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Hydraulic analysis of outflow winds in Howe Sound, British Columbia Finnigan, Timothy D. 1994

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HYDRAULIC ANALYSIS OF OUTFLOWWINDSIN HOWE SOUND, BRITISH COLUMBIAbyTIMOTHY D. FINNIGANB.A.Sc., The University of British Columbia, 1991A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTSFOR THE DEGREE OF MASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIES(Department of Civil Engineering)We accept this thesis as conforming to the required standardTHE UNIVERSITY OF BRITISH COLUMBIAAugust 1994© Timothy D. FinniganIn presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)______________________________Department of C,vi/The University of British ColumbiaVancouver, CanadaDate 3aDE-6 (2188)AbstractPrevious studies (Jackson, 1993) suggest an outflow wind, which flows below aninversion in a well defined layer through Howe Sound, may exhibit hydraulic behaviour.Strong outflow winds in Howe Sound are simulated in the laboratory using a single fluidlayer in a small scale one-dimensional physical model. Model results are presented andcompared with observations recorded in Howe Sound during a severe outflow wind eventin December, 1992. Field observations affirm the findings of the physical modelling withboth indicating the presence and location of controls and hydraulic jumps in the windlayer. Hydraulic behaviour is found to change as the synoptic pressure gradient and theflow rate increase. An additional comparison is made with output from the computermodel, Hydmod of Jackson and Steyn (1994b). Numerical simulations, configured forthe conditions present in Howe Sound during the December, 1992 event, indicate channelhydraulics (and thus spatial wind speed variation) closely resembling the physical modeland field results.Outflow winds are studied in more detail through a series of experiments conducted witha three-dimensional physical model which is geometrically and kinematically similar tothe prototype, Howe Sound. The results reveal the structure of the wind layer over a widerange of possible field conditions. Hydraulic features, which do not behave in atraditionally one-dimensional manner, are identified. The 3D model results, althoughmore detailed, verify the findings of the 1D modelling in general. Together the resultsprovide a predictive tool for determining hazardous zones of extreme wind during anoutflow event.IITable of ContentsAbstract iiTable of Contents iiiList of Tables vList of Figures viForeword viiiAcknowledgment ixIntroduction 1Introduction 1Outflow Winds 2Hydraulic Theory 5Previous Work 8Gap Winds 9Downslope Winds and the Hydraulics of Layered Flows 11One Dimensional Modelling and Field Investigation 16Physical Model Study 17Experimental Methods 17Results 19Results for flow rate A 20Results for flow rate B 21Field Program 21Field Experiment 22Field Data Interpretation 24Results for Period 1 25Results for Period 2 26Comparison of Physical Model, Hydmod and Field Results 27Period 1 (flow rate A) 27Period 2 (flow rate B) 29Further Comparison with Hydmod Output 29Discussion 31111Three Dimensional Modeffing .33Description 33Design Considerations 34Model Design and Construction 43Data Aquisition 45Data Aquisition System 45Depth Data Aquisition 46Velocity Data Aquisition 49Results 50Important Parameters 50Model Results 51Discussion of Cases 1 Through 8 52Discussion and Conclusions 56Comparison of 1D Modelling and 3D Modelling 56Comparison of field results with 3D model results 57Summary and Conclusions 59List of Symbols 62Bibliography 63Appendix A 66Appendix B 70ivList of TablesTable page1 Values of parameters as observed during Period 1 and Period 2 which 72were used in Hydmod comparisons.2 Scale numbers resulting from Froude number similarity between model 72and prototype.3 3D Model parameters and corresponding values scaled to prototype 73dimensions.4 Model parameter settings and some important physical aspects of the 73results for the eight simulated cases.5 Case 6 of 3D model results compared with Period 1 of field study 74results.6 Case 7 of 3D model results compared with Period 2 of field study 74results.vList of FiguresFigure Page1 Schematic representation of outflow wind system. 752 Geographical location and important features of region surrounding 76Howe Sound.3 Howe Sound; locations and topography. 774 Schematic drawing of experimental apparatus used for 1D physical 78modelling of outflow winds.5 Channel axis shown with respect to the model of Howe Sound (a) and 79Howe Sound (b).6 (a) Depth, (b) wind speed, and (c) Froude number along Howe Sound: as 80predicted by the physical model for flow rate A ; as measured during theDecember, 1992 outflow event for Period 1; and as produced byHydmod for Period 1.7 (a) Depth, (b) wind speed, and (c) Froude number along Howe Sound: as 81predicted by the physical model for flow rate B; as measured during theDecember, 1992 outflow event for Period 2; and as produced byHydmod for Period 2.8 Composite chart of atmospheric pressures recorded at 5 stations in Howe 82Sound over a 9 day period.9 Relative pressures, with respect to that at station 1, at each of the five 83field stations in Howe Sound for (a) Period 1 and (b) Period 2.10 Photograph of 3D model topography. 8411 Cross sectional sketch of 3D model topography construction. 85viFigure Page12 Schematic view from above of the video apparatus cart and rail system 86(a) and schematic side view of complete 3D model equipment set up (b).13 Photograph of 3D model. 8714 Definition sketch for depth data aquisition. 8815 Plots for validation of video techniques for depth data aquisition. 8916 Reference diagram for 3D model results (a) and Topography of region 90covered by model results (b).17 3D Model. Case 1 - Q=L, hf=L, dP/dx=L 9118 3D Model. Case 2 - Q=H, hf=L, dP/dx=L 9219 3D Model. Case 3 - Q=H, hf=L, dP/dx=H 9320 3D Model. Case 4 - Q=L, hf=L, dP/dx=H 9421 3D Model. Case 5 - Q=L, hf=H, dP/dx=L 9522 3D Model. Case 6 - Q=H, hf=H, dP/dx=L 9623 3D Model. Case 7 - Q=H, hf =H, dP/d =H 9724 3D Model. Case 8 - Q=L, hf=H, dP/dx=H 9825 Microbarograph pen tracings from 28 December 1992 for stations at 99Porteau Cove (a) and Lions Bay (b).viiForewordThe work reported in chapter 2 of this thesis forms the contents of a paper entitled,“Hydraulic physical modelling and observations of a severe gap wind”. This paper wasaccepted for publication in Monthly Weather Review (AMS journal) in April 1994 and iscurrently in press. The authors are as follows; Finnigan, T.D., Vine, J.A., Jackson, P.L.,Allen, S.E., Lawrence, G.A. and Steyn, D.G. The first author, Finnigan (also author ofthis thesis) wrote the paper in its entirety including composition of the text, analysis of alldata, interpretation of results and drafting of figures. Finnigan also conducted the fieldinvestigation. Vine conducted physical model experiments and contributed the data.Jackson developed the computer model and helped with the simulations. Jackson alsoprovided the interpretation of the synoptic weather conditions during the recordedoutflow event of December 1992. Allen, Lawrence and Steyn supervised the work,contributed many helpful suggestions and corrected drafts of the manuscript.viiiAcknowledgmentSeveral people contributed their efforts during the two year period this research wasconducted. The author wishes to thank Dr. S. Allen (Oceanography) and Dr. G.Lawrence (Civil Engineering), who supervised the research and provided guidance fromstart to finish. Dr. D. Steyn (Geography) supplied the microbarographs and participatedin several useful discussions about the field investigation. Dr. P. Jackson of TheUniversity of Western Ontario, who developed the Hydmod model, helped with thecomputer simulations and the interpretation of the synoptic conditions for the field work.Kurt Nielson of the Civil Engineering shop assembled the video apparatus for the 3Dmodel and helped with many technical aspects of the model itself.I would also like to thank Sewell’s Marina (Horseshoe Bay), Lion’s Bay Marina, theCunneyworths (Porteau Cove), Britannia Beach Arts and Crafts and the SquamishTerminals for allowing microbarographs to be stationed on their premises duringDecember 1992 and January 1993. The Pacific Region of the Atmospheric EnvironmentService provided the supplemental field data from Pam Rocks. The research wassupported by grants from the Atmospheric Environment Service of Environment Canadaand the Natural Science and Engineering Research Council.ixChapter 1 - Introduction1.1. IntroductionLocal meso-scale1 windstorms occur in many parts of the world with various synopticconditions responsible for their creation and unique local features influencing theirbehaviour. Downslope winds result when air is forced over topography and accelerateddown the lee side of a mountain, possibly being enhanced by vertical propagation ofwave energy and hydraulic effects. Mountain valley winds are common and often diurnalin nature with cool air drainage at night and warm, daytime heating induced, upslopeflow in the day. Gap winds can be described as flow of relatively dense low lying airthrough natural channels. These flows, which are generated when a synoptic pressuregradient is aligned with the channel, are often constrained above by an inversion2 andsurmounted by a stable layer. The term gap wind was first coined by Reed (1931) whothus defined the flow of low lying air through “gaps” in a mountain barrier when anacross-barrier pressure gradient is present. In some locations the interaction oftopography and regional or meso-scale pressure gradients can produce very complex andsometimes violent gap winds.Gap winds are most pronounced where a mountain range separates two climaticallydifferent regions. Coastal mountain ranges are special cases where a topographicalbarrier separates drastically different oceanic and interior climatic zones. When airbodies of different temperature, and therefore density, develop on either side of thebarrier, the situation is favorable for gap winds to occur. Since the air in the coastal1 of or relating to a meteorological phenomenon approximately 1 to 100 kilometers in horizontal extent.2A thin layer across which the temperature increases dramatically in the upward direction. This is areversal of the normal atmospheric temperature gradient.1region is moderated by the ocean, extreme conditions in the interior will produce apressure gradient resulting in a flow of air.During hot weather, daytime warming induced vertical convection inland will producelower pressure at the surface relative to that in the cooler ocean region. This results in apressure gradient perpendicular to the coast and landward flow (seabreeze or inflow)which, when funneled through mountain valleys, is accelerated sometimes producingbrisk winds.The result is much more extreme during cold winter weather when the situation isreversed. If cold (relatively dense) air occupies the interior and warm air remains in thecoastal region the pressure gradient is directed inland perpendicular to the mountainbarrier. The resulting seaward flow of cold air remains close to the land surfacedisplacing the lighter air above as it flows in a well defined layer towards the ocean. Theair movement is restricted by the mountains resulting in low lying flow through valleysand mountain passes. Seeking the most direct route to relieve the pressure, the airdescends the lee slope of mountain valleys, accelerating under the additional influence ofgravity, and enters the coastal region through inlets and fjords that dissect the coast. Thescenario is depicted simply in Figure 1 and is described in more detail by Jackson (1993).1.1.1 Outflow WindsStrong gap winds are encountered in the valleys and inlets of coastal mountainous regionswhere cold weather is prevalent. During the winter months the British Columbia coast isgeographically suited to extreme gap winds. Here such phenomena are referred to asoutflow winds; a term which implies the flow of air from the interior of the province out3Outflow wind is an example of a gap wind phenomena. The term outflow wind best describes the windsystem under study and will therefore be used preferentially throughout this thesis.2towards the coast. These winds occur when an Arctic outbreak forces cold air south intothe interior plateau region of British Columbia (see Figure 2). The cold air, beingrelatively dense, deepens over a period of days becoming ttpooledu between the Coast andRocky mountain ranges. The Coast mountains act as a partial barrier separating cold, dryinterior air from warm air on the coast. The resulting across-barrier pressure gradientoften produces outflow winds in valleys and inlets along the coast.The present study focuses on the outflow winds, or as locally known Squamish winds,that occur in Howe Sound which is a fjord located in the southwest corner of the BritishColumbia mainland (see Figures 2 and 3). This inlet is typical of many along the coast ofBritish Columbia which also experience strong outflow winds during the winter months.The topography of the channel drastically varies over short distances. Rugged mountainsinterspersed along the channel give it a tortuous shape with many abrupt expansions andcontractions. Steep mountain faces rise dramatically from the sea to heights of 1600 m insome parts of the Sound and combine with islands to influence and control the flow ofair.Outflow events in Howe Sound occur during the winter with durations as short as 8 to 10hours but often lasting for 4 to 5 days. Windspeeds commonly reach 20 m/s with gusts to30 or 40 rn/s (1 rn/s = 1.94 knots). The wind layer is generally less than 1000 m deep atall locations along the channel (Jackson, 1993). On average, outflow winds occur on 4 to5 days in each of December and January (Schaeffer, 1975).The cold temperatures that accompany these winds and their unpredictability make thema serious hazard. During outflow events power loss and substantial property damage arecommon. Navigation in the region, whether by land, sea or air, is difficult and can bedangerous. Extreme wind conditions throughout the Sound during events are3detrimental; however, the single most dangerous aspect of the outflow winds may be theirspatial variability. The wind flows in a complicated layer through the channel. In severallocations velocities change abruptly over short distances. This is largely due to hydrauliceffects (discussed below) and flow separation. Localized regions of very intense windwill develop during an outflow event. Problems arise when people expect conditions tobe similar throughout the Sound. Traveling into or building in one of these high windpockets will generally cause unexpected problems.The severity of problems and extent of dangerous conditions associated with the strongwinds can be expected to increase in local areas of maximum windspeed. Theimprovement of predictive capabilities for the above mentioned aspects of the outflowwinds is part of the motivation for this study. The primary goal is to identify the regionsof most intense wind and predict velocities throughout Howe Sound. The analysis isdone for a range of typical conditions found in Howe Sound during an outflow event.The research reported in this thesis is centered around the application of hydraulic theoryto describe the flow during outflow events. There are two parts comprising the work; aone-dimensional (1D) study which combines physical modelling, computer modellingand a field investigation; and a three-dimensional (3D), fully representative, physicalmodel study.The remainder of this chapter includes a description of hydraulic theory, as it is applied tothe wind system under study (section 1.2), and a review of previous research on relatedsubjects (section 1.3). The 1D modelling and the field investigation are decribed inchapter 2 and the 3D modelling is described in chapter 3. Results are discussed andconclusions drawn in chapter 4.41.2. Hydraulic TheorySingle layer hydraulic theory was originally developed for engineering applications inopen channel flow (see Henderson, 1966). For a single-layer flow, the ratio of convectivevelocity, u, to surface wave speed, c = (gh)1”2,is known as the Froude number,F=(g;:)1I2 (1)where h is fluid depth and, g, gravitational