UBC Faculty Research and Publications

Physical modeling of an outflow event in Howe Sound, British Columbia. Finnigan, Timothy D.; Allen, Susan E.; Lawrence, Gregory A. Feb 28, 1998

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata


52383-Allen_AGU_97JD03430.pdf [ 1.89MB ]
JSON: 52383-1.0041902.json
JSON-LD: 52383-1.0041902-ld.json
RDF/XML (Pretty): 52383-1.0041902-rdf.xml
RDF/JSON: 52383-1.0041902-rdf.json
Turtle: 52383-1.0041902-turtle.txt
N-Triples: 52383-1.0041902-rdf-ntriples.txt
Original Record: 52383-1.0041902-source.json
Full Text

Full Text

JOURNAL  OF GEOPHYSICAL  RESEARCH,  VOL. 103, NO. D4, PAGES 3937-3950, FEBRUARY  27, 1998  Physical modeling of an outflow event in Howe Sound, British  Columbia  Timothy D. Finnigan• Department of Civil Engineering,Universityof British Columbia,Vancouver,Canada  Susan E. Allen Department of Earth and Ocean Sciences,University of British Columbia, Vancouver, Canada  Gregory A. Lawrence Department of Civil Engineering,Universityof British Columbia,Vancouver,Canada  Abstract. Outflow winds occurwhen differing air massesare separatedby a coastal mountain barrier. In extreme casesthe cross-barrierpressuregradient and the high degree of stratification(often approachinga distinctlayeredstructure)resultin channelwinds which exhibit hydraulicfeatures.We present a studyof outflow winds in Howe Sound, British Columbia. A field investigation,aimed specificallyat locating and quantifying hydrauliceffects,was undertaken during the winter months of 1992/1993.Microbarographs positionedin the region recordedpressurechangesat discretelocationsin the streamwise direction.The pressuresobtainedduring a severeoutflowwind event,which occurred from December 27, 1992 to January1, 1993, showa highlyvariable lower-layerdepth suggestiveof hydrauliccontrol. Experimentswere conductedwith a three-dimensional physicalmodel that is geometricallyand kinematicallysimilar to Howe Sound.Synoptic conditionsrecordedduring the outflow wind event in Howe Sound in December 1992 were usedto determineappropriatemodel flow forcing.The expanseof supercriticalflow area was observedto be relatively sensitiveto changesin along-channelpressuregradient and downstreamdepth,when comparedto changesin discharge.Channel sinuosityand local topographyappearedto force critical conditionsat specificlocations.For example,a channel bend combined  with headlands  was observed to force a situation  where  subcritical  and supercriticalstreamsflow side by side. Flow separation,resultingin lateral shear discontinuities,producedsimilar conditions.These effectsare discussedand put into contextwith field observations.Field and model resultsshowgood agreement. force for outflow winds in valleys and inlets along the coast. The wind systemis staticallystable,but the degreeof stratifiGap winds,first describedby Reed [1931], are characterized cation depends on the local conditions present. In extreme by the flow of low-lyingair throughgapsin a mountainbarrier casesthe air massesdiffer substantiallyin their physicalpropwhen an across-barrierpressuregradientis present.Stronggap erties,and stratificationis enhanced,often approachinga twowindsare often encounteredin the valleysand inlets of coastal layer structurewith a distinctand stableinterface at the invermountainousregionswhere cold weather is prevalent.During sion level [Jackson,1993]. the winter months,the British Columbiacoast (Figure 1) is The present study focuseson outflow winds that occur in geographicallyand climaticallysuited to extreme gap winds. Howe Sound,which is a fjord located in the southwestcorner Here suchphenomenaare referredto as outflowwinds;a term of the British Columbiamainland(see Figure 1). We present which impliesflow of air from the interior of the provinceout resultsfrom a field experiment,which captureda severeout1.  Introduction  toward  the coast.  flow wind event, and a laboratory experiment, designed to reveal the detailed structureof the wind system. into the interior plateau region of the province, and the cold Howe Sound is typical of many fjords along the coast of air, being relativelydense,deepensover a period of daysbe- British Columbia which also experiencestrongoutflow winds coming "pooled" between the Coast and Rocky Mountain during the winter months. The topography of the channel ranges.The Coastmountainsact asa partial barrier separating varies drasticallyover short distances.Rugged mountains incold, dry interior air from warm Pacific air on the coast.The terspersedalong the channel give it a tortuous shape with resultingacross-barrierpressuregradientprovidesthe driving many abrupt expansionsand contractions. Steep mountain facesrisefrom the seato heightsof 1600m in somepartsof the •Nowat Centrefor WaterResearch, University of WesternAustra- Sound and combine with islands to influence and control the The occurrence  of an Arctic  outbreak  forces cold air south  lia, Nedlands, Australia.  flow of air. Some important topographicalfeatures of Howe Sound are shown in Figure 2a, and the complexity of the terrain is shown in Figure 2b. Outflow eventsin Howe Sound typically have durations as  Copyright 1998 by the American GeophysicalUnion. Paper number 97JD03430. 0148-0227/98/97JD-03430509.00 3937  3938  FINNIGAN  ET AL.:  PHYSICAL  MODELING  OF AN  OUTFLOW  EVENT  [1994a] suggestedthat the flow is stronglyinfluencedby local topography, and a hydraulic analysisof their model output supported this. In a subsequentpaper, Jacksonand Steyn [1994b] described a one-dimensional hydraulic computer model that was more successfulat predicting observations. Here they extended classicalhydraulic theory by adding the influenceof a synopticpressuregradientin the form of a slope. Finniganet al. [1994] (hereinafterreferred to as F1) presented results from a one-dimensional hydraulic physical  BRITISH COLUMBIA  o  o  model  of outflow  winds  in Howe  Sound.  Model  results were  compared with observationsfrom a severe outflow event in Howe Sound, which occurred in December 1992, and with  output from Jacksonand Steyn's[ 1994b]hydraulicmodel. The paper identified the major topographicalfeatures that act as hydraulic controls. In a paper describingshallowwater flow and vorticity production over isolated topography,Schi•rand Smith [1993] used one-dimensionalhydraulic theory to help characterizedifferent flow regimes. For subcriticalupstream flow encounteringa three-dimensionalhill, the followingthree regimesoccur:(1) fore-aft symmetry,essentiallyinvisciddynamics,and entirely subcriticalconditions;(2) transitionto supercriticalflow and the occurrenceof a hydraulicjump over the lee slope; and (3) the inability of the flow to climb the mountaintop resultingin flow separationfrom the sidesof the obstacle.These flow regimeshave particular relevanceto the  ß  ..  PACIFIC  OCEAN  WA.  .... ::?'----.:':'"':: ......... -":':..?:s.;'•(T'.:"•E.' 10.'.'.': . ..:' ....... :•:"• .......... :.:'w.....•-. l  ;:.:.. ":f::** -.:.:. ...•F., ./:*'%:.:.;....;.:.:. .: -.-  Figure 1. Geographicallocation of Howe Sound.  .... .:  ':;'"*• .... ::"½'" '•2•;:'•" ';'  20 .... ':..":':...; ........... •...:,.  ..  short as 8-10 hours but can last 4 to 5 days. Wind speeds  ,0-:.•......... .: :/.:-:,...:--. .... <:':.....]...*'. .... ".W.;?7" '"• •, .... .:.,p  commonly reach20 ms-• with guststo 30 or 40 ms-•. The lowerlayerof coldair (windlayer) isgenerallylessthan 1000m deep at all locations along the channel [Jackson,1993]. On average,outflowwindsoccuron 4-5 daysin eachof December and January[Schaeffer,1975]. Cold temperaturesthat accompanythese winds and their unpredictabilitymake them a serioushazard. Extreme wind conditionsthroughoutthe Soundduring eventsare hazardous; however,the single,most dangerousaspectof outflow winds may be their spatial variability. The wind flows in a complicatedlayer throughthe channel.In severallocations,velocities change abruptly over short distances.This is largely due to hydrauliceffects(discussed below)and flow separation.Localized regionsof very intensewind develop during an outflow event. Improvement of predictive capabilitiesfor the above mentionedaspectsof outflowwindswas part of the motivation for this study. Severalgap wind studieshave been conductedover the past 40 years with some researchersreporting flow features that resemble internal hydraulicjumps [Bond and Macklin, 1993; Lackmann and Overland, 1989]. Jacksonand Steyn [1994a] comparedobservationsof a moderate outflow event in Howe Sound with output from a three-dimensionalmesoscalenumericalmodel.Althoughtheir resultsagreedin general,model flows underestimatedactualwind speedsin the channel,and small-scaleflow featureswere not captured.Jacksonand Steyn  •  •/'::,....";/:**' .