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Wind waves and internal waves in Base Mine Lake Hurley, David Lee 2017

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Wind Waves and Internal Waves inBase Mine LakebyDavid Lee HurleyB.S., North Carolina State University 2013A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Civil Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2017c© David Lee Hurley 2017AbstractSyncrude’s Base Mine Lake is the first commercial scale demonstration ofend pit lake technology in the Canadian Oil Sands. Following its commis-sioning in 2012 significant efforts have been made to monitor and understandits evolution. Of particular interest is the impact of surface and internalwaves on the resuspension of fluid fine tailings and the effect of hydrocar-bons on surface wind wave formation and growth. In this study the firstcomplete description of the wind and internal waves in Base Mine Lake ispresented.Observations of surface wind waves were collected using two subsurfacepressure gauges. Data revealed that wind waves in Base Mine Lake haveshort residence times and rarely generate bottom orbital velocities capableof resuspending fluid fine tailings. Additionally, numerical simulations ofthe wind waves in Base Mine Lake were performed with the SWAN model.Modeled wave heights were in good agreement with observations, and re-suspension of fluid fine tailings was minimal even during the 10 year stormevent.As the surface of Base Mine Lake contains a hydrocarbon film its impacton surface wind waves was investigated in the laboratory and field. It wasfound that the hydrocarbon film dampens high frequency wind waves andresults in a slower growing wind wave field dominated by longer wavelengths.Additionally, the presence of hydrocarbons also increases the critical windspeed needed to initiate wave growth. From these findings it is postulatedthat the hydrocarbon film on Base Mine Lake acts to decrease the fluxes ofmomentum, gas, and heat.The internal waves in Base Mine Lake were simulated using Delft3DFlow. Simulated wave heights as large as 3 m were shown to oscillate formultiple days with little dampening, and despite the small surface area ofBase Mine Lake (8 km2) the internal waves were significantly influenced bythe Coriolis force. This influence was seen in the form of simulated Kelvinand Poincare´ waves which resulted in complex circulation patterns withinthe lake. The findings presented here provide a first picture into the impactsof waves on the reclamation of Base Mine Lake.iiLay SummarySyncrude’s Base Mine Lake is the first attempt at reclamation of a pit lakein the Canadian Oil Sands industry. Several lake features, such as increasedamounts of sediment and decreased concentrations of oxygen in the watercolumn, are currently slowing recovery efforts. These features are a resultof mixing, which is often driven by surface wind waves and internal waves,waves that travel below the waters surface. In this study the surface andinternal waves in Base Mine Lake were measured and modeled on a computerand in a laboratory. Results showed that surface waves led to minimalsediment resuspension and internal waves created complex lake circulations.Additionally, a surface oil film on Base Mine Lake slowed the growth andformation of surface wind waves. Ultimately, this research provides a firstpicture into the impacts of waves on pit lake reclamation.iiiPrefaceThis thesis presents the original research of the author, conducted underthe supervision of Dr. Gregory Lawrence and Dr. Edmund Tedford. I per-formed the data collection of Chapter 2 and designed the laboratory andfield experiments of Chapter 4 in collaboration with Dr. Tedford. I wassolely responsible for the design and implementation of the numerical simu-lations in Chapters 3 and 5. A version of Chapter 4 has been submitted forpublication as “Effects of Hydrocarbons on Wind Waves in a Mine Pit Lake”by D. Hurley, E. Tedford, and G. A. Lawrence. I was the lead investigatorfor the work presented in this chapter. E. Tedford assisted in the design andexecution of laboratory and field experiments. I wrote the manuscript andmy co-authors provided comments.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . xii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Study Site . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Thermal Stratification . . . . . . . . . . . . . . . . . . . . . . 51.3 Wind Induced Processes . . . . . . . . . . . . . . . . . . . . 