acceleration. The flow is termed subcriticalwhen F < 1, critical when F =1 and supercritical when F> 1.In open channels flow is controlled by channel features that determine a depth-dischargerelationship (Henderson, 1966). Such features (local contractions or changes in surfaceelevation) are called hydraulic controls, or simply controls, and the flow changes fromsubcritical to supercritical as it passes through them. At a control the flow is critical.Where a region of subcritical flow exists some distance downstream of a control thesupercritical flow must somehow connect with the subcritical region. For supercriticalflow gravity waves can not propagate upstream transmitting information about thesubcritical region downstream. Therefore the flow undergoes a spontaneous transitionfrom super- to subcritical flow through what is called a hydraulic jump. Enhancedturbulence intensity and energy loss accompany the hydraulic jump as the flow abruptlydecreases in speed and increases in depth.The extension to multiple fluid layers has made the hydraulic theory useful in the study ofgeophysical flows. Outflow wind in Howe Sound is suitable for the application ofhydraulics since it is comprised of a stratified two-layer system with the cold wind layerflowing beneath an essentially infinitely thick warmer layer. The two layers are generally5separated by a distinct interface in the form of an inversion. While there may be regionswhere the interface is relatively thick and fluid is exchanged between layers it isreasonable and quite accurate to idealize the system, for analysis purposes, as two distinctlayers (Jackson, 1993).The hydraulic theory of layered flows makes the following assumptions: the fluids areinviscid, the pressure is hydrostatic, and within each layer the density is constant and thevelocity varies only in the flow direction. For two-layer flows solutions of the hydraulicequations, as described by Armi (1986) and Lawrence (1990), yield characteristicvelocities for both external (free surface) waves and internal (interfacial) waves.Lawrence (1990) investigated the solutions and presented exact expressions for internaland external Froude numbers based on celerities of infinitesimal long waves. Lawrence(1990) shows that, if we assume the relative density difference between the layers issmall (Boussinesq approximation),(P2—P1)/ <<1, (2)then the internal Froude number for a two-layer flow is expressed as,Fu1h2+u3(g’hkh21-F))”2where,(4)6is the stability Froude number, h = h1 + h2 the total depth of fluid, g’ = (p2 —p1 /p2)g thereduced gravity and the subscript 1 refers to the upper layer while the subscript 2 refers tothe lower layer. When F >1 internal phase speeds are imaginary and internal hydraulictheory no longer applies. The internal Froude number,F1, determines the internal>1 supercriticalcriticality of two-layer flow, i.e., when F1 = 1 the flow is internally critical<1 subcriticalIn the context of outflow winds the internal Froude number describes the hydraulicbehaviour of the wind layer. If we assume the upper layer, h1 >> h2 and therefore thath h1 then with u2 >> u1 and F —*0, which is the case during outflow events, equation(3) reduces to,F1(g’Ijj”2(5)which is exactly analogous to the single-layer Froude number (equation (1)) with greplaced by g’. This indicates that the lower layer of the outflow wind system behaveshydraulically like a single layer of fluid reacting under a reduced gravitational force (i.e.g’). When the upper layer is much thicker than the lower layer, the approximation (5) isvalid and the upper layer thickness is unimportant. As described in chapter 2 and in moredetail in chapter 3, this simplification allows us to accurately model the two-layer windsystem using only a single layer of fluid.Following Lawrences (1990) discussion, the external Froude number is,FE(gh)112’(6)7where the flow weighted mean velocity ü = (uhj +u2h)/h. This Froude number, whichis expectedly similar to that of single layer flow, is of little significance in the outflowwind scenario since the upper layer is essentially infinitely thick and FE 0.The criticality and hydraulic features determined, for single-layer flow, by equation (1)are determined in precisely the same way, for the two-layer wind system, by the internalFroude number (5). In the vicinity of controls and hydraulic jumps the wind velocitychanges abruptly over short distances, and with time, making them serious hazards.Supercritical flow that spans the regions between controls and hydraulic jumps ischaracterized by high windspeeds and should also be identified as a hazard. The researchdescribed in chapters 2 and 3 is aimed at determining where these flow features occur,what regions of Howe Sound are occupied by sub- and supercritical flow, and what theresulting velocities are.1.3. Previous WorkOf all the mesoscale wind phenomena discussed in literature, the two most relevent to thestudy of outflow winds are gap winds and downslope winds. These wind phenomena areclosely related and might only be distinguished from each other by their geographicalinfluences. We refer to gap winds as flow through topography (mountain channels) andto downslope winds as flow over topography (mountain ridges). In terms of hydraulics,gap winds are generally controlled by changes in channel width while downslope windsare controlled by changes in elevation. In many cases, effects of both types arecombined. Both gap winds and downslope winds can be generated by similar synopticconditions. Below we discuss separately previous work related to both wind phenomena.As discussed above in section 1.2, some wind systems are well described by hydraulictheory. In the following discussion, where possible, emphasis is given to studies8concerned with the hydraulics of layered flows. Most of the previous hydraulic studieshave dealt with flow over obstacles rather than flow through channels. Since thesestudies relate closely with downslope winds we discuss them in combination withdownslope wind studies.1.3.1 Gap WindsGap winds in the fjords and valleys along the west coast of North America have beenobserved from Alaska (Bond and Mackim, 1993) to as far south as Oregon (Cameron andCarpenter, 1936). Over the last century many occurrences have been documented and allreported to be triggered by similar synoptic conditions; high pressure inland forcing lowlying cold air through mountain barriers towards low pressure regions on the coast.Observational studies have been reported by several researchers (Lackman and Overland,1989; Mass and Aibright, 1985) and wind record data has been analyzed over many yearsby Schaeffer (1975), revealing the statistical properties of outflow events in southwesternBritish Columbia.Some attempts have been made to explain the structure and dynamic behaviour ofspecific events. Overland and Walter (1981) described two distinct gap wind cases in theStrait of Juan de Fuca (see Figure 2) in February 1980. They identified the synopticpressure gradients responsible for driving the flows and, through research aircraft and adense network of surface stations, revealed the structure of the wind layer. Majorcharacteristics of the wind field were accounted for by the combined effect of thesynoptic pressure gradients and local topography. Notable features of both cases were aninversion layer which capped the flows and an abrupt transition resembling a hydraulicjump.9An example of a gap wind case from another part of the world is the well known“Mistral” which flows through the Rhône Valley in France. Pettre (1982) conducted amonth long observational study of this violent wind with high spatial resolution and finetemporal scale. The results emphasized the prominent role played by an inversion layerin the air flow dynamics. Pettre adopted a two-layer model of the system and comparedobservations with a hydraulic computer simulation. The simulated transition tosupercritical flow and subsequent hydraulic jump coincided with observed conditions inthe field. In particular, the existence of an observed hydraulic jump was welldocumented.Some theoretical studies such as that by Mackim et a!. (1990) have had success indescribing the causes and dynamics of gap winds. No physical model studies specificallypertaining to gap winds, prior to the present study, have been found. Numerical modelstudies are also rare. Recently Jackson and Steyn (1 994a) reported observations of amoderate outflow event in Howe Sound and compared these with output from a three-dimensional mesoscale numerical model. Although their results agreed in general, modelflows underestimated actual windspeeds in the channel and small scale flow features werenot captured. Jackson and Steyn suggested that the flow is strongly influenced by localtopography and a hydraulic analysis of their model output supported this. In a subsequentpaper Jackson and Steyn (1994b) described a simple 1-dimensional hydraulic computermodel which was more successful at predicting observations. Here they extended theclassical hydraulic theory by adding the influence of synoptic pressure gradient in theform of a slope. This model, called Hydmod, is used in the present study to generateoutput for comparison with field observations and physical model results. It will bediscussed further in chapter 2.10An in depth review of the phenomenological studies on gap winds and related mesoscalewinds, reported before 1992, was done by Jackson and Steyn (1993, 1994a) and will notbe repeated here. It is useful, however, to summarize some of the basic characteristics ofoutflow winds on the west coast of North America. In general, the wind layer is between50 and 1500 m thick, it is capped by an inversion layer which varies in thickness andstability depending on windspeed and the difference between the lower and upper layertemperatures, average wind speeds of 20 m/s with gusts of up to 50 mIs are notuncommon.1.3.2 Downslope Winds and the Hydraulics of Layered FlowsDownslope winds have received much attention and are the subject of numerousexperimental and theoretical studies. Although fundamentally different in nature fromoutflow winds, downslope winds possess some related characteristics and can beinformative. The utility of the hydraulic theory has long been recognized in thedescription of the general nature of geophysical flows encountering topography. Despiteits relative simplicity, this theory is of great value since it retains the essential nonlinearity of the flow. The one-dimensional hydraulic formulation has allowed thedevelopment of relatively simple theoretical and experimental models which have shownsuccess in describing otherwise very complex flows.The original work on downslope winds was by Long (1953) who performed laboratoryexperiments simulating the “Bishop Wave” phenomenon, which is thought to resemble anatmospheric hydraulic jump. The flows were produced by towing an obstacle through arectangular channel filled with three layers of stationary immiscible fluid. Each interfacebetween layers represented an atmospheric temperature inversion. Long (1954)11performed similar, but more refined experiments and reported the upstream motions thatare generated over the obstacle.Many experimental efforts have since been made to explain the flow of stratified fluidsover topography. These are reviewed by Baines and Davies (1980) who discuss in detailsingle-layer, two-layer and continuously stratified flows. In every case the flows areproduced in the same manner as by Long (1953); by towing two-dimensional idealizedrepresentations of mountain ridges along channels filled with fluids at rest. More recentlyBaines (1984) elaborated on the experimental base by performing more towing-tankexperiments over a wide range of parameters. By varying the obstacle height and speed,and the relative layer depths, Baines investigated the factors governing the nature andmagnitude of upstream disturbances (e.g. turbulent bores and rarefactions) in the generalflow of stratified fluid over topography. Although the unsteady upstream effects alwayspresent in towing-tank experiments may be important in certain atmospheric flows overmountain ridges, they are not often observed and do not play an important role in thebehaviour of outflow winds.Lawrence (1993) reported results of a theoretical and experimental study of steady two-layer flow over a fixed two-dimensional obstacle. His approach avoided the problem ofupstream effects inherent to towing tank experiments. The hydraulic theory was used todevelop a classification scheme, which differed from that based on the previous towingtank experiments, to predict the flow regime for various experimental parameters. Thefixed obstacle experiemnts enabled Lawrence to study approach-controlled flows in detailand thereby show that non-hydrostatic forces, rather than a hydraulic drop (Baines, 1984),are important in their understanding.12In the above studies, the flow behaviour over the obstacle (mountain ridge) could beanalogous to that within the realm of outflow winds when an isolated ridge or island isencountered.Downslope windstorms are relatively common and have been studied extensively forover 30 years. However, their dynamics are still not well understood. Three differenttheoretical mechanisms have been proposed to explain strong downslope winds. The firstis based on linear theory of internal gravity waves in a continuously stratified, semi-infinite fluid. The second is based on numerical integrations of the governing equations.Some numerical results suggest that as wave amplitudes aloft are increased and breakingoccurs, lee slope flow plunges beneath the mixed region (Smith, 1985, Rottman andSmith, 1989). The third mechanism is based on the hydraulic theory (Long, 1954;Houghton and Kasahara, 1968). A transition to supercritical flow over the mountainridge produces strong supercritical flow down the lee slope and a subsequent hydraulicjump. This approach has been quite successful in explaining observed downslopewindstorms. The disadvantage of hydraulic theory is that it requires flows to bestructured in discrete layers. This only allows one internal wave mode (per layer)whereas continuously statified flows support many.In a paper by Durran (1986) the role played by hydraulics and vertically propagatinginternal waves on the development of large-amplitude waves was investigated.Numerical simulations were conducted to investigate the various amplificationmechanisms responsible for the waves. When the static stability has a two-layerstructure, with linear stratification within each layer, the lower layer behaves analogouslyto that of a single layer of fluid. A direct comparison of hydraulically interpretednumerical results with observations from the Boulder 1972 windstorm (Bower and13Durran, 1986) reveal that an inversion plays a key role in the development of asupercritical region and following hydraulic jump.When flow over three dimensional topography is considered the analyses becomesubstantially more complex. Experimental studies are often used to determine somecriteria for flow behaviour for certain conditions. Hunt and Snyder (1980) describe theflow over a bell-shaped hill which was placed first in a large towing tank containingstratified saline solutions with uniform stable density gradients and second in anunstratified wind tunnel. Flow visualization techniques were used to obtain mostlyqualitative information about the flows. Snyder et al. (1985) elaborated on this byintroducing a dividing streamline concept and performing experiments which could becompared with field observations. Through an energy argument the dividing streamlinewas defined as that which separates streamlines which pass over the hill from those whichgo around. The concept was applied to a variety of shapes and orientations of hills withdifferent upwind density and velocity profiles.In a paper describing shallow water flow over isolated topography, Schär and Smith(1993) used the fundamentally one dimensional hydraulic theory to characterize differentflow regimes. For subcritical upstream flow encountering a three dimensional hill, thefollowing three regimes occur: (1) fore-aft symmetry, essentially inviscid dynamics, andentirely subcritical conditions; (2) transition to supercritical flow and the occurrence of ahydraulic jump over the lee