•  -.:; .*-': '•.' .-  ::  • 30 ?......... :?,-..-...:..:•, ..... ;*: ........... •  *l ""•  '-  •  .....  • ;..-....  • 30  ......... '"% '•'"":½;;;*:a•"*:..: '"::':; % '*:..a•.-< .... '  ::i;•::** :::::::::::::::::::::::: ............. :.:::,: .....  '  ,  .-.:....•.. :..;}-:: .:  -:  -..::..,--,:::::.-:.... ;:::...  :":, .-:' .7'"".:• ' :..,."'  40,  '" •: ....::....::.:  ::&  *../  :":  '•"  ,.;:.'S;*:*  ....  6o a> 0  10  20  10  distance(km)  distance(km)  Figure 2. (a) Sketch of Howe Sound region. Shaded areas indicateland (darker shadingbeing above 900 m elevation) and  nonshaded  areas  indicate  the  ocean  surface.  Micro-  barographlocationsin the field are numbered1 through 5 in the direction  of flow. Permanent  weather  stations are located  at Squamish(SQ), Pam Rocks (PR), and Mount Strachan (MS). (b) Photographfrom aboveof the portionof the physical model for which results are presented.This figure showsthe varied topographyof the region.  FINNIGAN  ET AL.: PHYSICAL  MODELING  studyof outflow windswhere an essentiallyshallowfluid encounters semi-isolated  mountains  and islands. Schiir and Smith  [1993] borrowedfrom the field of gasdynamicsand drew an analogy with shallow water flow. Shear discontinuitiesand obliqueshockswere identified as important featuresof flows describedin their paper and may play a role in the spatial variationof outflowwinds.A thoroughsummaryof the theory of two-dimensional hydraulicjumps(and layeredhydraulicsin general)may be found in a recentbook by Baines[1995]. The presentpaper reports measurementsmade in the field during a severeoutflowwind event in Howe Sound. The field experimentwas aimed specificallyat capturing some of the hydraulicfeaturesof the stronglystratifiedsystem.Laboratory model experimentswere performedfor comparisonwith the field resultsand to specifyconditionsthroughoutthe regionin greater detail and for a wider range of possibleflows. Internal hydraulictheory refers specificallyto the application of hydraulicsin the study of the internal behavior in a multilayer system.In section2, internal hydraulictheory, as it pertainsto outflowwinds,is briefly introduced.Field observa-  OF AN OUTFLOW  EVENT  3939  and within each layer, the densityis constantand the velocity varies only in the flow direction. For a two-layerflow, Armi [1986]definedthe compositeFroudenumber  G2= F 2 • + F22 - eF •2F 2  (2)  where  (3)  are the densimetricFroudenumbersfor eachlayer;#' = e# = g(P2 -- P•)/P2 is the reducedgravity;hn are the individual layer depths;and subscript1 refers to the upper layer, while subscript2 refers to the lower layer. The compositeFroude number(2) determinesthe internalcriticalityof the two-layer flow in the samemannerasthe Froudenumber(1) determines the criticality of a single-layerflow. More recently,Lawrence[1990] solvedthe hydraulicequationsyieldingcharacteristic velocitiesfor both external(free surface)wavesand internal (interfacial)waves.He derived tions from an outflow event in December 1992 are discussed in exact expressionsfor internal and external Froude numbers section3, and laboratoryexperimentsare discussedin section based on the phase speed of infinitesimallong waves.From 4. Comparisonsbetween the field and laboratory results are Lawrence's[1990] results,if we assumethe relative density made in section5, and some conclusionsare drawn in section6. differencebetweenlayersis small(Boussinesq approximation), e << 1, then the internal Froude number for a two-layerflow is expressedas  2.  Internal Hydraulic Theory  uih2 + u2hi  Single-layerhydraulictheoryis usefulfor engineeringapplicationsin open channelflow [see Henderson,1966]. For a single-layerflow the ratio of convectivevelocityu to surface  F•=(g'hh•h2(1 - F2•)) •/2' where  wavespeedc = (#h) •/2 is knownasthe Froudenumber  F: x/•h ,  (4)  F2 •_-(u2 - ul)2  (1) is the stabilityFroude number, and h =  h • + h 2 is the total  whereh is fluid depth, and # is gravitationalacceleration.Flow  depthof fluid. When F2• > 1, internalphasespeedsare  is termed subcritical when F < 1, critical when F = 1, and  imaginaryand internal hydraulictheoryno longer applies.The internal Froude number alsodeterminesthe internal criticality of two-layerflow by the criteria mentionedabovefor a singlelayer flow. The internalFroude number(4), whichrepresentsthe ratio of internal convectivevelocityto internalphasespeed,hasthe advantageof describingthe behavior of oblique waves that appearin regionsof internallysupercriticalflow. It is related to the compositeFroude number by  supercriticalwhen F > 1. In open channels,flow is controlledby channelfeaturesthat determine a depth-dischargerelationship[Henderson,1966]. Suchfeatures(local contractionsor changesin surfaceelevation) are calledhydrauliccontrols,or simplycontrols,and the flow changesfrom subcriticalto supercritical as it passes through them. At a control the flow is critical (F = 1). Transitionfrom supercriticalto subcriticalflow occursthrough a hydraulicjump. Enhancedturbulenceintensityand energy loss accompanythe hydraulicjump as the flow abruptly decreasesin speedand increasesin depth. Despite its simplicity, hydraulictheoryis of great usein the studyof channelflowsas it retains the nonlinear  advective term.  Extensionto multiplefluid layershasmade hydraulictheory useful in the study of geophysicalflows. Outflow winds in Howe Sound are suitablefor applicationof hydraulictheory sincethey are composedof a stratifiedtwo-layersystemwith a cold wind layer flowingbeneathan essentiallyinfinitelythick warm layer.The two layersare generallyseparatedby a distinct interface in the form of an inversion.While there may be regionswhere the interface is relativelythick and fluid is exchangedbetweenlayers,it is reasonableand quite accurateto idealizethe system,for analysispurposes,astwo distinctlayers [Jackson,1993]. Hydraulic theory of layered flows makes the following assumptions:the fluids are inviscid,the pressureis hydrostatic,  G 2 - F2•  F•2=1-F2•'  (6)  where the approximationis valid when • << 1. In the context of outflow  winds the internal  Froude  number  describes the  hydraulicbehaviorof the wind layer [Finnigan,1994]. If we assumethe upper layer, h• >> h 2 and therefore that h • h •  thenwith u2 >> u• andF2• --• 0, whichis the caseduring outflowevents,(4) reducesto /2 2  F,= (#,h2)•/2,  (7)  which is exactlyanalogousto the single-layerFroude number (1) with # replacedby #'. This meansthat the lower layer of the outflow wind systembehaveshydraulicallylike a single layer of fluid reactingunder a reducedgravitationalfield (i.e., #'). When the upper layer is much thicker than the lower  3940  FINNIGAN  ET AL.: PHYSICAL  MODELING  layer,the approximation(7) is valid and the upperlayer thicknessis unimportant.The simplificationof (4) into (7) allowsus to accuratelymodel the two-layerwind systemusinga single layer of fluid. The methodsused are discussedin section4. FollowingLawrence's[1990] discussion, the externalFroude number  OF AN  OUTFLOW  EVENT  a zone of very large horizontalsea level pressuregradient, oriented perpendicularto the coast,resulted in stronglowlevel gap windsthroughthe valleysand fjords dissectingthe coastrange.The strongpressuregradientand resultingwinds beganto weaken after December29, when the upper level ridge-troughpattern decreasedin amplitude,the Yukon high moved southeastwardin British Columbia but weakened, and  FE• (gh)l/2,  (8)  the arctic front moved farther 3.2.  