispersion occur • Amplitude dispersion (larger waves move a little
faster, steepening wave crest) • Wavelength dispersion (longer wavelengths move
faster)… similar process as shoaling of water waves
Solitary waves
• Cause temporary increase in pressure (as opposed to bores that cause more permanent increase in pressure), temporary warming and drying.
Solitary waves
Currents and Bores and Waves, Oh My!
• Densitycurrents,bores,andsolitarywavescanbeplacedonasortofone-direcNonspectrumofevoluNon
• Knupp(2006)detailstheevoluNonfromdensitycurrenttoboretosolitarywavesduringanIHOP(InternaNonalH2OProject)IOPon21June2002
ATS454/554Mesoscale 48
FromKnupp(2006)
Gravity Waves – Surface Trends • DensityCurrent
• Tempdecrease,pressureincrease,RHmayincrease.• Bore
• Tempsteadyorincrease• sharppressureincrease(maybesemi-permanent)• RHdecrease(mixing)
• SolitaryWave–DuctedGravityWave• Tempincreaseorsteady-Mixing• TemporarypressureincreasewithU’windincrease• PossibleRHdecreaseduetomixing
Overview
• Topographycanimpactatmosphericflowsthroughavarietyofforcingsandscales
• PVstretchinganditseffectsonRossbywaves(synopNcscale–DynamicsIandII)
• ThermodynamicvariataNons(mesoscale)• Slopeflows• Valleyflows
• Parceldisplacement(mesoscale)• Mountainwaves• Downslopewindstorms• Terrainblocking
• UniqueregionalclimatologicalfeaturesoQenassociatedwithtopography
• DenverCyclone/DenverConvergenceVorNcityZone(DCVZ)• CatalinaEddies
Slope Flow • DrivenbybuoyancyvariaNonsalongamountainslope• Atmosphereheatsfromthegroundupwardduringtheday,coolsfromthegroundupwardatnight
• ChangeinelevaNonoflandsurface=horizontaltemperaturegradient• BuoyancygradientduetohorizontaltemperaturegradientyieldshorizontalvorNcitygeneraNonandbothhydrostaNcandnonhydrostaNcp’(p’handp’nh)
• Result:upslope(anabaNc)flowduringthedayanddownslope(katabaNc)flowatnight
• AnabaNcflowp’• Whentheslopeoftheterrainfeatureisgentle(small),p’hisdominant• DepthofwarmsurfacelayertypicallyincreaseswithincreasingelevaNon,leadingtoanupslopePGF• p’isconstrucNvetoupslopeflow
• KatabaNcflowp’• Whentheslopeoftheterrainfeatureisgentle(small),p’hisdominant• CoolairnearsurfaceusuallybecomesdeeperwithincreasingelevaNon,leadingtoanupslopePGF• p’isdestrucNvetodownslopeflow
• ImplicaNon:anabaNc(upslope)windstypicallystrongerthankatabaNc(downslope)winds
• Forsteepslope,p’nhoQendominates,leadingtop’overallacNngagainstbothanabaNcandkatabaNcflows
• UpslopeflowtendstopeakafewhoursaQersunriseanddownslopeflowtendstopeakrightaroundsunset–peakdifferencebetweenmodifiedsurfacethermodynamicsalongslopesvs.valleytemperatures
• AnabaNcflowstypically50-150mdeep,katabaNcflowstypically10-40mdeep
• DepthofanabaNcflowincreaseswithincreasingelevaNon,whiledepthofkatabaNcflowincreaseswithdecreasingelevaNon
Fig.11.1fromMR10
UpwardPGFAnabaNcWind
AdaptedFig.11.3fromMR10Depthofwarmersfcairincreases
Slope Flow • Convergencezoneforms
nearzoneofpeaktemperaturegradient