slope; and (3) the inability of the flow to climb the mountaintop resulting in flow separation. Numerical simulations were performed and thecontrolling parameters determined. This paper has particular relevance to the study ofoutflow winds where an essentially shallow fluid encounters semi-isolated mountains andislands. Schär and Smith borrow from the field of gas dynamics and draw an analogy14with shallow water flow. Shear discontinuities and oblique shocks are important featuresin the flows described and may play a role in the spatial variation of outflow winds.15Chapter 2 - One Dimensional Modelling and Field InvestigationIn this chapter results from a 1D physical model study of extreme outflow winds in HoweSound are presented (also found in Finnigan et. al., 1994). The results are compared withobservations from a field study and with output from the hydraulic computer model(Hydmod) of Jackson and Steyn (1994b). The field data acquired are from a severeoutflow event in Howe Sound which commenced on 27 December 1992 and persistedthroughout the following four days while an Arctic airmass and anticyclone resided in theinterior of British Columbia. Channel hydraulics, predicted by the physical model study,provided guidance in establishing the field research program.Hydraulic theory, as described in chapter 1, is used throughout this chapter to interpretthe flows. The physical model and Hydmod are referred to as one-dimensional because,for both of these, the main channel of Howe Sound is idealized as rectangular in cross-section, with the channel width, flow depth, flow velocity and Froude number varyingonly in the along channel, or x, direction.We are able to show, by comparing field study results with model predictions, thatdistinct hydraulic profiles persist in Howe Sound for long periods of time during anoutflow event. The term hydraulic profile refers to the variation in depth and densimetricFroude number in the along-channel direction. The identification of these hydraulicprofiles allows the specification of which flow regime (sub- or supercritical) occupiesspecific sections of Howe Sound, thereby indicating the areas of most intense wind.162.1. Physical Model StudyThis study was designed specifically to investigate the hydraulics of an extreme outflowwind in Howe Sound. The following section describes the experimental arrangement andthe results are discussed in section 2.1.2. The hydraulics of the wind layer, as predictedby the model, are presented for two flow rates.2.1.1 Experimental MethodsIn order to determine the underlying dynamics, some simplifying assumptions were madein the development of the model study program. Although some of these assumptionslead to characteristics of the model being quite different from those of the prototype(Howe Sound), the topographical aspects of the prototype that most influence thehydraulics of the flow were retained.The laboratory model system consists of a Plexiglas channel, a six inch wide flume and avideo camera with which to document the flow (see Figure 4). As shown in section 1.2,the equations for a single inviscid incompressible homogeneous layer of fluid flowingbeneath another homogeneous fluid, which is effectively infinitely deep, are identical tothose for a single fluid alone if g’is replaced by g. It is readily shown that this analogyholds independently of any mean horizontal motion in the deep upper layer, and hence awide range of two-layer flows may be modelled with a single layer (Benton, 1954,Baines, 1980). Lackman and Overland (1989) suggest that gap wind is primarily aboundary layer phenomenon with little influence from opposing winds above. Thesearguments allowed a one-layer model to be used in the present study with waterrepresenting the outfiowing wind layer. Effects due to the upper atmospheric layer andmixing and friction between the layers were neglected.17Although the complicated topography of the actual channel is likely to produce anequally complicated flow, we are only interested here in the layer averaged behaviour thatis governed by the basic hydraulics of the flow. This idealization permits the design of amodel with a straight central axis in the flow direction across which there is symmetry(Figure 4). A further simplification was made by assuming that the slope of the channelwalls does not greatly influence the hydraulics. This assumption allowed the model tohave vertical side walls. For a channel with vertical walls and flat bottom the flow iscontrolled by changes in width. The depth of the wind layer during an extreme event wasexpected to be approximately 1000 m (Jackson, 1993) so the width variation along HoweSound was taken to be the width at an elevation of 500 m.To accommodate the large passage between Anvil Island and the west coast of the Sound(123°17’W, 49°35’N - Figure 3) the model was simply widened out to the walls of theflume. Smaller passages between the three main islands were assumed to be insignificantrelative to the main channel and were incorporated into the model in the form ofwidening.The prototype to model horizontal length ratio was 68000 and the vertical length ratiowas 16600. Froude number equivalence between model and prototype was used to matchthe flows and to scale model results to prototype dimensions.The model was placed in the flume with the camera’s viewing axis positionedperpendicular to the flow direction as shown in Figure 4. While being videotaped forlater analysis, water was allowed to flow through the model continuously. The recordedvideo images were digitally processed to extract depth measurements so as to compilesurface profiles of the flow. The mean flow velocity upstream of the model was18measured using a propeller type flow meter. This information was used to calculate theFroude number throughout the channel, determining the locations of controls andhydraulic jumps and defining the regions of sub- and supercritical flow. Further detailsof the experimental procedure may be found in Vine (1992).Uncertainty in model results can be attributed to various sources. Hydraulic theoryassumes the flow velocity is parallel to the channel axis and constant over each cross-section. This assumption neglects boundary layers and secondary flows. The modelresults aie obtained from measurements along the channel axis which are then assumed tobe constant across the channel width. In some parts of the channel, depth varied slightlyacross the channel width, indicating velocities not parallel with the channel axis. As well,the Reynolds number of the prototype flow is generally several orders of magnitudelarger than that of the model flows, which does not affect the results as far as hydraulicproperties are concerned, but may produce different velocity distributions.2.1.2 ResultsModel runs were performed for several flow rates. The lowest flow rates did not forceany channel features to act as hydraulic controls, leaving the flow subcritical throughoutthe channel. As flow rates were increased, certain features of the channel began tocontrol the flow. The hydraulic profile changed when critical flow was achieved at aparticular location in the channel (i.e. u =A curvi-linear channel axis through Howe Sound is shown along with its straightenedmodel counterpart in Figure 5. In each of the figures (6 and 7) which present the spatialvariation of quantities along Howe Sound, the length scale represents the distance alongthe channel axis in the direction of flow. Results from the physical modelling, field19experiment and Hydmod output appear together in Figure 6 and Figure 7 in order tofacilitate direct comparison. Each set of results is introduced separately before beingcompared in section .2a Results for flow rate AFor a model flow rate of 0.032 m3/s (hereafter referred to as flow rate A) the predictedwind layer elevation (or depth) is shown in Figure 6(a). The horizontal model lengthscale has been converted to that of the prototype to allow for direct comparison with fieldmeasurements (Period 1, described below). Flow is from left to right with the 0 kmlocation being the upstream end of the channel and the 60 km location being downstreamof the channel terminus. Wind speed variations along the channel are shown in Figure6(b) where high wind speeds coincide with regions of supercritical flow. Figure 6(c)shows the Froude number as it varies along the model channel for flow rate A.Upon entering the channel, flow is accelerated by the contracting walls and reaches thecritical point (F = 1) at about km 17. It appears that supercritical flow exists for a shortdistance beyond the control section before a sudden expansion (km 25) in the channelinduces a hydraulic jump (km 20) transforming the flow from supercritical to subcritical.The flow again becomes supercritical near km 35 following the contraction imposed byAnvil and Gambier Islands. This controlling feature is much stronger than the first as isevident in the high values of F. Another expansion beyond Gambier Island (km 40)forces the occurrence of a hydraulic jump at about km 48. The narrow passage betweenBowen Island (km 50) and the east side of the channel forces a transition to supercriticalflow which extends beyond the channel terminus where a hydraulic jump reconnects theflow with subcritical conditions in the Strait of Georgia.202.1 .2b Results for flow rate BResults for a higher model flow rate of 0.043 m3/s (hereafter referred to as flow rate B)appear in Figure 7. An increase in flow rate from A to B produced similar results to thoseexplained above but with some notable differences. The same features act to control theflow but the hydraulic profile is expectedly characteristic of a stronger flow.Supercritical flow is first reached further upstream (km 14) and extends for severalkilometers before the expansion near km 25 induces a hydraulic jump. The position ofthe jump at km 22 is further downstream than that for flow rate A. The higher flow ratehas extended the supercritical flow region here by moving the critical point upstream andthe hydraulic jump downstream.The flow rate increase from A to B does not seem to enlarge the supercritical regionbetween km 35 and km 48. It is likely that the positions of the control and subsequenthydraulic jump that encompass this region are fixed by the channel topography (for flowrates A and B) and essentially confine the supercritical region. The flow exits the channelin much the same way as for flow rate A.2.2. Field Program2.2.1 Synoptic Weather Conditions for the December, 1992 Event in Howe SoundThe evolution of synoptic scale weather patterns creates the atmospheric boundaryconditions within which gap winds occur. The synoptic conditions in the December,1992 case were typical of other gap winds (Jackson, 1993). An upper level ridge, lyingnorth-south across the Aleutian Islands (Figure 2), increased in amplitude during 26 - 27December 1992. Meanwhile, an upper level cold low and an associated 998 mb sea levellow developed in a trough to the east and moved southward down the British Columbia21coast to a quasi-stationary position 900 km southwest of Vancouver Island by 0400 LST27 December. This pattern resulted in east to northeasterly flow aloft over the coastalzone. Linked with the upper level ridge, a 1060 mb surface high pressure zone,associated with very cold Arctic air, formed over Alaska and moved to a quasi-stationaryposition over central Yukon Territory by 0400 LST 27 December. Associated with thesedevelopments, an Arctic front moved southwards across Howe Sound during the day on28 December. Behind the Arctic front, a zone of very large horizontal sea-level pressuregradient, oriented perpendicular to the coast, resulted in strong low-level gap windsthrough the valleys and fjords dissecting the coast range. Sometime during the night of28 December a large emergency ferry wharf located near Porteau Cove (Figure 3) wasdamaged by the storm resulting in approximately $250 000 damage. The strong pressuregradient and resulting winds began to weaken after 29 December when the upper levelridge-trough pattern decreased in amplitude; the Yukon high moved southeastwards inBritish Columbia, but weakened, and the Arctic front moved further offshore.2.2.2 Field ExperimentTo further document the existence of hydraulic controls in Howe Sound and attempt toidentify their locations, a field investigation was undertaken. The field research programwas initiated at the beginning of the 1992/93 winter season and the extreme outflow eventdescribed above occurred in December, 1992. Measured pressure variations betweenselected sea-level stations along the Sound during the event show distinct along channelhydraulic profiles. The interpretation of the pressure data allows determination ofcontrols in the channel.Surface pressures during the strong outflow event that commenced on 27 December1992, were recorded by microbarographs placed at five stations along Howe Sound. The22pressure variation with time, recorded at each location, indicates the relative thickness ofthe outfiowing layer at each station. Pressure differences between stations indicate achange in depth of the outfiowing layer. The mean pressure due to the entire atmosphereis assumed to be approximately equal at all stations (which lie within a 50 km range)before the onset of outflow. When an outflow event occurs, the added pressure, due todenser air in the outfiowing layer, varies between stations indicating changes in layerdepth along the channel. Since the pressure measurements are static, as opposed todynamic, and were recorded from within enclosed shelters, the wind velocity is notthought to affect them.Jackson (1993) shows that the flow is confined, to some degree, to the main easternchannel of Howe Sound, with Bowen Island, Gambier Island and Anvil Island forming apartial barrier to the flow (see Figure 3). For this reason instruments were placed alongthe eastern shore of the main channel. An effort was made to place the instruments atlocations on the shore as close as possible to the central axis of the channel. Since themodel (and hydraulics in general) produces cross-sectionally averaged quantities, thefield results are assumed to be representative of the cross-sectional average.The instrument locations relative to the model are indicated in Figure 5(a) as pointsnumbered 1 through 5. These locations are situated between predicted control sectionsand correspond to actual locations in Howe Sound where the instruments were placed(shown in Figure 5(b) and Figure 3). The physical model results were used to predict thepoints of hydraulic control and indicate roughly where to position the instruments. Adifference in recorded pressure across a control section during an outflow event indicatesa change in depth (between those stations) and a possible transition between flowregimes. The transition may occur either smoothly from sub- to supercritical flow orrapidly as a hydraulic jump from super- to subcritical. A decrease in pressure in the23direction of flow would indicate the former while an increase would indicate the latter.This information leads to the determination of which flow regime occurs at each of thefive field stations.2.2.3 Field Data InterpretationFigure 8 is a composite of the pressure recordings of all five stations over a period of nineand a half days where hour 0 coincides with 0000 LST 25 December 1992 (raw data maybe found in Finnigan, 1993). Each pressure trace corresponds to one of the stationsshown in Figure 8. At each station the pressure initially varies only with the large scalesynoptic field. This variation is seen in Figure 8 up until about hour 52. On 27December at about hour 60, winds, and relative pressure deviation among stations,increased in the channel. These pressure differences represent depth changes in the windthat develop as the flow accelerates and decelerates through the channel topography. Theflow is unsteady with the pressure differences (depth differences) increasing during theonset and varying through the duration of the outflow event. Finally as the wind subsides(hour 180), the pressure differences among stations decrease and pressure coincides withthe mean regional pressure.Data acquired from an automatic weather station, located at Pam Rocks (see Figure 3) inthe middle of the channel near station 