51.4 Thesis Motivation & Objectives . . . . . . . . . . . . . . . . 81.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Measuring Wind Waves . . . . . . . . . . . . . . . . . . . . . . 102.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Subsurface Wave Properties . . . . . . . . . . . . . . . . . . 112.2.1 Pressure Transfer Function . . . . . . . . . . . . . . . 132.3 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . 162.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4.1 Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . 182.4.2 Wave Environment . . . . . . . . . . . . . . . . . . . 19vTable of Contents3 Modeling Wind Waves . . . . . . . . . . . . . . . . . . . . . . 233.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.3.1 Model Calibration . . . . . . . . . . . . . . . . . . . . 263.3.2 Model Validation . . . . . . . . . . . . . . . . . . . . 293.3.3 Resuspension . . . . . . . . . . . . . . . . . . . . . . . 323.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 Effects of Hydrocarbons on Wind Waves . . . . . . . . . . . 374.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2 Historical Background . . . . . . . . . . . . . . . . . . . . . . 384.3 Theoretical Background . . . . . . . . . . . . . . . . . . . . . 384.4 Experimental Method . . . . . . . . . . . . . . . . . . . . . . 404.4.1 Laboratory . . . . . . . . . . . . . . . . . . . . . . . . 404.4.2 Field . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.5.1 Laboratory . . . . . . . . . . . . . . . . . . . . . . . . 434.5.2 Field . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 Modeling Internal Waves . . . . . . . . . . . . . . . . . . . . . 495.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.2 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.2.1 Wind Drag Coefficient . . . . . . . . . . . . . . . . . 515.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.3.1 Rotational Effects . . . . . . . . . . . . . . . . . . . . 565.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606.2 Impacts on Reclamation . . . . . . . . . . . . . . . . . . . . 636.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Appendix C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76viList of TablesTable 3.1 Comparison of simulated and observed wind waves: 2015 28Table 3.2 Comparison of simulated and observed wind waves: 2016 31Table 5.1 Comparison of simulated and observed isotherms . . . 53Table B.1 SWAN parameters . . . . . . . . . . . . . . . . . . . . . 74Table B.2 Delft3D Flow parameters . . . . . . . . . . . . . . . . . 75viiList of FiguresFigure 1.1 Base Mine Lake map . . . . . . . . . . . . . . . . . . . 4Figure 1.2 Lake thermal stratification . . . . . . . . . . . . . . . . 6Figure 1.3 Wind setup . . . . . . . . . . . . . . . . . . . . . . . . 8Figure 2.1 Deep- and shallow-water waves . . . . . . . . . . . . . 12Figure 2.2 Pressure transfer function . . . . . . . . . . . . . . . . 14Figure 2.3 Base Mine Lake bathymetry . . . . . . . . . . . . . . . 17Figure 2.4 Pressure sensor setup . . . . . . . . . . . . . . . . . . 18Figure 2.5 Wave validity diagram . . . . . . . . . . . . . . . . . . 19Figure 2.6 Observed wind waves: 2015 . . . . . . . . . . . . . . . 21Figure 2.7 Observed wind waves: 2016 . . . . . . . . . . . . . . . 22Figure 3.1 SWAN computational domain . . . . . . . . . . . . . . 25Figure 3.2 Simulated wind waves: 2015 . . . . . . . . . . . . . . . 28Figure 3.3 Simulated wind wave spectra: 2015 . . . . . . . . . . . 29Figure 3.4 Simulated wind waves: 2016 . . . . . . . . . . . . . . . 30Figure 3.5 Simulated wind wave fit: 2016 . . . . . . . . . . . . . . 31Figure 3.6 Simulated bottom orbital velocities . . . . . . . . . . . 33Figure 3.7 Forecast bottom orbital velocities . . . . . . . . . . . . 34Figure 3.8 Simulated 10 year bottom orbital velocities . . . . . . 34Figure 4.1 Dispersion relation . . . . . . . . . . . . . . . . . . . . 40Figure 4.2 Laboratory setup . . . . . . . . . . . . . . . . . . . . . 41Figure 4.3 Field setup . . . . . . . . . . . . . . . . . . . . . . . . 42Figure 4.4 Measured wind waves: Laboratory . . . . . . . . . . . 44Figure 4.5 Measure wind wave spectra: Laboratory . . . . . . . . 45Figure 4.6 Measured wind waves: Field . . . . . . . . . . . . . . . 47Figure 4.7 Measured wavelengths: Field . . . . . . . . . . . . . . 47Figure 5.1 Delft3D Z-model computational domain . . . . . . . . 51Figure 5.2 Simulated and observed wind drag coefficient . . . . . 52Figure 5.3 Simulated isotherms . . . . . . . . . . . . . . . . . . . 