wherethe flowweightedmeanvelocity• = (u •h• + tt2h2)/h. This Froude number, which is expectedlysimilar to that of single-layerflow, is of little significancein the outflow wind scenariosincethe upper layer is essentiallyinfinitelythick and F E • O.  3.  Field Experiment  flow wind event that commenced on December 27, 1992, and  continueduntil January1, 1993.F1 presentedcrosssectionally averagedmodel resultscomparedwith microbarographfield field data were  used to infer  mean  depth, velocity,and Froude numbervariation alongthe channel for two separatehydraulicregimes.Some of the flow features observedin the model were confirmedby the field data althoughthe conclusions were mostlyqualitative.Comparison of the results with a one-dimensionalhydraulic computer model [Jacksonand Steyn,1994b] also showedpositiveagreement.  In section3.1 we describethe synopticconditionsthat led up to the December 1992 event. Following this, we introduce some additional data recorded during the December 1992 event at permanent weather stationsin the Howe Sound region. These data are then used to reinterpret the microbarographrecordings,previouslydiscussed by Fl. 3.1. Event  Synoptic Weather Conditions for the December 1992 in Howe  Sound  The evolutionof synoptic-scale weatherpatternscreatesthe atmosphericboundary conditionswithin which outflow winds occur.The synopticconditionsin the December 1992 caseare typicalof other outflowwind cases[Jackson,1993]. An upper level ridge, lying north-southacrossthe Aleutian Islands (Figure 1), increasedin amplitude during December  26-27, 1992.Meanwhile,an upperlevelcoldlow andan associated998 mbar sealevel low developedin a troughto the east and moved  southward  down  Station  Data  As describedby F1, the onset of outflow winds coincided with the occupationof Howe Sound by a shallowlayer of relativelycoldand denseair of interior origin.This occurredat approximately1800 PST, December 27, 1992. Hourly averageddatafor wind speed(u), temperature(T), and pressure(P) were obtainedfrom three weather stations during the event. The stations were located at Pemberton  Finnigan et al. [1994] discussed results from a onedimensional laboratory model of outflow winds in Howe Sound.The initial modelingwas followedby a field investigation conducted during the winter of 1992/1993. With some prior knowledgeof the flow behavior(from the initial modeling) it waspossibleto strategicallypositionmicrobarographs in Howe Soundat locationsthoughtto be betweencontrolpoints and hydraulicjumps. The instrumentsrecordeda severeout-  data for this event. The  Weather  offshore.  the British  Columbia  coast to a  quasi-stationaryposition 900 km southwestof Vancouver Island by 0400 LST, December27. This patternresultedin east to northeasterlyflow aloft over the coastalzone. Linked with the upper level ridge,a 1060mbar surfacehigh-pressure zone, associatedwith very cold arctic air, formed over Alaska and moved to a quasi-stationaryposition over central Yukon Territory by 0400 LST, December 27. Associatedwith these developments, an arctic front moved southward across Howe Soundduringthe day on December 28. Behindthe arcticfront,  (PM), Squamish(SQ), and Pam Rocks(PR). Data for potential temperature(0) wasalsoobtainedfrom a mountainstation at Mount Strachan(MS). All stationsare shownin Figure 2a with the exceptionof PM, which is located about 50 km upstreamof SO. SO and PR are both locatedat approximately sea level, whereas MS is at an elevation of 1450 m, which is  presumablyabovethe inversionheight. Figure3a showsthe evolutionof the pressuregradient(dP/ dx) betweenPM and SQ, computedby simplytakingthe pressure differencebetweenthe stationsdivided by the distance separatingthem. Wind speedsrecorded at SO and PR are shownin Figure 3b wherecorrelationwith the pressuregradient is obvious.It is interestingto note that althoughPR is only 23 km downstreamof SQ, wind speedsat PR are typically2-3 timesgreaterthan at SO throughoutthe event.This exemplifies the high streamwisevariabilityof the flow and pointstoward someform of hydrauliccontrol. The ideal gaslaw wasusedto computethe fluid densityat SQ and PR throughoutthe event. The resultsare shownin Figure 3c where it is evidentthat the flow consistently becomes less dense en route between SQ and PR.  Sinceonlypotentialtemperaturedatawere availablefor MS (i.e., raw data for temperatureand pressure,and therefore density,were not available),it wasnecessary to alsocompute0 for SQ and PR in order to determinethe reducedgravity#' at thoselocations(reducedgravityis computedhere using#' #(0• - 02)/0 • as opposedto the definition introducedin section2). It wasassumedthat the upper layer potentialtemperaturewas a functionof time but did not vary with location over the area of Howe Sound.Therefore the potential temperatureat MS wasusedat both SO and PR in the calculation of #'. Potentialtemperature(referencedto sealevel)is shown in Figure 3d. Relativelylow temperaturesrecordedat SQ and PR confirmthe presenceof the wind layer flowingbeneaththe ambientwarmer air (MS). The potential temperaturedifferencebetweenlayersis nearlyconstantwithin the time frame of high-pressuregradients.The fact that PR has a consistently higherpotential temperaturethan SQ may be a signatureof some vigorousmixing processoccurringsomewherebetween the two stations.We will showin the followingsectionsthat a complexflow with hydraulicjumps lies betweenthe two stationsand would likely causesignificantentrainmentof warmer fluid from aboveinto the lower layer. This is consistentwith the densityvariationsshownin Figure 3c. Temporalvariationof reducedgravityis shownin Figure3e. As the cold air invadesHowe Soundand the potential tern-  FINNIGAN  ET AL.:  PHYSICAL  MODELING  OF AN  OUTFLOW  EVENT  +-' 0.02 (a) /•/x•-•.g•-•.•v ' • o.m  '  '  '13  I  I  I  ,  ,  ,  0  I  40  v  •  I  ,  3941  20 0  •  •  •  •  •  1.35 [ . .  ,  [  ,  ,  ,  ß  1.25  .-. 2ø i(d)  ..... ß ''''......... "'i....'  -20 •  I (e) g  ' ''' '' '  '  .....  0.5  0  20  40  60  80  100  120  Time (hours)  Figure 3. Time variation of severalparametersrecorded during an outflow wind event in Howe Sound.The start time coincideswith 0200 PST, December 27, 1992. (a) Pressuregradient between Pemberton and  Squamish.(b-e) Wind speed,density,potentialtemperature,and reducedgravity,for SQ, dotted line, PR, solid line, and MS, dashed-dottedline, respectively.  perature in the lower layer decreases(hour 15-60), indepen- the pressurerecordingsat each stationroughlycoincided(up dently of the upper layer,•7' showsa marked increaseat both to abouthour 14), indicatingan almostuniform synopticpreslocations.High valuesof •7' persistuntil approximatelyhour sure distributionover the 50 km spanof the instruments. 110 when the event beginsto subside. When the cold interior air occupiedthe lower elevationsof the region,the gravitationalresponseof this wind layer to the 3.3. Microbarograph Data drastictopographyof Howe Sound causedits depth to vary The locationsof the microbarographsare shownin Figure significantlyin the flow direction.Depth variation may be due 2a as black dots numbered 1-5 in the direction of flow. An to a combinationof simple massconservation,hydraulic coneffort was made to place the instrumentsat shore locations, trol, and interfacial waves. whichwere not immediatelybelowvalleywalls. Ideally, all of Beginningat approximatelyhour 14, the wind layer develthe instrumentswould be placedroughlyalong the centerline oped rapidly, and depth differencesbetween stationsare reof the valley.All of the instrumentswere closeto sealevel, and flected in the separationof the pressurelines (although all estimatesof their elevations(z) are given in Table 1. The stationsstill follow the synoptictrend). Note that thiscoincides microbarographs continuallyrecordedpressureat the five sta- with the rapid increasein pressuregradientas shownin Figure tions from December 1992 to February 1993. Here we present 3a. Microbarographdata at stations3 and 4 betweenhour 29 resultsfor five dayscorrespondingto the weather stationdata and 47 were lost due to instrument failures. Dashed lines described above. indicate sectionsof lost data, and it is apparent that the wind Pressure variation at each station for the duration of the layer changedsignificantlyduring this time. event is shownin Figure 4. Prior to the onset of strongwinds  4. Table 1.  