4, were used to confirm the pressures recorded atstation 4. As well as pressure, the Pam Rocks station recorded wind velocity andtemperature. From the velocity, temperature in the wind layer, temperature in theatmosphere above the wind layer (estimated from recorded temperatures just before onsetof outflow) and relative pressure information, it is possible to estimate the absolute depthof the wind layer at station 4. The calculations involved in this estimate are outlined inAppendix A. Converting the relative pressure at each station to relative depth (assuming24hydrostatic pressure variation), and using the known depth at station 4, the depths at allstations can be determined at any time. From the information at station 4, the volumetricflow rate in the wind layer can be calculated. By estimating the average width of thechannel at each station from topographic maps (width at half depth), and assuming thevolumetric flow rate to be constant throughout the channel, the Froude number, F, canbe determined at each station at any particular time during the outflow event (seeAppendix A for details on the calculation). If a change in depth between stations isaccompanied by a change in flow state (indicated by a change in F from >1 to <1 or viceversa), then it is assumed that a control or hydraulic jump exists between the stations.Through the course of the four day outflow, two distinct along channel hydraulic profilesare evident. The first lasts from the onset of the outflow until the flow is well established.The second, being forced by a higher horizontal pressure gradient and characterized by anincreased flow rate, persists for approximately 12 hours before the wind begins tosubside. The period of time occupied by each is indicated on Figure 8 as Period] andPeriod 2, respectively. Both hydraulic profiles are described below.The acquisition of the field data and the process by which the acquired data weretransformed into the final results introduce some uncertainty. The instruments contributesome error to the raw data (± 0.25 hrs, ± 0.2 mb) but the main sources of overall error aredue to the process of approximating channel dimensions and averaging the results overtime.2.2.3a Results for Period]Following the initial increase, the wind layer develops a steady hydraulic profile whichpersists for 12 hours: from hour 60 to hour 72 during the day of 27 December. This time25frame is indicated in Figure 8 as Period 1. In order to more clearly see the changesbetween stations, the field results are shown again in Figure 9 where the difference inpressure from station 1 (P1) is plotted for each station. For station 1 the difference is ofcourse zero resulting in a straight line. During Period 1 (Figure 9(a)) the pressure andhence depth decreases between stations 1 and 2 and is only slightly higher at station 2than at station 3. Beyond station 3 the pressure drops substantially at station 4 beforeincreasing again at station 5.The winds during Period 1 are thought to be associated with a transient stage in theoutflow event. This stage represents the onset of the flow and is characterized by lighterwinds with stronger winds occurring once the flow is fully established. This low flowrate stage of the outflow approximately corresponds to the low flow rate run (A) of themodel results. The average depth, wind speed and Froude number calculated for thisstage of the flow are plotted (as solid square points at each of the five stations) along withthe results for the physical model flow rate A in Figure 6.Between hour 72 and hour 88 data at stations 3 and 4 were lost due to instrument failures.2.2.3b Results for Period 2As the winds increased during the evening of 28 December, the along channel hydraulicprofile changed to a new state. This is indicated as Period 2 in Figure 8 and Figure 9(b).Referring to Figure 9(b) the pressure now drops substantially between stations 1 and 2before increasing again at station 3. Following station 3 the pressure drops again betweenstations 3 and 4 and now remains low at station 5.26This period of the event is characterized by higher winds and more closely resembles thephysical model results for the higher flow rate (B). The average depth, wind speed andFroude numbers for this period are plotted (as solid square points at each of the fivestations) on Figure 7 along with the model results for flow rate B.2.3. Comparison of Physical Model, Hydmod and Field ResultsSince the field results only indicate the conditions at five points along the channel it ispossible that some aspects of the hydraulics are not revealed by them. However, bycomparing the field results directly with hydraulically similar model results (i.e.approximately equivalent Froude numbers) the conditions throughout the channel can beinferred.2.3.1 Period 1 (flow rate A)During the onset of an extreme gap wind event, before the winds have reached fullstrength, the hydraulics of the wind in the main channel of Howe Sound are expected toresemble what is shown in Figure 6. The field results confirm model predictions ofsubcritical flow at the channel entrance (station 1). The flow accelerates as it progressesdownstream toward station 2, as indicated by increasing Froude number and decreasingdepth. Field results indicate that the flow is subcritical at stations 2 and 3, as do physicalmodel results. However, the numerical model indicates that a control and subsequenthydraulic jump can develop between stations 2 and 3 if the flow rate is high enough. Theresulting region of supercritical flow between stations 2 and 3 will expand upstream withincreasing flow rate (as will be discussed below) and eventually encompass station 2.The combined effect of the expansion in the channel near km 25 (just upstream of Anvil27Island) and flow blocking due to Anvil Island results in subcritical flow limiting theextent of the supercritical region upstream.Beyond station 3 the flow is accelerated through the contraction imposed by Anvil Islandand passes through a control point near km 35, before reverting to subcritical flow in ahydraulic jump near km 48. The physical model and field results agree in this region,although the Froude number at station 4 is less than that predicted by the model.Substantial error associated with the estimation of Froude numbers from field results(estimation of average depth, width and velocity) and modelling inadequacies canaccount for this discrepancy. The lower Froude number reported from the field resultsmay be due to the existence of the side channels between the islands which were ignoredin the model. Despite minor discrepancies, the model and field results confirm thegeneral hydraulic behaviour in this region. The supercritical region which reaches itsmaximum expanse (at low flow rates) between km 35 and km 48 is confined on both endsby regions of subcritical flow.Beyond station 5 no field results are available. The model predicts that, downstream ofstation 5, the flow is controlled again as it passes through the contraction between BowenIsland and the protrusion on the east side of the channel (Figure 3). From field results, asimple calculation shows that the width reduction between station 5 and this point mayforce transition (see Appendix B for the calculation). The flow exits the channelsupercritically and must then reconnect to subcritical conditions in the Strait of Georgiathrough a hydraulic jump downstream. The hydraulic jump was observed in the model,downstream of the channel terminus, but was not documented.282.3.2 Period 2 (flow rate B)For the higher flow rate some of the hydraulic characteristics of the model flow arereadily confirmed by the field results, while others require some interpretation.Throughout most of the channel the situation is much the same as described above. Flowenters the channel subcritically and is accelerated (Figure 7). However, with increasedflow rate, the control that was between stations 2 and 3 in the above discussion hasadvanced upstream beyond station 2. The model now indicates supercritical flow atstation 2 and the field results confirm this. The flow returns to subcritical before station 3as the expansion (km 25) forces transition through a hydraulic jump.As is the case for the lower flow rate, the flow is controlled near Anvil Island (km 35)before reaching station 4. Through the region spanned by stations 4 and 5, the model andfield results differ in some respects. The field results indicate supercritical flow at station5, whereas the model results indicate subcritical flow (although near critical) there. Sinceboth model flows produce subcritical conditions at station 5, it is possible that the modelstrongly confines the region of supercritical flow upstream of station 5, while in realitythe hydraulic jump (Figure 7, km 47) may be washed downstream and possibly out of thechannel. The extension downstream of this supercritical region would explain thefindings at station Further Comparison with Hydmod OutputFor further comparison, the hydraulic computer model, Hydmod, was run for theconditions in Howe Sound during Period 1 and Period 2. Input parameters werecalculated from measurements obtained during the December 1992 event. The averagealong channel synoptic pressure gradient, dP / dx, for each period was calculated from29direct observations at two government stations (Pemberton, 67 km upstream fromSquamish and Pam Rocks). Table 1 lists the values of each input parameter for bothperiods. With these input data, Hydmod ‘steps’ along the channel determining points ofpossible control. The energy equation is solved over finite steps, in an upstream directionfor subcritical flow, and in a downstream direction for supercritical flow. The sectionsbetween control points are added together to form a complete solution over the length ofthe channel. The hydraulic jump equation (momentum) is used to determine theconditions at a hydraulic jump in reaches where there is supercritical flow from anupstream control, and subcritical flow from a downstream control. The reader is referredto Jackson (1993) and Jackson and Steyn (1994b), who created the model, formathematical details.Hydmod results appear as a thin line, along with the physical model and field results, inFigure 6 and Figure 7. Near the channel entrance, the supercritical flow is predicted tojump to subcritical. Although not within the range of the physical model or field results,this jump may actually occur with the wind descending the mountain slope upstream ofSquamish in the supercritical regime before entering a flat expansion which could inducea hydraulic jump. Referring to Figure 6 and Figure 7 Hydmod predicts that the channelhydraulics are governed by the same controls identified by the physical modelling andfield observations. The two models show slight differences in the exact location of thesecontrols and the ensuing hydraulic jumps. This is due to the vastly different nature of thetwo models and the different representations of channel topography and frictioncoefficients (among other things) that each relies on. One notable difference is the largesupercritical region predicted by Hydmod between km 12 and km 25 in Figure 6 whichdoes not appear in the physical model results for flow rate A. In Figure 7 Hydmodindicates the flow is controlled near km 12 but passes through a hydraulic jump andsubsequent control before reverting to subcritical flow near km 24. This additional30control and jump is not predicted by the physical model and can not be detected by thefield measurements. Upstream depths differ substantially between the two models whichis likely due to each models deficiency in simulating the upstream boundary conditions.The physical model appears to overestimate the upstream depth for both flows (Figure 6and Figure 7). This may be because the fluid enters the model from a narrow flumerather than entering from an essentially infinite reservoir. Despite the differences, theHydmod results serve to confirm the existence of the hydraulic profiles as predicted bythe physical model and as suggested by field observations.2.4. DiscussionPhysical modelling of gap winds in Howe Sound, followed by field measurementsrecorded during an actual outflow event, led to an understanding of the hydraulicbehaviour of the wind layer for two distinct flow rates: one representing lighter windstypical of the onset period of an outflow event, the other representing the fully establishedflow. Comparison of the physical model and field results confirmed the model findingsat specific points and thereby allowed the inference of prototype behaviour from modelpredictions at other locations in the channel. For the lower flow rate (Period 1, flow rateA) short regions of supercritical flow were observed. With an increased flow rate (Period2, flow rate B) these regions were observed to expand and occupy more of the channel.In some cases, fixed control points limited the expansion of the supercritical regions,effectively confining them between regions of subcritical flow.The two modelling exercises serve to reinforce the findings of the observational programand allow the specification of which hydraulic regime is prevalent at locations alongHowe Sound during an outflow wind event. Supercritical flow and correspondingextreme wind conditions are defined in Figure 6 and Figure 7. Model results show some31deviation from field results for fully established flow. Insufficient similarity between thephysical model and the prototype near the channel terminus and beyond may explain thefixed control that exists in the model, but is not observed in the field. In chapter 3 wedescribe another physical model study that improves on that described above byincorporating geometric and kinematic similarity and proper simulation of the boundaryconditions.32Chapter 3 - Three Dimensional Modeffing3.1. DescriptionThe 1D study described in chapter 2 considered flow through topographically simplifiedrepresentations of Howe Sound and was intended to provide one dimensional, crosssectionally averaged results along the main channel. Predicted hydraulic profilesindicated approximately where extreme conditions occur in the Sound and wherehydraulic jumps are expected to form. The relatively simple study, involving manyassumptions, can be considered to only approximate actual conditions.We now wish to address many of the questions left unanswered by the 1D study. To gaina more realistic understanding of the outflow winds in Howe Sound, and extend theknowledge gained by the 1D study, we developed a more elaborate physical model studywith fewer simplifying assumptions. In particular, the three-dimensional (3D) physicalmodel described in this chapter includes the following which were not considered in the1D study:• proper simulation of boundary conditions• effects due to channel sinuosity and elevation changes• flow over and around, and effects due to, islands in the channel• variation in wind across, as well as along, the channel• energy losses due to form drag and skin friction drag• geometric and kinematic similarity• realistic reproduction of Howe Sound topography• simulated pressure gradients33A single layer of water was again used to simulate the outfiowing wind layer and mixingand friction between the layers were ignored. To document the flows, a unique methodof data collection, using video/image analysis, was developed. This method provides acomprehensive and realistic set of predictive results. The complicated hydrauliccharacteristics of the outflow wind system were accurately reproduced, and conditionswere predicted in detail throughout the Sound, for several different synoptic cases.3.1.1 Design Considerationsa. SimilarityObtaining useful results from hydraulic physical models requires careful planning in thedesign stage. If a model is to be similar to the large scale original, also called theprototype, then it is not enough that the solid boundaries be geometrically similar in thetwo systems; it is also necessary that the two flow patterns be similar. If this is true thenit is said that kinematic similarity holds between the two systems. Without going intodetail on the laws of similitude we simply state that if viscosity, surface tension andcompressibility effects are negligible then only Froude number,F, is important.However, to ensure the absence of viscous effects in the model special attention must bepaid to the Reynolds number. Therefore, we invoke Froude number similarity betweenmodel and prototype and use the Reynolds number for guidance in designing a physicalmodel with the same flow conditions as found in the field.b. Scale RatiosRepresentative model flows are based on the constancy of F between model andprototype. The detailed interpretation of model measurements then requires that scale34numbers be available for translating model values of various quantities intocorresponding prototype values. With F defined as in (1) we require,F1=F, (7)where the subscripts m and p refer to model and prototype respectively. Since thesingle layered model flows are influenced by gravity, g, and the two-layered prototypeflows are influenced by reduced gravity, g’, substitution from (1) and (5) into (7) leadsto,u It/h(8)Urn gh11or, by indicating the ratio of prototype:model quantities with subscript r,/ , \1/2Ur=:[hr1 (9)‘\g )where g’ must be estimated or known from field observations.A list of relevant scale numbers, based on Froude number similarity and the relation (9),is given in Table 2, where the vertical and horizontal scales (hr and Lr respectively) havebeen defined separately to accommodate depth exaggeration (discussed below). In thecase of a geometrically similar model hr = Lr With the length scale numbers known, theremaining scale numbers allow model measurements to be translated into prototypevalues.35c. Reynolds Number andModel DistortionHowe Sound prototype flows, like many geophysical flows, have a high ReynoldsNumber and are not influenced by viscous effects. Here we define Reynolds Numberbased on fluid depth, i.e.