• DMCcanformwithinthisconvergencezone,orDMCthatformsattopofmountaincanintensify
• CommonformaNonmechanismforlong-livedPlainsMCSs/MCCs
• WithoutDMC,erodedinversionwillleadtomixingdownofflowaloQanddestroyslopeflow(e.g.westerlyflowovertheRockies)
• DuraNonandstrengthofslopeflowinverselyproporNonaltostrengthofflowaloQinthedownslopingdirecNon(westerlyflowaloQfortheRockies)
Valley Flow • DrivenbythermodynamicvariaNonsalongtheaxisofavalley
orbetweenavalleyandaplainlocatedattheendofavalley
• Diurnalwindsflowup-valleyduetoairinsidethevalleywarmingmorethantheairabovetheplain,whilenocturnalwindsflowdown-valleyduetoairinsidethevalleycoolingmorethantheplain
• Down-valleywindscanbeamplifiedbydownslopeflow,leadingaphenomenonknownasadrainageflow
• Valleyflowcanbeexplainedbythefirstlawofthermodynamics
𝑄= 𝜌𝑐𝑝𝑉𝑑𝑇/𝑑𝑡
• Keyvariable->volume(V)• AssumingequalheaNngovervalleyandplain,slopededgesof
valleydecreasethevolumeofairimpactedbysameheatflux• GivenconstantQ,ρ,andcp,Nmerateofchangeoftemperature
mustchange• Result:greatertemperaturevariaNonwithinvalleythanacross
plain
• ThevalleydoesNOTneedtoslopeforvalleyflowtooccur!• Amodifiedslopeflowup/downvalleycanoccurinslopedvalleys
andcontributetovalleyflow
• TopographicamplificaNonfactor(TAF)canquanNfyhowamplifiedthediurnalcyclebecomeswithinavalley
𝑇𝐴𝐹= 𝐴𝑥𝑧𝑝𝑙𝑎𝑖𝑛/𝐴𝑥𝑧𝑣𝑎𝑙𝑙𝑒𝑦
• Magnitudeofvalleyflowcanreach5-10ms-1Fig.11.8and11.9fromMR10
Slope and Valley Flows – Combined Summary
Sunrise• Down-valleywindpersists
• Upslopeflowbegins• Valleycolderthanplain
Mid-morning(0900LST)• ValleyflowtransiNoning
fromdowntoup• Strongupslopeflow
• ValleysameTasplain
Noon/earlyaQ.• Up-valleywindisstrong• Upslopeflowbeginsto
weaken• Valleywarmerthanplain
LateaQernoon• Up-valleyflowconNnues
• Noslopeflow• Valleywarmerthanplain
Evening• Up-valleywindweakening
• Downslopeflowbegins• Valleybarelywarmerthanplain
Earlynight• ValleyflowtransiNoningfromuptodown
• Downslopeflowpeaks• ValleysameTasplain
Middleofthenight• Down-valleywindmature
• DownslopeflowconNnues
• Valleycolderthanplain
Latenighttomorning• Down-valleywindfillsvalley
• Noslopeflow• Valleycolderthanplain
Fig.11.10fromMR10
Mountain Waves • Internalgravitywavesforcedbyflowapproximately
perpendiculartoaridgeorseriesofridges• MR10discussesthecomplexdynamicsofthese
waves–wewillnot!• Reviewandexpansionofinternalgravitywavesfrom
Unit3• Cause:mechanicaldisplacementofaparcelthat
maintainsconstantbuoyancyintoalayerofdifferingbuoyancycharacterisNcs
• Thus,buoyancyservesasthe“restoringforce”,i.e.theforcethataimsto“restore”theparcelbacktoastateofrest
• Foraninfiniteseriesofsinusoidalridges:• DerivaNonofw’forwavesoveraseriesofridges,the
wavecrestNltsupstreamforarealverNcalwavenumber(m)
• Ifmisimaginary,thenwavesbecomeincreasinglyevanescentwithheight
• Forasingularridge:• Evanescenceforimaginarym• Differentwavelengthsnowsupportedbythe
topography• ImplicaNon->WemustapplyaFouriertransform(ugh!)