Estimated Elevation, Above Mean Sea Level, of  MicrobarographInstrumentsPositionedin Howe Sound During the December 1992 Outflow Wind Event Station  Elevation, m  1  3  2  2  3 4 5  2  2.5 0.5  Exact elevationmeasurements were not possible.  4.1.  Laboratory Experiments Description  Finnigan et al. [1994] presented results from a physical modelwhosedimensionsvaried only in one direction.For this reasonit may be referredto as a one-dimensional model (even though the flow is at least two-dimensional).The model describedthere was designedby using estimatesof the average channelwidth at severallocationsalong the east channel of Howe Sound. The channel was effectively closed along the west sideby assuminga wall roughlyalignedwith Anvil, Gambier, and BowenIslands(seeFigure 2). In the resultingmodel  3942  FINNIGAN  103  PHYSICAL  i  102  •.  ET AL.:  MODELING  i  OF AN  i  OUTFLOW  EVENT  I  -  _  123  101  -  100  -  99  0  I  I  I  I  20  40  60  80  I  1 O0  120  time (hr)  Figure 4. Pressurevariation at microbarographstations1-5.  tively small compared to the surface drag [Turner, 1973, p. 184). Therefore surfacefriction was modeled by applying While the F1 model was successfulin predictingthe basic surfaceroughnesselementsto the land and water areasof the hydraulicbehavior of the wind system,it was limited in its model. The element size and spacing,representingthe actual resolutionand accuracy.The resultswere particularlyusefulin terrain, were determined through energy considerationsand determiningappropriatelocationsto situateinstrumentsin the scalinglaws [Chow, 1959]. field. In the model, water entersover a weir at the upstreamend The physicalmodel describedin the presentpaper has di- (see Figure 5) and flowsthroughthe model terrain to a weir, mensionsvaryingin all three coordinatedirections.The model beyond the downstreamchannelterminus,which establishes includesthe following,which were not consideredin the pre- the downstreamdepthha (or ambientinversionheight). Representativemodel flowsare basedon the constancyof vious model studyreportedby Fi: (1) correct simulationof boundaryconditions;(2) effectsdue to channelsinuosityand Froude number between the model and the field flows. The elevationchanges;(3) flow over and around,and effectsdue model Froude number has the single-layerform of equation to, islandsin the channel;(4) variationin wind acrossaswell as (1) and the field Froudenumber(7) is that for two-layerflow alongthe channel;(5) energylossesdue to form drag and skin friction drag; (6) more accuratesimilarity;and (7) simulated pressuregradients. flows,velocityand depthwere assumedto vary only in the flow direction.  In the field  the Coriolis  force  is associated  with  a small  changein the height of the interfaceacrossthe valley. Taking rough estimatesof the channelwidth W, the flow velocity U, the Coriolisparameterf, and #', we may estimatethe tilt as  Pemberton  A• = WfU/#' = [(8000 m)(10-4 s-•)(12 ms-•)]/(0.4ms-2)  Valley  = 24 m, which is quite insignificantrelativeto the undulations in the interfaceobservedin the modelflows(-500 m). Rotation was therefore not includedin the model study. The topographyof the Howe Soundregionwas reproduced and extendedin the upstreamand downstreamdirectionsto minimize boundary effects. The model is shown in Figure 5 which is the view up the channelfrom the downstreamend. This model was producedby replicatingeach 150 m contour level from contourmapsof the Howe Sound area. The levels were built up by sequentiallystackingsheetsof cork material (-5 mm thick),eachcut to the shapeof a singlecontourlevel. The stepsin betweencontourswere then filled by hand resulting in a model which resolvesmap detail to a resolution of  upstream weir  ...:.:.-'.-• ß  ß  .-.. .;•::../..-  :.•::•.• ..  ..)!:.;. ::  .•.•.." :!::  ..... .:.;:  ..... :..:  .  ::•...... '•::•:  •::: .. 5..  ...  150 m in the vertical.  In the upstreamdirection the model extendsto the nearest large reservoirof cold air that existsin the field (Pemberton Valley). By making this extensionthe inflow conditionsare properly simulated.In the downstreamdirection the model extendsapproximately10 km into the Strait of Georgia. A singlelayerof waterwasusedto simulatethe lower (wind) layer of the actualtwo-layersystem.By omitting an upper layer in the model,mixingand frictionbetweenlayerswere ignored. Mixing of upper layer fluid likely occursin the field which may affect the buoyancyof the lower layer and modify the dynamics slightlyfrom what we see in the model. As far as friction is concerned,sincethe velocity in the upper layer is small, the frictional drag at the interfacebetweenthe two layersis rela-  Figure 5. View of physicalmodel from downstreamend.  FINNIGAN  ET AL.:  PHYSICAL  MODELING  with an infinite, slow-movingupper layer. Froude number similarity is achievedby equating(1) and (7) which leadsto  =  Field  where subscriptm refers to model and subscriptf refers to field. If the ratio of field to model quantities is indicated by subscriptr, then (9) becomes  Low (L) High (H)  • must be estimated  or known  from  field observations.  With knowledgeof model and field dimensions,(10) can be usedto derive expressions for scaleratiosfor severalquantities suchas total dischargeQ. The model was designedto produceflows having Reynolds number,Re = ldrnhrn/V , large enougheverywherethat viscous effectsare insignificant,as they are in the field (v is the dynamicviscosityof water at the laboratorytemperature).This conditionwas achievedthrough a slightvertical distortion of the model which effectivelyincreasedthe fluid depth (and Reynoldsnumber)while maintaininggeometricand kinematic similaritywith the field (full dynamicsimilarityis impossible  3943  Discharge,  Weir Height,  m3 s- •  mm  Slope  32 41  0.039 0.053  Model  Range where  EVENT  Dimensions  Range  '  OUTFLOW  Table 2. Model Parametersand CorrespondingValues in  (9)  /gm  •  OF AN  Model  Parameters  3.8 X 10-4 5.7 x 10-4 Discharge,  Inversion  Pressure  m3 s-•  Height,rn  Gradient,Pa m-•  Corresponding FieM l/alues  Low (L) High (H)  1.7X 107 2.6 x 107  960 1200  -0.015 -0.020  Thefollowing valueswereused:g', 0.51ms-l; density,1.31kgm-3.  and obtain adequate overall particle density, several source imageswere acquiredat each location, and multiple measurements were averagedto produce each data value (refer to Finnigan[1994] for further details). 4.3.  Results  sinceit requiresRem : Rer). With Lr representing the ratio  Resultswere obtained for eight different flows, each simulating outflow winds under a different set of synopticconditions expectedin the field. Velocity, depth, and Froude number, for each flow, reveal the subcritical and supercritical hr and some of the dynamicfeaturespresentin the wind (ll) regions layer. The model flows were based on synoptic conditions which is equal to the ratio of slopesSr and is usually_<1.The present in Howe Sound during December 1992, described model describedhere has L• = 48,000 and h• = 27,500 and above and previouslyreported by Fl. therefore a distortion factor of e - 0.57 which is well above 4.3.1. Governing parameters. Aside from model slope the acceptablelower limit of 0.25, as suggestedby Nicollet (describedabove)the other two parameterswhichdeterminea [1989].The actualdimensionsof the model are approximately model flow are total dischargeQ and downstreamdepth (in3.5 m in the streamwise direction and 1 m in the cross-stream version height) h j. Estimates of these two parameterswere direction. made by conductingseveralpreliminary experimentsto deterTo simulatesynopticpressuregradients,an equivalentgrav- mine which gave reasonableresults(in comparisonwith preitational force was imposedby sloping the model along the viousobservationsmade by Jacksonand Steyn[1994a]). Two values for each of the three model parameterswere channelaxis.The pressuregradientin the field, dP/dx, may be used (see Table 2). All possiblecombinationsof thesevalues expressedas slope of horizontal distancesa vertical distortion factor may be defined by  &= (a'p) • dP/dx,  (12)  which is positivefor increasingpressurealongthe channelaxis in the downstream,or positivex direction.As statedabove,the distortioncoefficientis equal to the ratio of slopes;that is, e -  were usedresultingin 23 = 8 cases.Table 3 outlinesthe parameter settingsfor each caseand lists somephysicalcharacteristics, in field dimensions, from the results. The overall  effect of each parameter on the wind systemis suggestedby these results.  