(10)where a represents fluid speed, h, fluid depth and v, dynamic viscosity. With thisdefinition, and considering the results of chapter 2, Re is on the order of 106 for allprototype flows. It is impossible to produce this magnitude of Re in laboratory flows.Low Reynolds numbers are not a concern as long as the model operates in the fully roughturbulent region at all important locations, which depends on both Re and the modelboundary roughness. For typical roughnesses, the flow will generally be fully rough forRe>1500 (Gibson 1934, Yalin 1989). If this requirement is satisfied then the effects ofviscosity will be negligible and model flows can be assumed to represent prototype flows.Although turbulence scales will differ between model and prototype, they are notimportant as we are studying flow features much larger than turbulent structure and arenot concerned with diffusion or mixing.Reynolds number dictates to some extent the minimum size of an acceptable model. It isthe depth of flow that is the limiting factor. As a general rule in channel flow modellingthe flow at all locations should be at least 2 cm deep and fully turbulent (Yalin, 1989).Considering typical depths of prototype flows this translates into a scale model with verylarge horizontal extent. However, it is common practice in river flow modelling tovertically exaggerate, or distort, model dimensions to obtain sufficient flow depth and36ensure high enough Reynolds number, while maintaining horizontal scales which arereasonably easy to work with.A distortion factor may be defined by,e=--, (11)which is equal to the scale of slopes, Sr and is always 1. The model described here hasa distortion factor of e = 0.57 which is well above the acceptable lower limit of 0.25, assuggested by Nicollet (1989). The reasons for choosing this particular value stem frombuilding supplies and construction limitations which are discussed below. Distortion willcause secondary flows, velocity distributions and mixing to differ between model andprototype. This is not a concern as we are interested only in mean velocities andhydraulic behaviour which are not affected.d. Boundaiy Conditions andModel SizeAlthough the results of chapter 2 indicated subcritical flow at the upstream end of thechannel near Squamish, we have no way of prescribing or ensuring this. To properlysimulate the conditions at this location the model was extended up through theCheakamus Valley to the Pemberton Valley which acts as a reservoir for the cold air.This guarantees that the boundary conditions near Squamish are simulated correctly. Theentire model topography is pictured in Figure 10.Upon steady state, the flow some distance downstream of the channel terminus, in theStrait of Georgia, is subcritical as it must connect with the mass of cold air built up there.37The subcritical downstream boundary condition is set by a weir, at a model locationcorresponding to approximately 20 km beyond the actual mouth of the channel.The entire model covers a region that is actually 128 km long and 40 km wide. Lab spacelimitations and restrictions due to building materials led to model dimensions of 270 cmlong and 84 cm wide which translate into a horizontal length scale number ofLr = 48000. The process of forming the topography, which is described in more detailbelow, limited the choice of vertical scale factors which would produce deep enoughflows. A layering method was used to reproduce the contour intervals from topographicmaps. The maps used had 500 ft intervals and the material used to represent each intervalin the model had a thickness of 5.5 mm. This led to a vertical scale number ofhr = 500fl/5.5mm =27548. These values together give the distortion factor,e = hr /Lr = 0.57, as mentioned above.e. Frictional EffectsEnergy losses in the flow, resulting from both form drag and skin friction drag, caninfluence the flow and affect the location of hydraulic jumps. Form drag, induced bycomplicated channel boundaries, is simulated in the model by replicating the channelfeatures present in the prototype. To properly simulate skin friction, or surface drag, thethe surface roughnesses of the prototype and model channels must be considered. It iscommon to use the Manning-Strickler resistance formula (Henderson, 1966),(12)where R is the hydraulic radius (cross sectional area/wetted perimeter) and K obeys38the following empirical relationship,K=26/d”6, (13)with d representing the size of bed roughness elements.For wide channels (12) becomes,__h2,/3c12 l4U 1/6 ‘with h representing the mean fluid depth. This simplification is quite approximate atsome locations in our system where the channel is narrow and the fluid relatively deep.Comparing this with the Chézy (Darcy-Weisbach) equation,(15)gives the roughness coefficient 2 as a function of the relative roughness hid:* = 2.9353.). (16)which is true for 5 < h/d < 500. This states that the dimensionless roughness coefficient2. will be the same in prototype and model if the hid ratio is the same. The validity ofthis argument requires that the model operates in the hydraulically rough region(Henderson (1966), pp. 98 and 492).39Since the model is vertically distorted we must consider the effect this has on surfacefriction. The distortion modifies the shape of cross sections, involving a variation of thehydraulic radius. Considering the Chézy equation in scale number form,, SrRrhrRrRr (17)r u Lr hr Lr’the roughness scale number, Ajr, depends on the hydraulic radius, which appears to makecomplete similarity impossible. However, if the channel is assumed wide enough toapproximate R by h then ‘r = e, the distortion coefficient. The above relation (12)gives the scale number equation,(18)or dr/hr = e3 which means that the relative size of the roughness elements varies like thethird power of the distortion coefficient. The greater the model is distorted, the greaterthe exaggeration of the roughness elements.We have prescribed the distortion coefficient (e = 0.57) as described above by buildingthe model with specific dimensions. Surface roughness elements in the field wereestimated, from visual observations, at 5 to 10 m on land, due to tree tops and large rockyprotrusions. Similarly, visual estimates made by BC Ferries crew (Whailin, 1993) duringa severe outflow event, give values of 1 to 2 m on water, due to enhanced sea state.Considering an average prototype flow depth of 800m, the approximate relative40roughness in the field is:= 5 to 10 metres= 0.006 to 0.013 on land800 metres= 1 to 2 metres(19)0.0012 to 0.0025 over water800 metresNow using equation (18) the relative roughness values for the model are:tin, — 0.00625 to 0.0125e3ti,,, 0.00125 to 0.00250.O3toO.06 onland(20)= 0.006 to 0.012 over waterh1 e3With these values the appropriate sizes of roughness elements were chosen for the modelsurface. The average model flow depth is approximately 3 cm which gives roughnesselement sizes of about 1 to 2 mm over land and 0.2 to 0.4 mm over water. The particleswere applied to the model surface and some attention was paid to the spacing in an effortto approximate the concentrations found in the field. In general, trees have a relativelydense concentration in the area. Wave heights and wavelengths vary throughout thechannel but were given average values from visual estimates in the field.The simulation of surface friction in the model is approximate. More elaborate modelstudies often include lengthier processes which include trial and error application ofsurface elements and careful calibrations which require detailed records of fieldconditions (Nicollet, 1989). Since form drag induced by the complex topography of theregion, which is replicated in the model, is the dominant source of energy losses, thesurface friction simulation methods used here are sufficiently accurate.41e. Pressure GradientOutflow winds in Howe Sound are driven by synoptic pressure gradients which resultwhen cold air resides inland of the Coast mountain range and relatively warm airoccupies the coastal region. Generally, a significant component of the pressure gradientlies parallel to the channel axis, which is oriented almost perpendicular to the mountainbarrier. Since we can not simulate an external pressure gradient in the laboratory weimpose a physically equivalent gravitational force by sloping the model in thedownstream direction, parallel to the channel axis. The model was fitted with a hinge atthe downstream end and a jacking mechanism at the upstream end so that the slope couldbe varied.If the external pressure gradient, dP/dx, is defined as a slope, S, and made positive forincreasing pressure along the channel axis in the upstream, or positive x direction, thenS, = (g’p) dP/dx. (21)As stated above in equation (11) the distortion coefficient is equal to the scale of slopes,i.e. e = Sr = S, /S,,,. Therefore, with observed values of the quantities in (21) (examplesfrom the December 1992 event appear in Table 1) we are able to predict a range ofsuitable model slopes which will simulate pressure gradients expected in the field.423.2. Model Design and Constructiona. TopographyThe complicated topography of the Howe Sound region was reproduced, on a small scale,in the 3D model described here. This was done in an effort to recreate the flowconditions present throughout the Sound during extreme outflow events. A rectangularregion that encompasses all of Howe Sound and the Cheakamus Valley was selected andcompiled from Government of Canada topographic maps with 500 ft contour intervals.The maps were enlarged so that the region to be modelled was exactly the intended sizeof the model. From these, templates for each contour level were made and then used tocut the shape of each individual contour out of sheets of cork material 5.5mm thick. Thecontour interval on the maps and the choice of material thickness sets the vertical lengthscale number, and therefore, the distortion coefficient.The cork material was successively stacked up and glued together starting at the 0contour and progressively building up to the mountain peaks. A clay filler material wasthen applied to the model to fill in the “steps” left by the stacking process (see Figure 11).This method produces a model that resolves the detail of the actual topography to 500ft.Smaller features, consumed by the smoothing process between steps, would likely onlyaffect the flow through surface friction, which is included through the application ofroughness elements as described above.b. Video ApparatusThe aquisition of data from the model flows was achieved through video techniques.Since the model topography is complicated and not transparent the video must view the43flows from above rather than through the model from the side. This constraint requiredan apparatus, on which a camera and light source could be mounted, which would movearound the model, above the flow domain, in a precise manner. As described below insection 3.3, the camera moves up the length of the model stopping every 2 cm to record.It then moves across one view width and repeats the procedure. To accommodate thismovement an aluminum frame was constructed, on which rails were mounted andsuspended approximately 1.75 m above the model. A small cart, fixed with wheels, wasmade to run on the rails and carry the video equipment the length of the model. The cartwas fitted with a mechanism to allow the camera and lighting equipment to be movedsideways. Figure 12(a) shows the rail and cart system and its motions. A mechanismwas fitted to the cart which allows the operator to externally move the cart, fix its positionand track its location. The system is shown schematically in Figure 12 and in aphotograph in Figure 13.c. Fluid SupplyThe single layer of water used to model the outflow winds was dyed with flourescein toenhance video images and improve data accuracy. To conserve dye a recirculating fluidsupply system was required. The simple circuit, as shown in Figure 12(b), includes acentrifugal pump, flow meter, valve, diffuser, the model and a retrieval tank. Water ispumped up through the valve, which controls the total discharge; through the diffuser andover a weir, which provides an even flow; through the model; then over the downstreamweir and through a drain into the retrieval tank.443.3. Data Aquisition3.3.1 Data Aquisition SystemVideo image analysis techniques were chosen to record and analyze the flows because ofthe relative ease with which large amounts of information can be obtained and processed.These techniques are non-invasive, more thorough, and require less time to obtain datathan manual instrument techniques (i.e. point gauge, pitot tube etc.). Because the modeldesign imposed certain limitations, where data aquisition is concerned, a unique methodof recording the flows had to be developed. Physical complexity of the model requiredthat all video images be recorded from above. The aim was to collect data throughout theentire flow domain - both along the channel and across it. This required that the videosystem (VS) be mobile. A system was designed to move above the model collectinginformation, which would later be compiled to provide complete coverage of the flowarea.The VS acquires information that provides depth and velocity data throughout the flow.Both require a separate system operation and are thus recorded individually. First the VSmoves through the flow domain and records information for depth and then it isreconfigured and moves through again recording information for velocity. Once videofor a particular flow has been recorded, images are digitally captured and analyzed on acomputer. The method of image capture and the image to data translation are differentfor both depth and velocity. Depth and velocity data are referred to the same spatialcoordinates so they can both be specified at coinciding points throughout the flow field.A 2cm grid, with a depth value and a velocity value at each node, was selected as areasonable compromise between high data resolution and collection time.45Details of the VS design are best described by discussing its function in recording depthand velocity images. Below we describe, separately for depth and velocity, how the VSoperates and the transformation of the captured images into data.3.3.2 Depth Data AquisitionDepth information is recorded by a video camera directed down at an angle and focusedon a projected light sheet which illuminates a vertical cross-section through the flow,roughly perpendicular to the flow direction. Figure 12(b) shows the configuration ofcamera and light source and how the system is positioned over the model. The camera isangled