tofindthewavenumberssupported• k2<<m2forhydrostaNcwaves->theseareconfinedto
nearthemountainridge• Downstreamwaves,ifany,arenon-hydrostaNc• Unlesstrapped,energywillbetransportedupward
duetok2<<m2forhydrostaNcwaves(andfornon-hydrostaNcwavesforotherreasons)
Wavesoveraseriesofridges
Fig.12.3fromMR10
misreal
misimaginary
Mountain Waves Wavesformedoverasingularridge
Fig.12.4fromMR10
LenNcularcloud–causedbyliQingofparcelsbyupward-propagaNonofmountainwaves
Fig.12.2fromMR10
• OfparNcularinterestaremountainwavesthatbecometrappedbyverNcalchangesinstabilityandshear
• RecallfromUnit3:
𝑚2= 𝑁2/(𝑐−𝑢)2 − 𝜕2𝑢/𝜕𝑧2 /𝑐−𝑢 −𝑘2
𝑁2/(𝑐−𝑢)2 − 𝜕2𝑢/𝜕𝑧2 /𝑐−𝑢 =𝑙2 ->Scorerparameter
• Becausek2<<m2formostmountainwaves,wavebehaviorisapproximatedwellbyanalyzingl2
• SharpvariaNonsinstability(N2)andzonalwind(u)canleadtotwofluidlayersofdifferingScorerparameter,anupperlevel(lU)andalowerlevel(lL)
• IflU<lL(ldecreasingwithheight),thenwaveswherelU<m<lLwillpropagateverNcallywithinthelayerwherel=lLbutwilldecayinthelayerwherel=lU(evanescentlayer)• TheheightoftheinterfacebetweenlLandlUisdefinedasz=zr• zrisaheightofperfectreflecNonofthewaveenergywithwavenumberm• ReflecNonofwavesleadstoconstrucNveinterferenceamongwaveswithm=4zr(recallthatductdepth=¼verNcalwavelength,andzr=ductdepth)->thesewavesare“trapped”
Mountain Waves
Mountain Waves
Fig.12.1fromMR10
Visiblesatelliteimageryoftrappedmountainwaves
Fig.12.6fromMR10
Mountain Waves PicturebyT.LyzatakenSofMilesCity,MTonthemorningof9June2012,showingmountainwavecloudsoffoftheRockies
Fig.12.5fromMR10
LinearapproximaNon
Nonlinearapprox.–allowsforenhancementofwavesthroughnon-linearwaveinteracNons
Downslope Windstorms • Intensewindstormsthatformonthedownslopesof
mountains
• Associatedwithdeeplayersofairforcedoverterrain
• Surfacelayeratthetopoftheterrainbarrierisusuallystronglystable
• “CriNcallayer”presentabovestablesurfaceatcrest
• NOTthermally-driven
• Analogoustohydraulicjumps
• CanbeexplainedbyusingaraNoknownastheFroudenumber
𝐹𝑟= 𝑢/𝑐 , where 𝑐= √𝑔𝐷 (shallow-waterwavespeed)
• ForFr>1,flowissupercriNcaleverywhere(u>c)->flowslowsatopterrainpeakandacceleratesbacktooriginalvalueonthedownslope
• ForFr<1,flowissubcriNcaleverywhere(u<c)->flowacceleratesoverpeakanddeceleratespastit
• ForFr=1,flowisiniNallysubcriNcalbutacceleratestoasupercriNcalstate,peakingonthedownslopeoftheterrainfeatureunNlahydraulicjumprestoresflowtosubcriNcalstate
Fr>1
Fr<1
Fr=1
Fig.12.12fromMR10Fig.11.11fromMR10
• ThreemostcommoncondiNonsfordownslopewindstorms1. BreakingofwavesinverNcally-
deepcross-mountainflow2. BreakingofwavesatacriNcal
level(shallowcross-mountainflow)
3. Strongly-stableairatmountainpeakwithlessstableairabove(l2interface)
• Wavesamplifyduetowavebreaking
• “SeparaNonstreamline”important(seeFig.12.13)
Downslope Windstorms
Fig.12.13fromMR10
Downslope Windstorms Fixedinterface(3km) Fixedmountainheight(500m)
Fig.12.14fromMR10 Fig.12.15fromMR10