Referring to Table 3, it is apparent that the expanse of supercriticalflow (column 5) is governedmainly by hd and in (12), we were able to predict a range of suitable model dP/dx. The coupled effect of these parametersis reflected in slopesto simulatepressuregradientslikely to be encountered. a positiveinfluenceby dP/dx and a negativeinfluenceby h d. The dischargeQ has a lessereffect, and its influenceseemsto 4.2. Data Acquisition depend on the other parameters.These relationshipsare deVideo and image analysistechniqueswere used to obtain picted in Figure 6, where the solid lines are not intended to flow data. Velocity and depth values,which together give the show any intermediate trend but simply connectpoints with Froude numberusing(1), were obtainedat the intersectionsof correspondingvalues of h•. a 2 cm x 2 cm grid coveringthe model flow domain. Velocity 4.3.2. Topographical influence. As described in section and depth data, for eachmodel run, were recordedseparately 4.1, the data acquiredfrom the model provide the conditions by a mobile video systemmounted abovethe model. Individual throughout Howe Sound. Although velocitiesmay be largely frames from the recorded video were analyzed by using a three-dimensional in some locations, we are concerned with computerto extractdatavaluesat the desiredpoints.A vertical horizontalvariationson a relatively large scaleand have therelight sheetwas used to illuminate crosssectionsin the flow to fore presented only the horizontal component of the depthallow depth measurement,and flow was seededwith plastic averaged velocity. It is the hydraulic behavior of the wind particles(1 mm diameter) to producestreakswhichwere con- systemthat is of primary interest. verted to velocityvalues.To eliminate time-dependentnoise Results are referred graphicallyto the Howe Sound region  Sr = Ss/Sm.Thereforeusingobserved valuesof thequantities  3944  FINNIGAN  ET AL.:  PHYSICAL  MODELING  OF AN  OUTFLOW  EVENT  Table 3. Model Parameter Settingsand Some Important PhysicalAspectsof Resultsfor Eight Simulated Cases  Case 1 2 3 4 5 6 7 8  Settings  Maximum  Maximum  Maximum  Total Supercritical  Q, ha, dP/dx  Velocity,ms-•  Depth,m  FroudeNumber  Area,km2  22.6 25.1 28.6 25.5 16.8 19.8 25.8 24.4  833 1037 928 766 1151 1148 1031 975  L, L, L H, L, L H, L,H L, L,H L,H, L H,H, L H,H,H L,H,H  3.6 3.9 6.0 4.8 4.9 5.3 6.3 5.6  116 123 257 242 41 53 162 178  L refersto the lowersettingand H to the higher.The sensitivityto eachcontrollingparametermaybe observedby comparingthe followingpairs of cases:Q (1 versus2, 3 versus4, 5 versus6, 7 versus8), ha (1 versus5, 2 versus6, 3 versus7, 4 versus8), dP/dx (1 versus4, 2 versus3, 5 versus8, 6 versus7). Results are presentedin field dimensions.  as picturedin Figure 2a. This referencefigure may be usedto In somecasesthe flow may onlypassthrougha weak shockand identifylocationsand geographicalfeaturesthat appear in the still remain supercritical,althoughat lower Froude number on resultsof Figures 7-14, which are not extensivelylabeled to the downstream side. We now discuss the results for each modeled case individuavoid clutter. The spatial dimensionsin Figure 2 provide a coordinate systemfor reference, and the topographyof the ally. Case 1 is typical of a moderate outflow wind event and area canbe clearlyseen.The resultsappear,for the eight cases modeled, in Figures 7 through 14. The hydraulicsof three-dimensionalflow differs in nature from the simple, crosssectionallyaveraged,one-dimensional •;•:•:."•x.::•::ii:;:.;•;• •'"" "•..... •!:5:!i?•":."•'i•: •:•}• •;.,.:.;:: •...•::::•;:•: ..--:•:::•;•: flow case.Schiir and Smith [1993] investigatedthe hydraulic :-:-.-• -•:.-:..•::. structureof flows encounteringtopographyand characterized -•5': ............;•;•:'•;•:•::•' •'•:•:•:• ?... 10 .::•;':' .•::;;{'.;• 'i:•.:.• •:•.. -'• someimportantfeatures.In the caseof a complicatedchannel ::• :•:•:•..-;. ;• ......•:::.:::.::•: ..... ..'.. . ..:...5 • ..... • ,:.•:•..... like Howe Sound, such features as controls and hydraulic ..... Q:....•::: :........:. s ..• jumps are not likely to span the entire width of the channel •.--:::.:?• •=•= ;:•:. •,.•.:•. ::..: .•:...•}'•'• ... %•..•. 2o whereverthey occur.Often a portion of the flow width will be :' ...;5:.....' .'*•• :":•,:: ::;:•'::" ..;e•:•;..:• :. . ..}.,.•,•q.•... :.: ....... :.5:.:.::¾--..:.• .?:: .... •?:..":¾?-..::-:'•:.:-. controlled,while a region alongsideit is not. A supercritical • •":-::':{•::' :::'" T?..;.•'.-. region may be flanked on one or both sidesby regions of •-. .4. subcriticalflow. The lateral boundarybetween two flows of e 30 different criticalitymay be termed a shear discontinuitysince ,,, , t,'....... the flowwill havedifferentdepth,speed,and possiblydirection ,• •;•..•:.... on either side. Oblique shocksmay form where supercritical ,:.::..:•......::..•..;...•::•:•  ...  ......::..•:;•..,.-.-...•.,.;  .  flow encounters  an obstruction  which alters the flow direction.  4O  [::.:•-•:'•.:..':.:::':' ':•:: ':'' • • h ß•.•i '?.... '. •}<.'.' •  300  ..... .;  ..........  5O  .... •.. ß ,  •  .:•<•: :::::::::::::::::::::::: • .........  .....  -' ..... '.•.• .t:..t.--•;• "--• •.. '" "..'•:'.  250  -  60  • 200  hd(L•  o  500  lOOO o  depth (m)  ß • 150 ..• .•-  •- -•oo  Q (H)  ••  10  distance(kin)  20 0  10  20  distance{kin)  Figure 7. Casel:QL,h• =L, dP/dx = L. (a) Depth sectionalongchannelaxis.The line alongwhich the data were extractedis shownas a greyline in Figure7b. (b) Velocity (as  %(H)•  Q (L) •  arrows)and criticalFroudenumber{F = 1) distribution  Q (L)  x•  (contoured).Velocitieslessthan 1 ms-• not shown.The contours encloseregionsof supercriticalflow with the upstream portion of the contour itself indicatingthe location of a cono L H trol. The downstreamportion of the contourrepresentsa hydP/dx draulicjump and the side portionsindicate either a physical Figure 6. Effect of individual model parameters on super- boundaryor a lateral flow discontinuity. (c) Photographof the critical flow area. For the selected values, as shown in Table 3, model flow from above. Pearlescenceparticles have been changesin dP/dx and hd significantlyinfluencethe expanseof added to the water. This and subsequentfigurespresentedin supercriticalflow, while Q does not. The solid lines are not field dimensions. A separationpoint (number1) sheardisconintended to show any intermediate trend but simply connect tinuity (2), oblique hydraulicjump (3), and two-dimensional pointswith correspondingvaluesof hd. hydraulicjump with shearlines (4, 5) are shownin Figure 7c. i  i  FINNIGAN  ET AL.:  PHYSICAL  MODELING  OF AN  OUTFLOW  EVENT  3945  10 iT!:::•:•:•  ......... :::i•....?•. :.•:'  2o  ........  ;?. :'::, ....  .  . ,.:-.;,--:----  •  -:i;:i?!i;:,:•1%;. ":.i;;••':'"" .... :!; :•;½;} •,-,:;.;.•'....•; .%.:  ß;•  ..'...:.:,-'-a.;•*j.. ":.:;•: , .,,....:..:..  :.•½.•;...:½.::•: -  ...  ...................... ...........  -•,..:•:•j•;:a;S:>½ ...--::;•-... 40 ÷  40  .  ß ;$,... ..... 4;;•*j. "•:,:..  ": J  ...... ß  60  0  500  •  0  •0  depth (m)  20 0  distance(kin)  •0  20  500  0  distame (kin)  1000  0  t0  20 0  distance{km)  depth (rn)  •0  20  di•nce  Figure 8. Case2: Q = H, h,• = L, dP/dx = L. (a) Depth sectionalong channel axis. (b) Velocity and critical Froude number (F = 1) distribution.(c) Photographof the model  Figure 10. Case4: Q = L, h,• = L, dP/dx = H. (a) Depth sectionalong channel axis. (b) Velocity and critical Froude number (F = 1) distribution.