sharply down (approximately 500 from horizontal) in order to view the light sheetbehind islands and in deep valleys. As the camera and light sheet move throughout theflow domain, stopping momentarily at predetermined locations, a mapping of the flowdepth is compiled.The camera zoom is adjusted to a narrow field of view (15 cm wide) which covers only aportion of the model width but is necessary to record images free from wide angledistortion and with image depths substantial enough to provide accurate results. Thiscamera setting requires that the entire flow domain be swathed out in longitudinal parallelstrips. The viewing system moves the length of the model pausing at several locations,each 2 cm apart, for about 30 seconds each. The system is then moved transversely adistance of one view width and another longitudinal pass is made. The procedure isrepeated until the entire flow domain has been covered (3 passes). When the recordedvideo is later played back, images of flow cross-sections at each location where thecamera paused, are captured and analyzed with a computer. Since the flow is turbulent,with rapid small fluctuations at the surface, any instantaneous “snap shot” of a flow crosssection has a highly distorted bottom profile. This is due to refraction of light as it passes46through the fluid surface on its way to the camera. The problem is remedied by capturingseveral sequential images (about 15) of the same cross-section and digitally averagingthem together which eliminates most of the time dependent noise.The method of viewing requires that depth measurements taken from the captured imagesbe translated to obtain the correct or “true” depth. As depicted in Figure 12(b) the cameralooks obliquely at the vertical cross-section in the flow and therefore sees a skewedrepresentation of the actual depth (i.e. a projection along the camera’s viewing axis).Figure 14 indicates schematically how the depth is viewed by the camera. It is assumedthat the camera is far enough away that at any point along a cross-section the light raysleaving the water surface and reaching the camera are parallel to the camera viewing axiswhich lies at an angle, ‘, from the plane of the light sheet. Referring to Figure 14 thetrue depth of fluid, d, appears to the camera as the projection, d’, which is perpendicularto the viewing axis.In addition to the correction that must be made to compensate for the camera angle, twomore factors must be considered. The first involves refraction of light at the free surface.The true depth at any point along a cross-section can be considered as the verticaldistance between the light ray reflected up to the camera from the free surface and thatreflected from the bottom. The ray reflected from the bottom is refracted at the freesurface and bends toward the horizontal as shown in Figure 14. According to Snell’sLaw,nsinO=n’sinO’, (22)where 0 and 0’ are defined in Figure 14 and n and n’ are the indices of refraction ofwater and air respectively.47The second additional factor to consider is the width of the light sheet reflecting from thefree surface. This width,w, adds wcos8’ to the projected depth which must besubtracted to obtain the true depth.The three corrections discussed above are embodied in one relation,d’—wcosO’d= (cos 8’) tan(sin’(sin(23)which gives the true depth and where all quantities on the right side of the equation areknown.Each captured depth image is processed with thresholding and line detection routines toreveal the surface and bottom. The two resulting lines are then automatically discretizedinto data points and converted to projected depths which are transformed to actual depthswith equation (23). The results of one depth transformation are shown as a solid line inFigure 15(a). These results indicate the variation in depth across one 10 cm wide flowcross-section as measured using the video image analysis techniques described above. Toverify the method, direct measurements were taken across the same flow cross-sectionusing a manual point gauge system. Depths, recorded manually at 5 mm intervals, appearas solid squares in Figure 15(a). The same comparison for a different position (and flowregime) in the model is shown in Figure 15(b). The close agreement serves to validatethe video techniques.483.3.3 Velocity Data AquisitionFor velocity data, the camera is directed straight down and focused on a small region ofthe flow surface which is broadly illuminated from above. Positively buoyant plasticbeads are introduced into the flow upstream and videotaped as they flow through thecamera’s view. The beads, floating at or near the surface, are used to indicate velocitieswhich are assumed to approximate the mean velocity throughout the depth. The velocityactually varies slightly over the depth due to boundary layer effects and secondarycirculations; however; we are concerned here with variations on a larger scale so surfacevelocities adequately represent the mean.The VS moves throughout the flow domain in the same manner as described aboveexcept that it now focuses on rectangular portions of the surface rather than cross-sections. The region of the model viewed at each camera location corresponds to aknown portion of the 2cm grid described above. Within each image the grid contains 40points which coincide with points from the depth sections so that data can later becombined to give Froude number values.At each position the camera is allowed to record passing particles for a number ofseconds. Multiple images (about 20) from each location are captured on a computer. Thecamera frame rate determines the length of time each frame, or captured image,represents. In our case the camera was set to 1/30 second. The moving particles in theseimages appear as streaks which represent the distance traveled by the particle in 1/30second. Each image may have only a few or several streaks depending on the density ofparticles at the instant of image capture. In order to obtain measurements at all desiredgrid points, streaks are measured from the several captured images, at each cameralocation. The streaks are manually traced on the computer screen and automatically49scaled and stored. Approximately 160 streaks are measured for each location where only40 grid points require values. All streak measurements within a 20mm by 20mm boxaround each grid point are averaged together and the result is associated with theappropriate grid point. The location of a streak is identified by its midpoint. Theprocedure is repeated throughout the model domain resulting in a data set representingthe entire flow.3.4. ResultsUsing the data aquisition methods described above, results were obtained for eightdifferent model flows. Velocity, depth and Froude number, presented for each flow,reveal the subcritical and supercritical regions and some of the dynamic features presentin the wind layer. A range of conditions was simulated, including those most likely tooccur in the field. The modelling program was based on the conditions present in HoweSound during the December 1992 event (see section 2.2.1), but was broadened toencompass other possible flows.3.4.1 Important ParametersModel flows are governed by three parameters; total discharge, Q, downstream depth,hf. and external (or synoptic) pressure gradient, dP/dx. Each of these is prescribed, foran individual model flow, as described in the above sections. A valve sets the discharge,a weir the downstream depth and a model slope the pressure gradient. The settings arescaled from model to prototype in the manner described above in section 3.1.1. Twotypical values for each parameter were chosen and all possible combinations of the threeparameters were simulated. The values chosen appear in Table 3 and the eight resultingcombinations in Table 4.503.4.2 Model ResultsAs described in section 3.3 the acquired data for the 3D model provides a mapping ofconditions throughout Howe Sound. Although velocities may be largely threedimensional in some locations we are concerned with horizontal variations on a relativelylarge scale and have therefore presented only the horizontal component of the depthaveraged velocity. In particular, it is the hydraulic behaviour of the wind system that isof primary interest.Results are referred graphically to the Howe Sound region which is shown in Figure 16.This reference figure may be used to find locations which appear in the results figures(17-24), which are not extensively labeled to avoid confusion. The spatial dimensions onFigure 16 provide a coordinate system for reference and the locations of field stations forthe December 1992 outflow event are shown.The results appear, for the eight cases modelled, in Figures 17 through 24. In each figurethe first panel shows the velocity distribution, the second panel shows the depthdistribution and the third panel shows the Froude number distribution. Velocities arerepresented by vectors with length proportional to magnitude (velocities less than 1 m/sare not shown). Depth is represented by contours with a 200m interval. The 0 mcontour, or layer boundary, is not shown because the method of data aquisition wasunable to accurately resolve depths down to Om. Froude number is represented bycontours at F = 1, 3, and 5. The F = 1 contours enclose regions of supercritical flowwith the contour itself representing critical flow and indicating the location of controlsand hydraulic jumps.51The hydraulics of three dimensional flows differs in nature from the simple, crosssectionally averaged, 1D flow case. Schar and Smith (1993) investigated the hydraulicstructure of flows encountering 3D topography and characterized some importantfeatures. In the case of a complicated channel like Howe Sound, such features as controlsand hydraulic jumps are not likely to span the entire width of the channel wherever theyoccur. Often a portion of the flow width will be controlled while a region alongside itremains subcritical. The supercritical region may be flanked on one or both sides byregions of subcritical flow. The boundary between the two flows may be termed a sheardiscontinuity since the flow will have different depth, speed and even direction on eitherside.3.4.3 Discussion of Cases 1 Through 8The two values for each of the three model parameters appear in Table 3 where it isindicated that the lower setting of each value will be referred to by L and the highersetting by H. This convention appears in Table 4 which outlines the parameter settingsfor each case and lists some physical characteristics from the results. The overall effectof each parameter on the wind system is suggested by these results.The most important information in Table 4 is contained in the column listing the totalsupercritical area. The regions occupied by supercritical flow will have distinctly higher,more consistent and unidirectional winds and can therefore be labeled “danger zones”.Referring to Table 4 it is apparent that the expanse of supercritical flow is governedmainly by hf and dP/dr. The coupled effect of these parameters is reflected in apositive influence by dP/dx and a negative influence by hf. The discharge, Q, has alesser effect and its influence seems to depend on the other parameters.52The set of 3D model results was designed to encompass possible prototype flows.Therefore some of the extremely weak or strong cases modelled (i.e. Cases 3, 4, 5) maynot actually occur in nature.The topographical influence on the flow is now discussed for each case in succession(Figure 17 through 24). Locations will be referred by their Cartesian (x,y) coordinates.Case 1 - Q=L, hf=L, dP/dx=L - Figure 17Although mostly subcritical, the upstream region of the channel near Squamish (8,48), ishydraulically controlled by local elevation changes resulting in “patches” of supercriticalflow. The flow is controlled by the promontory near Britannia (9,38) but only across aportion of the channel. This partial control results in a shear discontinuity and a slowlyrotating clockwise eddy on the opposite side of the channel (not apparent in the figure butobserved). A hydraulic jump occurs before the flow is again controlled, this time acrossthe entire channel, by the contraction near (8,34). The abrupt widening of the channelnear (8,30) combined with upstream blocking from Anvil Island forces a hydraulic jumpnear (8,27). The shape and location of Anvil Island guide most of the flow through themain eastern channel where it is controlled by the “throat” between Anvil Island and theeastern shore. Some flow manages to enter the west arm (7,28) where an eddy forms. Aswas proposed by Jackson (1993) the flow is largely confined to the main channel by theislands (Anvil, Gambier, Bowen). A hydraulic jump occurs near (12,16) before the flowis again controlled, forming a small region of supercritical flow, near the headlands atHorseshoe Bay (14,12).Case 2 - Q=H, hf=L, dP/dx=L - Figure 18The increase in discharge increases the depth of flow. Although it seems to decrease thesupercritical region near Horseshoe Bay it has an overall effect of increasing the expanse53of supercritical flow. The deeper flow is now able to go over, rather than around, largerportions of Gambier and Bowen islands and it is controlled as it does so. Most of theflow is controlled in the same manner as for Case 1.Case 3 - Q=H, hf=L, dP/dx=H - Figure 19The increase in pressure gradient causes a substantial increase in supercritical flow. Thesupercritical region near Britannia (8,38), however, seems fixed in size as a hydraulicjump is forced on the lee side of the promontory. A large supercritical region now spansmost of the length of the lower channel, extending out beyond the terminus beforereverting to subcritical conditions through an apparent undulating hydraulic jump.Case 4 - Q=L, hf=L, dP/dx=H - Figure 20As expected a decrease in discharge causes only minor changes to the flow. Theundulating hydraulic jump does not form and the region of supercritical flow is slightlysmaller.Case 5 - Q=L, hf =H, dP/dx =L - Figure 21This combination produces a flow pattern which is different from those discussed above.The flow is substantially deeper and slower and although Anvil Island directs the flowinto the main channel the other islands do not confine it. The flow separates from theeast side of the channel (10,26) and proceeds in a direct path over the islands towards theStrait of Georgia. In the separated region (13,18) a slow moving counter-clockwise eddyis formed. The flow is predominantly subcritical but small regions of supercritical flowexist where local elevation changes induce transition.54Case 6 - Q=L, hf=H, dP/dx=L - Figure 22The increase in discharge from the previous case delays the separation from the easternside of the channel. The flow is again confined mainly to the main channel but a smallseparated region exists near (14,18). Relative to the first four cases the flow is slow anddeep and although supercritical regions near (8,30) and (8,38) are present the downstreamregion (8,22) is somewhat smaller than in the first four cases.Case 7 - Q=H, hf=H, dP/dx=H - Figure 23This case is similar to that of cases 1 and 2 but is characteristic of a stronger flow with alarger area occupied by supercritical flow. The three prominent regions of supercriticalflow are again present but are slightly larger.Case 8 - Q=L, hf =H, dP/dx =H - Figure 24The change in discharge has the opposite effect in this strong flow case as it did in theweak flow cases 1 and 2. With high forcing, the response to a decrease in discharge is aan increase in the amount of supercritical flow. Controls occur further upstream due tothe decrease in depth that accompanies a decrease in discharge. The two maindownstream supercritical regions have joined as in cases 3 and 4. A hydraulic jumplimits the extent of this region and it does not extend out of the channel as before.55Chapter 4 - Discussion and Conclusions4.1. Comparison of 1D Modeffing and 3D ModellingThe fundamentally different approach taken in the 1D and 3D studies makes themdifficult to compare. Since the 3D study was based, in some ways, on the findings of the1D study, it may be useful to simply compare the hydraulic characteristics of similarflows. For the two flows studied in the 1D experiments of chapter 2, the two 3D flowsthat most resemble them are Case 6 and Case 7.Through a qualitative comparison of the results presented in Figure 6(c) with those inFigure 22(c) it is possible to draw some conclusions. For a lower pressure gradient, theflow is controlled near Britannia Beach but remains supercritical only for a short distance.The 1D physical model does not predict the subsequent supercritical region which isproduced by the 3D model (centered at 8, 29 - Figure 22(c)). The Hydmod resultsappearing in Figure 6(c) do however indicate a supercritical region in this vicinity with ahydraulic jump at km 25 which corresponds to that indicated in the 3D results (9,25),Figure 22(c). The flow is then controlled through the contraction at Anvil Island and asubsequent hydraulic jump occurs some distance downstream before Horseshoe Bay.The hydraulic jump which occurs near Porteau Cove in the 3D model for Cases 1, 2, 6and 7 (near 9,25) is also present in the Hydmod results of Figure 6(c) (km 25) and boththe physical model and Hydmod results of Figure 7(c) (km 24). This jump occurs due tothe abrupt expansion near (8,30), Figure 16 and the upstream blocking effects of AnvilIsland. Although the 1D results indicate a point location for the jump and the 3D resultsindicate a line location, the actual hydraulic jump may occupy a region 1 or more km inlength. The existence of this jump in the field is supported by the microbarograph56tracings recorded during the December 1992 event. Figure 24 shows a portion of the pentracing from Porteau Cove and the corresponding tracing from Lions Bay. The erraticpen movements of the Porteau Cove tracing suggest strong low level turbulence due tothe presence of a hydraulic jump. The Lions Bay tracing is relatively stable whichsuggests a very steady, characteristically supercritical flow.Hydraulics of the higher pressure gradient scenario are shown in both Figure 7(c) andFigure 23(c). These indicate that the flow is again controlled near Britannia Beach andmay subsequently go through a hydraulic jump, control, hydraulic jump sequence beforereaching Anvil Island. This is supported by both the Hydmod results of Figure 7(c) andthe 3D model results of Figure 23(c). The flow is again controlled and may remainsupercritical throughout the channel or until another hydraulic jump is induceddownstream of Lions Bay.4.1.1 Comparison of field results with 3D model resultsa. Low pressure gradient, Case 6 - Period]Values of depth and Froude number, obtained from the 3D model for Case 6, are shownin Table 5. These values were taken from the five locations in the model domain whichcorrespond to the field study locations as described in chapter 2. The field results forPeriod 1 are also shown in Table 5 for comparison. Of the 8 3D model runs, Case 6results correspond best with Period] field results. However, by refering to Table 5, it isimmediately apparent that the overall depth of the two flows differs substantially. This isbecause some of the controlling parameters differ. Refering to Table 1 (field studyparameters) and Table 3 (3D model parameters), the pressure gradient is the same for57both flows but the discharge and depth settings are substantially greater for the fieldresults. This makes the two flows difficult to compare.Initially the 3D model was tested at flow rates corresponding to those found for the fieldresults for Period 1. However, these flow rates produced unrealistically strong modelflows. This suggests that the method used in chapter 2 to calculate depth and dischargefrom pressure data, may produce values that are too high. The process of estimatingchannel widths and averaging over an idealized rectangular channel may make the fieldresults subject to some uncertainty. The 3D model indicates that outflow winds in HoweSound are complicated in nature and often vary in velocity, depth and flow regime acrossthe channel width. Therefore, although the 1D study of chapter 2 is useful for predictingroughly the location of hydraulic controls and jumps, it does not capture some of thesmaller scale hydraulic features of the flow. As well, comparison of a single point in ahighly three dimensional flow with a corresponding cross-sectionally averaged value ofthe Froude number, is not likely to be informative. Table 5 shows that the two flowshave a similar trend in the along-channel direction. This substantiates the findings insome of the locations but does not allow for a detailed comparison.b. High pressure gradient, Case 7 - Period 2In the same manner as described above, the 3D model results for a higher pressuregradient, Case 6, are compared with Period 2 field results in Table 6. The depthdifference between flows is again apparent. The same parameter differences as describedabove, and the fundamental difference in the data types (i.e. single point as opposed tocross-sectional average), are responsible for the lack of overall agreement.584.2. Summary and Conclusionsa. SummaryThe work reported in this thesis is comprised of two separate but complementary studies;firstly a 1D study which combines results from physical modelling, field observations andcomputer modelling, and secondly a more accurate 3D physical model study. The 1Dstudy was intended to identify the hydraulic characteristics of the outflow wind system inHowe Sound. The results are simple yet useful in predicting roughly where extremeconditions will occur during an outflow event.The 3D physical model study broadens the knowledge gained by the 1D study byproviding a more accurate and comprehensive set of results. The wind system is studiedin detail through a series of experiments conducted with a three-dimensional physicalmodel which is geometrically and kinematically similar to the prototype, Howe Sound.Simulations covered a range of parameters representative of likely field conditions.Hydraulic features, which do not behave in a traditionally two-dimensional manner, areidentified.b. ConclusionsAs discussed above, a quantitative comparison of 1D model and field results with 3Dresults is difficult. It is, however, informative to briefly identify common predictions ofboth studies. We can specify conditions in Howe Sound, and possible locations ofcontrols and hydraulic jumps, during an outflow event.59In general the flow is subcritical in the vicinity of Squamish and is accelerated through acontrol over the promontory just upstream of Britannia Beach. This control may notextend across the entire channel, resulting in a shear discontinuity and subcriticalconditions near the west shore. A hydraulic jump and subsequent control may or may notform just downstream of Britannia Beach. Regardless, the abrupt expansion justupstream of Anvil Island and the blocking effects due to Anvil Island always force astrong hydraulic jump which piles fluid up on the steep north side of the island. The flowis controlled through the contraction inposed by Anvil Island and the west side of theSound and generally remains supercritical until a hydraulic jump occurs, across the mainchannel, at the north end of Bowen Island. The exact location of this jump can varyconsiderably.For stronger flows, a separated region can form along the west side of the lower Sound,as apparent in Figures 21 and 22. The large supercritical region downstream of AnvilIsland can, in some instances (Figures 7, 19 and 20), extend over portions of Bowen andGambier Islands and out into the Strait of Georgia.Some practical suggestions, regarding important weather dependent functions in HoweSound, can be made. The Atmospheric Environment Service weather station which islocated at Pam Rocks, just south of Anvil Island, is well situated to measure some of themore intense winds in the channel during an outflow event. The region surrounding PamRocks is generally occupied by strong supercritical flow, thereby producing wind reportswhich indicate a “worst case scenario”. The BC Ferries route, between Horseshoe Bay(on the east side of the mouth of Howe Sound) and Langdale (on the opposite side),follows a path around the north side of Bowen Island. During a severe event, this regionis occupied by supercritical flow. The reports from Whailin (1993) indicate that windsincrease substantially as the boat nears the northern tip of Bowen Island. This claim is60supported by the 3D model results which, in most cases (Figures 17, 18, 19, 20, 23, 24),indicate that the boat passes through a hydraulic jump into supercritical flow. Although itmakes the trip further, an alternative route south of Bowen Island may be advantageous.The 3D model results, although more detailed, verify the findings of the 1D study ingeneral. The two sets of results effectively compare in a qualitative manner and showwhere controls and hydraulic jumps, and therefore supercritical regions, are likely tooccur. Together the results provide a predictive tool for determining hazardous zones ofextreme wind during an outflow event.c. Recommendations forfurther researchThe comparison between field results and 3D model results, discussed above in section4.1.1, could be potentially very informative. Unfortunately the nature of the two sets ofresults makes them difficult to compare. The methods of determining average values forvelocity, depth and Froude number from the raw field data completely eliminates the 3Dcharacteristics of the actual flow. The difficulties in the interpretaion of the field data, asdescribed in chapter 2, arose due to the lack of velocity data at each field station.Therefore, a further field investigation is recommended which should involve measuringstatic pressure as well as velocity at several locations throughout the wind field.61List of Symbolsu fluid layer velocity Appendicesc long wave celerity depth difference across hydraulic jumph layer thickness p pressureg acceleration due to gravity T temperatureF Froude number R universal gas constantp fluid density p change in pressure across hydraulic jumpF1 internal Froude number q discharge per unit widthr’2 stability Froude number b mean channel widthA E specific energyh = h, + h2 total fluid depthg’ reduced gravity SubscriptsF external Froude number 1 upstream of hydraulic jumpxE along channel coordinate 2 downstream of hydraulic jumpdP I dx pressure gradientL horizontal lengthRe Reynolds numberV dynamic viscositye distortion coefficientS slopeR hydraulic radiusK Manning roughness coefficientd roughness element sizedimensionless roughness coefficients pressure slopeincident angle9’ refracted anglen index of refractionw light sheet widthQ total fluid dischargehf downstream fluid depthSubscripts1 upper fluid layer2 lower fluid layerm modelP prototyper prototype:model ratio62BibliographyArmi, L., 1986. The hydraulics of two flowing layers of different densities. J. FluidMech., 163, 27.Baines, P.G., 1984. A unified description of two-layer flow over topography, J. FluidMech., 146, 127-167.Baines, P.G. and Davies, P.A., 1980. Laboratory studies of topographic effects inrotating and/or stratified fluids. In Orographic Effects in Planetary Flows,chap. 8, pp. 233-299. GARP Publication no. 23, WMOIICSU.Benton, G.S., 1954. The occurrence of critical flow and hydraulic jumps in a multilayeredfluid system, J. Met., 11, 139.Bond, N.A. and Mackim, S.A., 1993. Aircraft observations of offshore-directed flow nearWide Bay, Alaska, Mon. Wea. Rev., 121, 150-161.Brinkmann, W.A.R., 1974. Strong downslope winds at Boulder, Colorado. Mon. Wea.Rev., 102, 592-602.Cameron, D.C. and Carpenter, A.B., 1936. Destructive easterly gales in the ColumbiaRiver Gorge, December 1935, Mon. Wea. Rev., 64, 264-267.Durran, D.R., 1986. Another look at downslope windstorms. Part I: the development ofanalogs to supercritical flow in an infinitely deep, continuously stratified fluid, J.Atmos. Sci., 43, 2527-2543.Finnigan, T.D., Vine, J.A., Jackson, P.L., Allen, S.E., Lawrence, G.A., Steyn, D.G., 1994.Hydraulic physical modeling and observations of a severe gap wind, in press,Mon. Wea. Rev.Finnigan, T.D., 1993. Microbarograph pressure recordingsfrom a severe outflow eventin Howe Sound in December, 1992. U.B .C. Oceanography data report #60.Gibson, A.H., 1934. Hydraulic and its Applications, Constable and Company Ltd.London.Henderson, F.M., 1966. Open Channel Flow, Macmillan, New York.63Houghton, D.D and Kasahara, A., 1968. Non-linear shallow fluid flow over an isolatedridge, Commun. Pure AppL Math., 21, 1-23.Hunt, J.C.R. and Snyder, W.H., 1980. Experiments on stably and neutrally stratified flowover a model three-dimensional hill, J. Fluid Mech., 96, 67 1-704.Jackson, P.L. and Steyn, D.G., 1994a. Gap winds in a fjord, part I: Observations andnumerical simulation, in press, Mon. Wea. Rev.Jackson, P.L. and Steyn, D.G., 1994b. Gap winds in a fjord, part II: Hydraulic analog,in press, Mon. Wea. Rev.Jackson, P.L., 1993. Gap winds in a fjord: Howe Sound, British Columbia, University ofBritish Columbia, Ph.D. thesis.Lackman, G.M. and Overland, J.E., 1989. Atmospheric structure and momentum balanceduring a gap-wind event in Shelikof Strait, Alaska, Mon. Wea. Rev., 117, 18 17-1833.Lawrence, G.A., 1990. On the hydraulics of Boussinesq and non-Boussinesq two-layerflows, J. FluidMech., 215,457-480.Lawrence, G.A., 1993. The hydraulics of steady two-layer flow over a fixed obstacle,J. FluidMech., 254, 605-633.Long, R.R., 1953. A laboratory model resembling the “Bishop-Wave” Phenomenon, Bull.Am. Meteorol .Soc., 34, 205-211.Long, R.R., 1954. Some aspects of the flow of stratified fluid systems, Tellus, 6, 97-115.Macklin, S.E., Bond, N.A. and Walker, J.P., 1990. Structure of a low-level jet over lowerCook Inlet, Alaska, Mon. Wea. Rev., 118, 2568-2578.Mass, C. F. and Aibright, M.D., 1985. A severe windstorm in the lee of the Cascademountains ofWashington State, Mon. Wea. Rev., 113, 1261-128 1.Nicollet, G., 1989. River Models, In Recent Advances in Hydraulic Physical Modelling,chap. 2, R. Martins (Ed.), Kluwer Academic Publishers, 39-63.64Overland, J.E. and Walter, B.A., 1981. Gap winds in the strait of Juan de Fuca, Mon.Wea. Rev., 109,2221-2233.Pettre, P., 1982. On the problem of violent valley winds, .1. Atmos. Sci., 39,542-554.Reed, T.R., 1931. Gap winds in the strait of Juan de Fuca, Mon. Wea. Rev., 109, 2383-2393.Rottman, J.W. and Smith, R.B., 1989. A laboratory model of severe downslope winds,Tellus, 41A, 401-415.Schaeffer, G., 1975. Climatology. The Squamish River Estuary Status ofEnvironmentalKnowledge to 1974, L.M. Hoos and C.L. Vold, Eds., Environment Canada.Schär, C. and Smith, R.B., 1993. Shallow-water flow past isolated topography.Part I: Vorticity production and wake formation, J. Atmos. Sci., 50, 1373-1400Smith, R.B., 1985. On severe downslope winds, J. Atmos. Sci., 42, 2597-2603.Snyder, W.H., Thompson, R.S., Eskridge, R.E., Lawson, R.E., Castro, I.P., Lee, J.T.,Hunt, J.C.R. and Ogawa, Y. The structure of strongly stratified flow over hills:dividing-streamline concept, J. Fluid Mech., 152, 249-288.Vine, J.A., 1992. Squamish Winds Research Project. Report EFM 92/02, EnvironmentalFluid Mechanics Group, Department of Civil Engineering, University of BritishColumbia.Whailin, C., 1993. BC Ferries Corporation, personal communication.Yalin, M.S., 1989. Fundamentals of Hydraulic Physical Modelling, In Recent Advancesin Hydraulic Physical Modelling, chap. 1, R. Martins (Ed.), Kiuwer AcademicPublishers, 1-37.65Appendix A: Calculation of Froude number, wind layer depth and velocity at each fieldstationi.) Description of the methodIn order to examine the hydraulics of the wind layer in Howe Sound during theDecember, 1992 event it was necessary to convert the recorded absolute pressures andrelative pressure changes along the channel to absolute layer depths. The absolute layerdepth at one field station had to be determined in order to use the recorded relativepressure change between each station (assuming hydrostatic pressure distribution) tocalculate absolute depth at each station.The Atmospheric Environment Servic&s (AES) weather station at Pam Rocks is situatednear our recording station at Lion’s Bay (station 4). Hourly pressure data acquired at PamRocks during the event were used to confirm our data at station 4. As well as pressure,the Pam Rocks station also records wind speed and air temperature. These data, alongwith our pressure data at stations 4 and downstream at station 5, were used to estimate theabsolute layer depth at station 4 and therefore at