(c) Photographof the model  flow from above.  flow from  above.  exhibitsmany hydraulicfeaturescommonto subsequentcases. extrapolateto briefly describethe other casesin comparison. The occurrenceand locationof hydrauliccontrolsandjumpsin Specificlocationsin resultsfigureswill be referredto by (x, y) the wind layer agreegenerallywith the resultspresentedby Fl. coordinates(panels b and c in each figure) where alongWe focus our discussion  of the flow field in case 1 and then  channel  distance  increases in the flow direction.  ": .........  ::::.:,::•.;•:"...'.,,-.-...., -....--';;;'•.,;.... ..• .½:  lO  ......  ....  :•.,  :•..:.:•..ß  ..•,% ...........  ..'-':--:*.-q.•X; . ':;*::..•::;t.' ........ß  ,.:,:....:..:.. ,•: -?•:::j•:l•*::*: ;:•,.'* •:•:"",...;;•,;,•:;:;.:,;;:,:. ..........  ".%•½:""-%. :.; ....  .....  2O  • •:•:;4•.•.;•-:  ,½..... •: •  ......  ...; :•:. '-:•'-..  ¾... • 30  4O  6O  0  500  1000  depth(m)  0  t0  dis•nce (km)  ................................. •"0" •o distance(kin)  0  500  1000  depth (rn)  0  10  distance(kin)  2O 0  10  2O  distance(km)  Figure 9. Case3: Q = H, h,• -- L, dP/dx = H. (a) Depth sectionalong channelaxis. (b) Velocity and critical Froude number (F = 1) distribution.(c) Photographof the model  Figure 11. Case5: Q = L, h,• - H, dP/dx = L. (a)Depth sectionalong channel axis. (b) Velocity and critical Froude number (F = 1) distribution.(c) Photographof the model  flow from above  flow from above.  3946  FINNIGAN  ......g•:.• •  ET AL.'  .-  PHYSICAL  MODELING  ....%  ,.'"':"•%. .............. ?:::•4•F:• ....... ..:.: ... .... •::••::•:: -•:I --•A :'• " '3• 5 5•..:•.•  •  :'i'% i&•... •::...:.;.: $-:•:.:-:•:•:•  •  .  OF AN  '  •  ....  x• x  .,-::•½•:•$•:f½3g•½•:• •:  channel. .... :.:.  6o  • ,  5•  • 000  The  subcritical  side channel  becomes  its lateral  boundaryin the form of a sheardiscontinuity. Anvil Islandappearsperfectlylocatedto deflectalmostall of  ..  the flow down the east channel. However, the deflection does  0  10  depth (m)  20 0  •0  distance(kin)  20  distance(•m)  Figure 12. Case6: Q = H, ha = H, dP/dx = L. (a) Depth sectionalong channel axis. (b) Veloci• and critical Froude number (F = l) distribution.(c) Photographof the model flow from  of  : :"........ :: .... ,.:[•::..:. ........................ . .,,•' not occurefficientlyasflow tendsto be blockedby Anvil Island  •  0  • •  to the west channel of the Sound. The location  the separationpoint is shownby arrow 1 in Figure 7c. Here the supercriticalflow (movingfasterthan the surfacewavespeed) hasno indicationof the abruptwideningand bifurcationof the  .. ....  , ..•:•.•:::::[• x ß ß:" ::•4:...•::•:)i •:<'  EVENT  criticalflow.The flowis controlledby the promontorynear (10, 18) but only acrossa portionof the channel.Here the control occursdue to flow over an obstaclewhichspansonlypart of the channel. The sharp bend in the channel at this location and relatively steep walls on the opposite side combine with the promontoryto producea complicatedflow patternwith a deep recirculatingflow (not apparentin the figure but observed) existingnextto a regionof supercriticalflow.A hydraulicjump occurson the lee side of the promontory. The flow is again controlled, this time acrossthe entire channel,by the contractionnear (10, 23). As the flowseparates from the westsideof the Soundnear (8, 27) it remainssupercritical for somedistancewhile flowingalongsidethe subcritical entrance  ............... •<....  OUTFLOW  above. Case I (Q = L, ha = L, dP/dx = L (Figure 7)): Although mostlysubcritical,the upstreamregionof the channel near Squamish(11, 15) is hydraulicallycontrolledby local elevation changesresultingin small patchesof weakly super-  and is forced through a stronghydraulicjump near (10, 33). Note the relative depth of this hydraulicjump as shownin Figure 7a. The partial blocking by the channel contraction imposedby Anvil Island is analogousto the well-knownchoking conditionfor supercriticalflow [Henderson,1966,pp. 248249].The abruptwideningof the channelnear (10, 27) possibly actsin combinationwith upstreamblockingfrom Anvil Island to causethe hydraulicjump in this case.Somedirect evidence for the occurrenceof thisjump was found in the field recordings [Finnigan,1994]. Followingthe hydraulicjump describedabove,the flow is  ...:.•:.:.  :.  eo  • :'  ..  •.':i'•--  .....• ß. ". ... •.•., '•] ...... t.....:...:....; :'.... ?•.-:'?• ....:..:.:  •  .  I  ....... ,:•.,;;. •;•[•½•  ....... •, ,:...... .... ,½  •..  ., ...•...  2O  ,.•  ,[...•..  .:.''--...,,t-:-' ....  __  '  "'"..:::::• .  . •::::-. •'...::•[•'%" -"'•] •. ..f.  -,•.•½ ....  .•.....  4O •'•;::[i'::':•%•'•½."L .' ,..;:'.e;:..  •  e....  • ," •<•...  .,•'•'  .,.  ::.•..'-:•--•.•-•,•:.•?;;½&•::::•...•; •, .,:'-...:.., :--.:• •:..•- .-.:----•-..• .e-. ...... •:.-)• :'•½z•,•-½••:.-. •f½.:.•-. ;....  5O  • •.. - -  '•'•:• "•" .....•.:•  6O .... •.  0  500 •0 0 depth (m)  0  distance(kin)  dista•e (km)  500  t000  depth (m)  0  10  distance(kin)  20 0  10  20  distance(kin)  Figure 13. Case7: • = H, ha = H, dP/dx = H. (a)Depth sectionalong channel axis. (b) Veloci• and critical Froude number (F = 1) distribution.(c) Photographof the model  Figure 14. Case8: Q = L, ha = H, dP/dx = H. (a)Depth sectionalong channel axis. (b) Velocity and critical Froude number (F = 1) distribution.(c) Photographof the model  flow from  flow from  above.  above.  FINNIGAN  ET AL.:  PHYSICAL  MODELING  immediatelycontrolledby the throat betweenAnvil Island and the eastsideof the channel.The supercriticalstreamseparates from the trailing edge of Anvil Island forming a lateral shear discontinuity.This featurecanbe seenin Figure 7c at arrow 2. As was proposedby Jackson[1993],the flow is largelyconfined to the eastchannelby the islands(Anvil, Gambier,Bo-  wen) forminga large supercriticalregion (see Figure 7b). A complicatedoblique shock occursnear (15, 44) acrossthe entireeastchannel(Figure7c, arrow3). This is clearlyseenin the data as the F - 1 line departsfrom the east side of the channelat an angle.Some slightdifferencesare apparentbetween the exact location of shock lines in Figure 7c and the F = 1 contoursin Figure 7b. This is due to the interpolation betweenthe discretedata points. On the oppositesideof the eastchannelthe jump formation is more complicated.Justupstreamof Bowen Island,it appears that part of the subcriticalstream(on the westsideof the shear discontinuity(2)) is controlledby a smallprotrusionof Gambier Islandnear (11, 40). This appearsin Figure 7b as a westward extensionof the F - 1 contour. The criticality of this streamis not the sameasthat of the flow to its left (subcritical) or to its right (supercritical). Here the flow is laterallydiscontinuous along two shear lines, shown by arrows 4 and 5 in Figure 7c. However, both supercriticalstreamsrevert to subcriticalflow within the samehydraulicjump (14, 44). Energy is dissipated,downstreamof the hydraulicjump, by intense  turbulence  which  is advected  downstream  in a well-  OF AN  OUTFLOW  EVENT  3947  Downstream,the flow now has enoughenergyto passover  the easternpart of GambierIsland,resultingin significantly higher velocitiesin the central part of Howe Sound.A weak oblique shock appears to form from both sides of the east channelnear (15, 48), and the data suggestthat the flow remainssupercriticalon the downstreamside.A stronghydraulic jump formsover the north end of BowenIsland (11, 48) and into the centralpart of the Sound.A supercriticalregionforms as fluid is forced through a valley on the southside of Bowen Islandnear (10, 52). The onsetof this conditionwould not be welcomedby the residentsof the area (Bowen Island is well populated). Case 4 (Q = L, ha = L, dP/dx = H (Figure 10)): As expected, a decrease in discharge causes only minor changesto the flow comparedto the previouscase.The undulating hydraulicjump doesnot form, and the region of supercritical flow is slightlysmaller. Case 5 (Q = L, ha = H, dP/dx = L (Figure 11)): This combinationproducesa flow pattern different from those discussedabove. The flow is substantiallydeeper and slower and althoughAnvil Island directsthe flow into the east channel, the other islandsdo not confine it. The flow subcritically separatesfrom the eastside of the channel(12, 32) and proceedsin a direct path over the islandstoward the Strait of Georgia. The subcriticalseparationdoesnot result in a shear discontinuitywhich only occursin supercriticalflow. In the separatedregion(16, 40) a slow-moving counterclockwise eddy  definedjet. The energeticsubcriticaljet extendsalmostunin- is formed. Case 6 (Q = H, ha = H, dP/dx = L (Figure 12)): terrupted through the channel exit region and out into the Strait of Georgia. It shouldbe noted that momentum com- The increasein dischargefrom the previouscase delaysthe binedwith the synopticpressuregradientcarriescold air from separationfrom the eastern side of the channel.The flow is this jet over the Strait, where it accumulatesmoisture.This is again confined mainly to the east channel and a small sepacommonlyobservedto resultin snowbelts alongthe eastcoast rated regionexistsnear (16, 40). Relative to the first four cases the flow is slow and deep, and althoughsupercriticalregions of southernVancouverIsland (seeFigure 1). At the channelexit, part of the jet overtopsthe headlands near (13, 28) and (12, 37) are present,the supercriticaldownnear (17, 48) and is locallycontrolledbut revertsto subcritical streamregion (12, 37) is somewhatsmallerthan the first four conditionsthrougha hydraulicjump on the lee of the obstacle. cases.This and the previouscasetypify conditionsexpectedfor It is interestingto note the presenceof obliquewavesthat low-pressuregradient forcingwith a relatively high inversion  form in supercritical regions(slightlyvisiblein Figure7c) at an  anglewiththesidewallsgivenbysin-• ( 1/F). Suchwaves have been observedin layered supercriticalgeophysicalflows [see Farmer and Armi, 1986]. Case 2 (Q = H, ha = L, dP/dx = L (Figure 8)): The increasein discharge,from that for case 1, increasesthe depth of flow. Although it seemsto decreasethe supercritical regionnear the channelexit (17, 48), it hasan overalleffectof increasingthe expanseof supercriticalflow. The deeperflow is now able to go over rather than around larger portions of  level. Case 7 (Q = H, ha = H, dP/dx = H (Figure 13)): This case is similar to that of cases 1 and 2 but is characteristic  of a strongerflow with a larger area occupiedby supercritical flow. The three prominent regions of supercriticalflow are again present but are slightly larger. As well, the laterally discontinuous supercriticalregion(centerednear (10, 40)), as describedabove for case 1, is present. Case 8 (Q = L, ha = H, dP/dx = H (Figure 14)): The changein dischargehas the oppositeeffect in this strong Gambier and Bowen Islands and is controlled as it does so. flow caseasit did in the moderateflow cases1 and 2. With high Small velocitiesdownstreamof the hydraulicjump near (16, forcing,the responseto a decreasein dischargeis an increase 45), combinedwith a greaterfluid depth, limit the size of the in the amountof supercriticalflow area. Controlsoccurfarther upstream due to the decreasein depth that accompaniesa supercriticalarea near (17, 48). decreasein discharge.The two main downstreamsupercritical Case 3 (Q = H, ha = L, dP/dx = H (Figure 9)): The increasein pressuregradientcausesa substantialincrease regionshave joined as in cases3 and 4. This occursdespite in supercriticalflow. The supercriticalregion near (12, 18), someflow blockingupstreamof Anvil Island.A hydraulicjump however,seemsfixed in size as a hydraulicjump is forced on limits the extentof thisregionand it doesnot extendout of the the lee side of the promontory.A large supercriticalregion channel as in cases 3 and 4. now spansmost of the length of the lower channel,extending out beyondthe terminusbeforerevertingto subcritical conditions 5. Comparison of Field and Model Results throughan apparentundulatinghydraulicjump. Although the flowis substantially blockedbyAnvil Island,resultingin a hydrau- 5.1. Pressure Comparison lic jump that tendsto "pile" fluid up againstthe steepslopesof To evaluate the ability of the physicalmodel to represent the island,it remainssupercriticalthroughpart of the channel. real flows, we present a comparisonbetween the laboratory  3948  FINNIGAN  Table 4.  ET AL.: PHYSICAL  MODELING  Values of Observed Quantities at Hour 57  Quantity  Value  Synoptic pressure gradient, dP/dx--(Pa m-•) Windspeed(SQ),u--(m s-•) Windspeed(PR), u--(m s-•) Reduced gravity(SQ),#'--(m s-2) Reduced gravity(PR),#'--(m s-2) Reduced gravity,average, #'--(ms -2) Lowerlayerdensity (SQ),p/--(kg m-3) Lowerlayerdensity(PR), p/--(kg m-3) Lowerlayerdensity,average, p/M(kgm-3)  -0.016 8.5 24.3 0.60 0.42 0.51 1.33 1.30 1.31  Differencein pressure,stations2-1, dP--(Pa) Difference in pressure,stations3-1, dP--(Pa) Difference in pressure,stations4-1, dP--(Pa) Difference in pressure,stations5-1, dP--(Pa)  233  245 448 467  The averagevalues of reduced gravity and densitywere used to scale-upfrom model results.  OF AN  OUTFLOW  EVENT  plotted in Figure 15. This casegave the best agreement.The field data and the model agreeremarkablywell exceptat station 3, Porteau Cove. This discrepancymay be explainedby consideringthe depthsobservedin the model, plotted in Figure 16. Porteau Cove is indicated by a solid circle. Just offshore,the model predictsa tongueof deeperflow (markedby the 400 m contour).In the field this deeperflow mustextend closer to shore and over station 3.  5.2.  Wind Speed Comparison  Wind speed records from SQ and PR were presentedin Figure 3b. The persistentlarge differencebetweentheselocations suggests a situationof supercriticalflow at PR and subcritical flow at SO. This is consistent with model results which  showthe samesituationin 7 of 8 cases(case5 is the exception). Wind speedsfrom the modelfor case6, takenfrom locations closest to SO and PR and converted to field dimensions, are  shownin Figure 17 along with field values at hour 57 (see Figure3b). The straightline in the figurewouldbe one-to-one and the field data. The pressuregradientpresentin the field correspondence.Case 6 gives a good approximationof the was simulatedby the tilt of the model in the lab, as explained observedwind velocityat Pam Rocks.However,it overpredicts in section4. The slopeof the physicalmodel Sm necessaryto the velocityat SO perhapsdue to shelteringof the anemometer at SQ.  represent a pressure gradientin the field(dP/dxf) is  Sm--(ep•))-•  (alP)  (•3)  wheree is the distortionof the modelandpf and!7}are the  The agreementbetweencase6 and the field observationsis fairly good.It is interestingto note that this occursdespitethe mixing (not modeled) which must occur betweenSquamish and Pam Rocks as witnessedby the change in density and reducedgravity.Further laboratoryexperimentsare underway in order to allow comparisonto more of the data recordand to data from Jacksonand Steyn[1994a].  densityand reducedgravityin the field, respectively. For comparisonbetween the model resultsand the field resultsit is necessaryto choosetimes in the field resultswhen the pressuregradient,density,and reducedgravitygiveone of the two slopesused in the lab. The pressuregradientvalues 6. Discussion and Conclusions representedby the two slopes(0.039 and 0.053) in the lab are Microbarographpressurerecordingsshowedthat the outgiveninTable2 for17'= 0.51ms-• andpf = 1.31kgm-3. flow wind event, which occurredin Howe Sound during DeMatching slopesand pressuregradientsis complicatedby the cember 1992, exhibitedlarge spatial variability. Comparison factthatSmis a functionof pf and17}aswellasthe pressure betweenthe field and the model resultsfor matchingaverage gradient.Calculationsshowthat the two slopesusedin the lab dP/dx allowed a more thorough descriptionof the alongeachmatchpressuregradientsin the field twice.The first two channel behavior. By producinga range of model flows we matchesoccurin the initial developmentphaseof the event at were able to span most of the field results and achieve a abouthour 10 and hour 15 for the low and high slope,respec- reasonableagreement.One flow period was identifiedduring tively. The secondmatch for the high slopeunfortunatelyoc- which the along-channeldepth variation was nearly constant. curs at about hour 45 when data were lost from two of the Very closeagreementwas found betweenthe field resultsat sensors.Thus a comparisonis made between the low slope hour 57 and the model values from case 6. The other model laboratorydata and the field data at its secondmatch, at hour 57. Values of the observedquantitiesat this time are givenin Table  4.  