all the stations.The procedure involves the assumption that during Period 1 of the event the increase inpressure between stations 4 and 5 is due to the presence of a hydraulic jump. The steadypressure difference between the stations, of approximately I mb during Period 1 (Figure9(a)), validates this assumption.66ii.) Method ofsolutionThe hydraulic jump equation, as described in Henderson (1966) and expressed in terms ofthe upstream conditions, can be used to predict the depth of flow just downstream of ahydraulic jump. In its usual form, which assumes the channel is rectangular in sectionand neglects friction and synoptic pressure gradients, the equation appears as,(Al)where F1 is the Froude number upstream of the jump and h1 and h2 are the upstream anddownstream depths, respectively. Expressing F12 as u/g’h1 and h2 as h1 + Ah, whereAh represents the change in depth across the hydraulic jump, and solving (Al) explicitlyfor h1, leads to the following form of the hydraulic jump equation:I 2 Ii’ 2N—I 3Ah—2- 1+111 3zh—2- I —8&?g’) gJ, (A2)4where the reduced gravity,g=(P2P1)g (A3)P2is a function of the upper and lower layer densities which we will call p1 and p2,respectively. Equation (A2) yields the depth of flow upstream of a hydraulic jump interms of the upstream fluid velocity, is1, the depth change across the jump, zTh, and thereduced gravity, g’.67The density can be determined from the ideal equation of state,p=—--, (A4)where P is the pressure and T is the temperature in the particular layer and R is the gasconstant for air. The data from Pam Rocks provides the temperature, T1, in the lowerlayer, whereas the temperature in the upper layer, T2, is approximated by surfacetemperature readings taken shortly before the onset of the event (before a lower layer ofintruding cold air occupied the region). Only pressure in each layer is then needed todetermine the densities and therefore the reduced gravity.The data at station 4 gives us the pressure at the ground surface which, considering therelatively small vertical extent of the lower layer, approximates the pressure, P1, in thelower layer. Pressure in the upper layer (near the interface) is determined, assuming thepressure varies hydrostatically, fromP1=P2—pg’h. (A5)This relation involves quantities described by the previous equations, which in turn relyon it.The only remaining unknown in (A2) is Ah. This quantity is determined from therelative pressure change across a hydraulic jump, zIP, as recorded between stations 4 and5, i.e.(A6)p1g’68Now all quantities in (A2) have been determined and the system consisting of (A2), (A3),(A4), (A5) and (A6) can be solved iteritively for h1.iii.) Calculation of layer depth, Froude number and velocity at each stationUsing the hydrostatic equation in the form of (A6) the layer depths at each station arefound from the relative pressure data, once the absolute depth at station 4 is determined.The Froude number can be expressed in terms of the flow rate per unit width, q, ratherthan the velocity, in the following manner,F2=4_.. (A7)ghThe total flow rate, Q = qb = uhb,where b is the average width of the channel, calculatedat station 4 using the known velocity, depth and width there, is assumed constantthroughout the channel. Since the average channel width, b, can be measured fromtopographic maps and the value of Q is known at each station location, the value of q isalso known. This, coupled with the known depth at each station, gives the Froudenumber and the velocity at each station.69Appendix B: Calculation of transition to supercritical flow downstream of station 5 forPeriod 1For the model results with flow rate A, the flow is predicted to transit from sub- tosupercritical downstream of the location corresponding to the field station 5. The fieldresults indicate subcritical flow at station 5 (F = 0.9), but no results are availabledownstream to directly confirm the model predicted transition.A simple calculation, using the known conditions at station 5 and the extent of furthercontraction in the channel beyond station 5, reveals that transition is likely immediatelydownstream as predicted by the model. Here, we use the concept of specific energy, fromhydraulic theory, to relate the flow between station 5 and the point of minimum channelwidth just downstream. Specific energy may be defined at a particular location in theflow by,(Bi)where synoptic pressure gradient is neglected and h is the depth of flow, q the flow rateper unit width and g’ the reduced gravity. Neglecting frictional losses between station 5(which we’ll refer to as location 1) and the point of minimum width (location 2) thespecific energy remains constant between the two points.The specific energy at 1 is calculated to be E1 = 1010 m which is also the value at 2. Theaverage channel width at 2 is reduced to approximately 60% of that at 1.70Therefore, the flow rate per unit width at 2 is,= 0.6= 22 x io—, (B2)where the numerical values are determined from the calculations described in AppendixA. Inserting these values into (B 1) for position 2 and solving the resulting cubic equationfor h2 yields two alternative depths at position 2: one for subcritical flow and one forsupercritical flow (see Henderson (1966)). The root corresponding to the supercriticaldepth of flow for the equivalent specific energy at 1 has the value y2 = 673 m, which islower than the depth at 1, y1 = 763 m. This state may be reached if the flow passesthrough the point of minimum specific energy (critical point). We have now determinedboth q2 and y2 which, using (A7), gives the Froude number at location 2. The valueobtained is F2 = 1.6 indicating supercritical flow at that location.The above calculation, from the field results, affirms the model prediction that atransition may occur from subcritical flow at station 5 to supercritical flow downstreambefore the channel terminus.71Input Variable Period 1 Period 2synoptic pressure gradient - dpi dx (Pa rn-1) 0.0121 0.0168initial height - h (m) 1200 1200total discharge - Q (m3is) 6.5 x 7.4 x 10lower pot. temp. - 8 (K) 272 265upper pot. temp. - °2 (K) 281 281drag coefficient - C (-) 0.02 land 0.02 land0.01 water 0.01 waterTable 1: Values of parameters as observed during Period] and Period 2 which were usedin Hydmod comparisons.Vertical Length hr = hrHorizontal Length Lr = LrMass Mr = Pr’’rVelocity Ur = (g’/g)”2h’2Time Tr = LrU;’ = (gig’)112Lrh;112Discharge Qr UrLrhr = (g’/g)1”2Lrh72Force Fr = MrLrT;2 = (g’/g)prLrhPressure = FrL2 = (g’/g)prhrTable 2: Scale ratios resulting from Froude number similarity between model andprototype.72Model Parameter Settin sWeir Height (mm)Table 3: 3D Model parameters and corresponding values scaled to prototype dimensions.Table 4: Model parameter settings and some important physical aspects of the results forthe eight simulated cases. L refers to the lower setting and H to the higher.Discharge (GPM) Model SlopeLow (L) 6 32 0.039High (H) 9 41 0.053Corresponding Prototype ValuesQ (m3Is) hf (m) dP/dx (Pa/m)Low (L) 1.72 x i07 965 0.0 123High(H) 2.58x107 1212 0.0165Max. Max. Max. TotalCase Q h dP/dx Velocity Depth Froude Supercriticalf (mis) (m) Number Area (km2)12345678LHHLLHHLLLLLHHHHLLHHLLHH22.625.128.625.516.819.825.824.4757943844696104610449378863. Model-Case 6 Field Results-Period]station depth (m) Froude number depth (m) Froude number1 560 0.79 (sub) 1290 0.55 (sub)2 605 0.64 (sub) 980 0.63 (sub)3 275 1.4 (sup) 980 0.55 (sub)4 270 0.22 (sub) 598 1.14 (sup)5 680 0.05 (sub) 763 0.95 (sub)Table 5: Case 6 of 3D model results compared with Period] of field study results.3D Model-Case 7 Field Results-Period 2station depth (m) Froude number depth (m) Froude number1 519 0.32 (sub) 1289 0.63 (sub)2 222 1.23 (sup) 857 1.18 (sup)3 292 1.3 (sup) 1117 0.55 (sub)4 399 2.33 (sup) 598 1.58 (sup)5 325 0.44 (sub) 598 2.10 (sup)Table 6: Case 7 of 3D model results compared with Period 2 of field study results.74Figure 1: Schematic representation of outflow wind system. Isobars indicate the synopticpressure gradient which drives the flow. Low lying cold air flows through a partialmountain barrier from the interior region towards the oceanic zone.75Figure 2: Geographical location and important features of region surrounding HoweSound.76Figure 3: Howe Sound; locations and topography. Instruments positioned in HoweSound are numbered 1 through 5 in the direction of flow.77STRAITOF GEORGIAI I72cmI model channel II Ivideocamera___sectionplanFigure 4: Schematic drawing of experimental apparatus used for 2D physical modeling ofoutflow winds. The line marked with the symbol V indicates a simulated water level inthe vertical section.-;;\20cm!1 5 cmU,’.78(a) Model (b) Howe SoundFigure 5: Channel axis shown with respect to the model of Howe Sound (a) and HoweSound (b). Distance increases in the direction of flow and the field station locations arelabeled 1 through 5.03:. I60km I792500-2000-1500-4-I -Q)D 500-Coa)a)Coa,Ea)t50I-I-0•Figure 6: (a) Depth, (b) wind speed, and (c) Froude number along Howe Sound: aspredicted by the physical model for flow rate A (thick line); as measured during theDecember, 1992 outflow event for Period 1 (squares); and as produced by the numericalmodel Hydmod (thin line) for Period]. Flow is from left to right and a point of hydrauliccontrol exists wherever the F = 1 line is crossed from less than 1 to greater than 1 (i.e.sub- to supercritical flow).Distance along channel N-S (km)802500-2000-Egg:1500-0-U)E10G)U,-1. 4a)-DEa)-0LLI I I0 10 20 30 40 50 60Distance along channel N-S (km)Figure 7: (a) Depth, (b) wind speed, and (c) Froude number along Howe Sound: aspredicted by the physical model for flow rate B (thick line); as measured during theDecember, 1992 outflow event for Period 2 (squares); and as produced by the numericalmodel Hydmod (thin line) for Period 2. Flow is from left to right.811040-Period 21030j101:ed1000-• Dec25 Dec26 Dec27 Dec28 Dec29 Dec 30 Dec 31 Jan 1 Jan 2 Jan 3990 I 11I1III11111111I11I1I1 I.’.0 24 48 72 96 120 144 168 192 216 240HoursFigure 8: Composite chart of atmospheric pressures recorded at 5 stations in Howe Soundover a 9 day period. Strong gap winds occurred from 27 December to 01 January.Individual pressure tracings are shown more clearly in Figure 9.82Period 1 Period 20— 0-i=1 1=1-6— -6 —(a) (b)-7 I I -7 I I60 62 64 66 68 70 72 96 98 100 102 104 106 108Hours HoursFigure 9: Relative pressures, with respect to that at station 1 (P1), at each of the five fieldstations in Howe Sound (i= 1 through 5) for (a) Period] and (b) Period 2.83Figure 10: Photograph of 3D model topography. View from downstream end.84Tj0CDCDC)I-._•I-..C)0CDCDC) CD0000I--00 0C)GCDCD-0Z CD 00CDCD_Q— 0 00 cqC,0 - cd CD CD 3 3rit Aflow directionrail(a)Figure 12: Schematic view from above of the video apparatus cart and rail system (a) andschematic side view of complete 3D model equipment set up (b).(b)86Figure 13: Photograph of 3D model and video apparatus.87Figure 14: Definition sketch for depth data aquisition. Fluid surface is indicated by V.88lightsheetwdistance across section (cm)(a)020406080100distance across section (cm)(b)Figure 15: Plots for validation of video techniques for depth data aquisition. Figureshows depth across a 10cm flow section as measured using the video process (solid line)and a manual point gauge (solid squares) for (a) a subcritical section, and (b) a partiallysupercritical section.8928‘‘- 26 (km)18-1614-12‘10-8‘6-4‘2-oFigure 16: Reference diagram for 3D model results (a) and topography of region coveredby model results (b).“S- - - AnydIsland -- PamGambiec RocksIslaac L-5•- -- HorseshQE-- - Bay -- - - Bawentsland -andSTRAIT OF overGEORGIA 9ø m26 (km)I I • I • I0 2 4 6 8 10121416(km)(a)I I I I0 2 4 6 8 10121416(km)(b)90441\ \ ‘ ‘..14.,1 +flS1jI I‘‘I, •- -• ••.-• —• I IIIl41’’I 4 I• I, I I 444 1• I 4 I I I41 II(a)j I I ‘ 1 ‘‘ I0 2 4 6 8 10121416= 30)fo&oI(b). I • I I •0 2 4 6 8 10121416distance (km)(c)I ‘ I • I ‘ I0 2 4 6 8 10121416Figure 17: 3D Model. Case 1 - Q=L, h=L, dP/dx=L(a) Horizontal velocity vectors. Reference arrow represents 30 m/s windspeed.(b) Depth contours. Interval is 200 m and the 0 m contour is not shown.(c) Froude number contours for F=l (critical flow), F=3 and F=5.:—8—4-291‘ii1,• ‘Sf f‘,, f..•!,i’• ti.• v• — .5 . .‘ •— .• - .S- -. ,,• ..• ‘• . ‘ \• ‘fi.• . S •-...•. ‘I• . .S5 .S •5, .Ik kf• SS., 5’. 5a) .5, .,,‘S ifo 2 4 6 8 10121416— = 30Figure 18: 3D Model. Case 2 - Q=H, hf=L, dP/dx=L(a) Horizontal velocity vectors. Reference arrow represents 30 mIs windspeed.(b) Depth contours. Interval is 200 m and the 0 m contour is not shown.(c) Froude number contours for F=1 (critical flow), F=3 and F=5.Q(b)02-14—12-10—8-6—4-2—0(c)I I I4 6 8 101214160distance (km)‘ I ‘ I ‘ I ‘ I2 4 6 8 1012141692.:.E1 /a ‘a(-\ \\ \ \‘.14 \\I /.:/ ‘f*I S 1 4a ‘ I / / / 1 f\ \ +S ‘ ‘ ‘ j ‘‘-/ k-I \ t r—tI \1 Itl//‘l.:t/,j?..I sSSf//S’.535EI. fSSSS’fV1,S5l,.SSSS 55.55555,5 \‘Si(a)p I I I4 6 8 10121416Figure 19: 3D Model. Case 3 - Q=H, hf=L, dP/dx=H(a) Horizontal velocity vectors. Reference arrow represents 30 mIs windspeed.(b) Depth contours. Interval is 200 m and the 0 m contour is not shown.(c) Froude number contours for F=l (critical flow), F=3 and F:=5.SS0oo(b) 6OO (c) C02•14-1210-86-4—-= 30• I I ‘ I0 2 4 6 8 101214160distance (km)‘2-0‘ I I ‘ I ‘ I2 4 6 8 1012141693‘ \\‘‘I4 144_...lI-l4 \‘i4‘:k\:JUiflfth+1414444 1\\\‘-SS - 1 4 1 / t114 \ 4• I/’y’——I IIII - LI I 4 4• — ‘fI’ 41• ‘I ‘141I - •:-‘. I 4 1•1IlI,._ .41• I I I I ‘— •— IIt I’ III,, I’ I 4•1(aFigure 20: 3D Model. Case 4 - Q=L, hf=L, dP/dx=H(a) Horizontal velocity vectors. Reference arrow represents 30 m/s windspeed.(b) Depth contours. Interval is 200 m and the 0 m contour is not shown.(c) Froude number contours for F=1 (critical flow), F=3 and F=5.94oj11(b (c)4 II4’’4’’4’’4 II441•14-12•10-86-42-0‘ I ‘ I ‘ I I I I I ‘ I I I I I0 2 4 6 8 101214160 2 4 6 8 101214160 2 4 6 8 10121416distance (km)= 30‘—I,‘‘‘/,I’f14fI,,, f• :w.II I III II— I I• I IfI. II.. IIf IIII I III(a) 1111II I‘ I ‘ I I I I—0 2 4 6 8 10121416= 30Figure 21: 3D Model. Case 5 - Q=L, hf=H, dP/dx=L(a) Horizontal velocity vectors. Reference arrow represents 30 m/s windspeed.(b) Depth contours. Interval is 200 m and the 0 m contour is not shown.(c) Froude number contours for F=l (critical flow), F=3 and F=5.954000 800’1k1Q00(b) 0‘ I I I10-86-4(c)0 2 4 6 8 101214160distance (km)2-0‘ I ‘ I I ‘ I2 4 6 8 10121416iti1 i’’‘11I ‘ /I I‘ iIk\‘I‘I‘I‘‘‘(‘‘S• 5’,’’’’‘ ‘(a) HFigure 22: 3D Model. Case 6 - Q=H, h=H, dP/dx=L(a) Horizontal velocity vectors. Reference arrow represents 30 m/s windspeed.(b) Depth contours. Interval is 200 m and the 0 m contour is not shown.(c) Froude number contours for F=1 (critical flow), F=3 and F=5.96500fl\5’‘‘S‘S\ ‘S(I\ \1II II I I I1OOO‘ I I I I-1210-8‘6-42-00 2 4 6 8 101214160 2 4 6 8 10121416distance (km)= 30(c)• I I I I ‘ I0 2 4 6 8 1012141641‘ \\ \I. \‘I—‘I I‘1 .1,‘It •.l I- li..14• 4.-- ‘‘I \\l \\- ‘/ II’ I I-, 4 .‘4 4. 44441.444.• I - -—‘ I 3 4 1 4 4 4.4 I, •!‘‘ II ‘ I I 1 4I I 4’. ‘ 4 1 I 4‘‘I’’’’4 I I 4 4• ‘44444’.44444’‘‘114 Ill‘‘‘4444’I I III 4’(a)‘ I I ‘ I Io 2 4 6 8 10121416= 30--- ooJ6O98OO-‘ I I I I I0 2 4 6 8 101214160distance (km)(c)‘ I I ‘ I ‘2 4 6 8 10121416Figure 23: 3D Model. Case 7 - Q=H, hf=H, dP/dx=H(a) Horizontal velocity vectors. Reference arrow represents 30 mIs windspeed.(b) Depth contours. Interval is 200 m and the 0 m contour is not shown.(c) Froude number contours for F=l (critical flow), F=3 and F=5.I,,’.-.‘114-86-4-2-097-.‘1/lii,‘‘‘S‘ \\\‘ \ \ \.14-. I 4‘I’I %\‘- ‘4 \\\\iii..\\\\\\. —16• I •-5 \ I I‘III 14‘ \ I I I-‘ I\\, —12--‘-.‘\‘ .10I \ -86IIIII I(a)2III_______________-o0Figure 24: 3D Model. Case 8 - Q=L, hf =H, dP/dx =H(a) Horizontal velocity vectors. Reference arrow represents 30 m/s windspeed.(b) Depth contours. Interval is 200 m and the 0 m contour is not shown.(c) Froude number contours for F=1 (critical flow), F=3 and F=5.5250-‘1—-(c)8OOrZ\6 8 10024—p-= 30I ‘[121416I J I J ‘ I J2 4 6 8 101214160distance (km)I J I J I J2 4 6 8 1012141698ç2() 4H-‘V.\.\ .. ... .,.... . _\ rv — \__ —N(a)(b)Figure 25: Microbarograph pen tracings from 28 December 1992 for stations at PorteauCove (a) and Lions Bay (b). The relatively erratic pen behaviour at Porteau Covesupports the existence of a strong hydraulic jump that is present in most modelsimulations.99-


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