0  To comparethe observed(field) pressurechangesto the model results,depth valueswere extractedfrom the model at locationscorresponding to the five field stations.The pressure betweentwo stationsis then givenby  -100  -200  AP  dP = pm17(dh - dz- Sfdx),  (14)  where dh is the differencein the depth of the water, dz is the differencein elevationof the stations(givenin Table 1) scaled by the scalefactor hr, and dx is the distancealongthe model between the two stations.When the pressurein the lab is calculated,it is convertedto field units through  dPf = (17'/17)(pf/pm)hr dPm,  (15)  where h r is the vertical scaleratio for the model. The changein pressurebetweenstations2-5 and station1 for the field and for lab case6 scaledup to field dimensionsis  ß  (Pa)  -300  -400  -500  -600  0  10  20  30  40  50  x (km)  Figure 15. Comparisonof field measurements(diamonds) with case 6 laboratory measurementsof zip as a function of distancealongthe channel.The error bars reflect uncertainty in scalingof the laboratorymeasurementsto field results.  FINNIGAN  ET AL.:  PHYSICAL  MODELING  casesmay occurin nature under different synopticconditions from what were presentduringthe December 1992 event. In general,the physicalmodel showsa highlyvariableflow field under different forcing and boundary conditions. The expanseof supercriticalflow is found to vary substantiallyin responseto a changingpressuregradient.This fact is impor-  OF AN  OUTFLOW  EVENT  3949  2s J  / / PainRocks  J  J J J J  Squamish  is  X  Oi,b  tantin practical considerations sincethegrowth of a super- {m/s) critical region could be predictedby forecastingthe pressure gradientin the field. As conditionschange,the flow regime may changein local-  40  izedareasbetween thethreeregimes discussed bySchi•r and  s  / / /  /J/  / / / / / / / / / / / / /  Smith[1993].In particular,it is evidentfrom modelresultsthat the flow may or may not be confinedto the easternchannelof 0  5  10  15  20  25  Ufield (m/s)  Figure 17. Comparisonof wind speedmeasuredat Squamish and Pam Rocks to results from case 6.  Howe Sound.In the casesthat it is confined(cases1, 2, 3, 4, 7, 8), flow separationoccursdownstreamof topographyresulting in shear discontinuities  with subcritical  flow in the lee of the  obstructionalongsidesupercriticalflow in the east channel. This situation is well known to ferry operatorswho traverse lower Howe Sound regularly, even in extreme winds (C. Whailin, personal communication,1993). On several occasions,in particular during the December 1992 event, the operator reported that intensewinds sharplydecreasedas the ship moved from the east channel to the passagebetween Gambier and Bowen Islands(i.e., acrossa sheardiscontinuity from supercriticalto subcriticalflow). In somecases,suchas that for model cases5 and 6, the wind  layer is deep enoughand has enoughenergyto overtop the islands.In these casesthe flow is primarily subcriticalin the vicinity of the islandswhich tend to causeundulationson the interfacedownstream.These casescouldbe importantin the generationof large-amplitudeinternal wavesat the inversion height. The resultspresented suggestthat the physicalmodel is capableof providinginsightinto the complicateddynamicsof outflow  winds in Howe  Sound. Since these winds occur infre-  quently and are difficult to predict, they constitutea system that is quite difficultto studyusingfield measurementsalone. Available data are generally limited to discrete locations. Therefore the high spatialvariability of the winds is not resolvedwell by stationaryweather stations.The model has allowedusto revealsomeof the complicatedflow structuresand hydraulic effects that characterizethese flows. Comparisons with field data have allowedan analysisof trendsand causesof certain flow phenomena,suchas hydraulicjumps. Future uses of the model may involveextendingthe parameter range and makingfurther comparisons with a data set acquiredby Jackson and Steyn[1994a].  0  •' !  I  •  i  '"  2  4  6  8  10  I  '  !  121416  Acknowledgments. The authors wish to thank D. Steyn and P. Jacksonfor their usefulcommentsand for providingsomeadditional field data. The assistance of K. Nielson  distance  (km)  Figure 16. Depth contours for model case 6. Interval is 200 m and the 0 m contour is not shown. Note tongue of deeperfluid near station3 (solidcircle).  in the construction  of the  laboratorymodel is alsogratefullyacknowledged. The manuscriptwas improved through the useful commentsof an anonymousreviewer. This work was funded through a joint grant from the Atmospheric EnvironmentService(AES) of EnvironmentCanadaand the Natural Scienceand EngineeringResearchCouncil (NSERC).  3950  FINNIGAN  ET AL.: PHYSICAL  MODELING  References  Armi, L., The hydraulics of two flowinglayersof differentdensities, J. Fluid Mech., 163, 27, 1986.  Baines,P. G., Topographic Effectsin StratifiedFlows,CambridgeUniversityPress,New York, 1995. Bond, N. A., and S. A. Macklin, Aircraft observations of offshore-  directedflow near Wide Bay, Alaska,Mon. WeatherRe.v, 121, 150161, !993.  Chow,V. T., OpenChannelHydraulics,McGraw-Hill, New York, 1959. Farmer, D. M., and L. Armi, Maximal two-layer exchangeover a sill and throughthe combinationof a sill and contractionwith barotropicflow,J. Fluid Mech., 164, 53, 1986. Finnigan,T. D., Hydraulic analysisof outflowwindsin Howe Sound, British Columbia, M.S. thesis, Univ. of British Columbia, Vancouver, 1994.  Finnigan,T. D., J. A. Vine, P. L. Jackson,S. E. Allen, G. A. Lawrence, and D. G. Steyn,Hydraulicphysicalmodelingand observations of a  severegapwind,Mon. WeatherRev.,122,2677-2687,1994. Henderson,F. M., Open ChannelFlow, pp. 248-249, Macmillan, Indianapolis,Indiana, 1996. Jackson,P. L., Gap windsin a fjord: Howe Sound,British Columbia,  OF AN OUTFLOW  EVENT  mentumbalanceduringa gap-windeventin ShelikofStrait,Alaska, Mon. WeatherRev., 117, 1817-1833, 1989.  Lawrence,G. A., On the hydraulicsof Boussinesq andnon-Boussinesq two-layerflows,J. Fluid Mech., 215, 457-480, 1990. Nicollet, G., River models, in RecentAdvancesin HydraulicPhysical Modeling,chap.2, edited by R. Martins, pp. 39-63, Kluwer Acad., Norwell, Mass., 1989.  Reed, T. R., Gap windsin the Strait of Juan de Fuca,Mon. Weather Rev., 109, 2383-2393, 1931.  Sch•ir,C., and R. B. Smith,Shallow-waterflow past isolatedtopography, I, Vorticity productionand wake formation,J. Atmos. Sci., 50, 1373-1400, 1993.  Schaeffer,G., Climatology,in The SquamishRiver EstuaryStatusof EnvironmentalKnowledgeto 1974, edited by L. M. Hoos and C. L. Vold, Environ. Canada, 1975.  Turner, J. S., BuoyancyEffectsin Fluids,CambridgeUniversityPress, 368 pp., New York, 1973. S. E. Allen, Departmentof Earth and OceanSciences,Universityof British Columbia, Vancouver, B.C., Canada. T. D. Finnigan, Centre for Water Research,University of Western  Australia, Nedlands,Perth, WA 6907, Australia. (e-mail: finnigan@ cwr.uwa.edu.au) Jackson,P. L., and D. G. Steyn,Gap windsin a fjord, I, Observations G. A. Lawrence, Department of Civil Engineering,University of Ph.D. thesis, Univ. of British Columbia, Vancouver, 1993.  and numerical simulation, Mon. Weather Rev., 122, 2645-2665, 1994a.  Jackson,P. L., and D. G. Steyn,Gap winds in a fjord, II, Hydraulic analog,Mon. WeatherRev., 122, 2666-2676, 1994b. Lackman,G. M., and J. E. Overland,Atmosphericstructureand mo-  British Columbia, Vancouver, B.C., Canada.  (ReceivedOctober22, 1996;revisedSeptember25, 1997; acceptedNovember7, 1997.)  


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items