54viiiList of FiguresFigure 5.4 Simulated 17 oC isotherm . . . . . . . . . . . . . . . . 55Figure 5.5 Simulated Kelvin and Poincare´ waves . . . . . . . . . 57Figure 5.6 Simulated Coriolis effects . . . . . . . . . . . . . . . . 58Figure A.1 Wind sensitivity analysis . . . . . . . . . . . . . . . . 72Figure A.2 Wind Sandhill Fen Site 3 . . . . . . . . . . . . . . . . 73ixList of SymbolsCd Wind drag coefficientco Deep water wave speedd Depth of fluidd1 Depth of upper layerDOY Day Of Yearf Coriolis parameterfs Sampling frequencyfc Cutoff frequencyg Gravitational accelerationg′ Reduced gravitational accelerationH Wave heightHs Significant wave heightk WavenumberKz Pressure transfer functionLR Rossby radius of deformationmn Spectral momentsp Absolute pressurepa Atmospheric pressurepd Dynamic pressurepg Gauge pressureS Spectral energySηη Surface elevation spectrumSpdpd Dynamic pressure spectrumT Wave periodTm01 Mean periodTm02 Average zero crossing periodxList of SymbolsTR Return periodTP Peak periodU∗ Momentum fluxU Wind speedUb Bottom orbital velocityUbs Significant bottom orbital velocityUCr Critical bottom orbital velocityW Noise floorz Distance from free surface (- down)η Surface elevationθ Latitudeλ Wavelengthρ Density of fluidρa Density of airρ1 Density of upper layerρ2 Density of lower layerσ Surface tensionτ Wind stressω Wave angular frequencyΩ Earths rotation ratexiAcknowledgmentsTo my parents, Terry and Beverly. Despite the lighthearted heckling whenI spent too much time in the mountains, I always received your unendingsupport. I am forever grateful to the both of you.My brother Matthew and friends Jack, Ming, Rory, and Will. Your en-couragement of my wanderlust life was only exceeded by your unfalteringsupport when times were tough. Thanks!To my grandmother, M. Metzger. Your interest in my work, encourag-ing attitude, and sense of humor always brightened my day.A recognition to the National Sciences and Engineering Research Councilof Canada (NSERC), Syncrude Canada Ltd., and the University of BritishColumbia for funding my studies.Many thanks to my supervisor Dr. Gregory Lawrence and research asso-ciates Dr. Edmund “Ted” Tedford and Dr. Roger Pieters. You encouragedme to forge my own research and for that I am grateful.A special mention to EFM group members Dr. Andrew Hamilton, KellyGraves, Mark Sumka, and Sam Brenner for entertaining my questions andtolerating my quirks. Additional thanks to Co-op students Simon Fang andJared Zhang for helping me prepare Chapter 4 for publication.To all the folks at Syncrude Reclamation and Closure “Building 578”. Yourday in and day out cheerful moods, even in light of the Fort McMurray fires,were infectious. What a difference it made.A very special thanks to Ted. Without your scientific curiosity and muchwelcomed insight this thesis would not be what it is now. I am extremelygrateful for all the time you devoted to helping me succeed, and for being agreat field partner even when the world was literally on fire.xiiChapter 1IntroductionThe Canadian Oil Sands contain an estimated 166 billion barrels of recover-able oil, making it the third largest known oil reserves in the world (Govern-ment of Alberta, 2016 (retrieved August 3, 2017; Dompierre et al., 2017).However, unlike conventional oil reserves, where the oil deposits are foundin subsurface reservoirs, the oil sands deposits are a below ground mixtureof sand, water, and bitumen (Suncor, 2016 (retrieved August 3, 2017). Bi-tumen, a complex hydrocarbon with a viscosity approximately 100 timesgreater than blackstrap molasses, is extracted with surface and subsurfacemining techniques (Strausz and Lown, 2003; Suncor, 2016 (retrieved August3, 2017). Subsurface techniques, such as Steam Assisted Gravity Drainage(SAGD), use steam to heat the bitumen in situ so that it can then be pumpedto the surface (Suncor, 2016 (retrieved August 3, 2017). Surface mining onthe other hand requires the movement of oil sands from the ground to anextraction facility where hot water is used to strip the bitumen from thesands (Suncor, 2016 (retrieved August 3, 2017). Although less than 20% ofall oil sands are recoverable via surface mining this technique has disruptedvast tracts of land and resulted in large quantities of mine byproducts, suchas oil sands process affected water (OSPW) and fluid fine tailings (FFT)(COSIA, 2014 (retrieved August 3, 2017; Suncor, 2016 (retrieved August3, 2017). In 2013 an estimated 900 km2 of land had been disturbed by oilsands mining and less than 1% had been labeled as reclaimed (Dompierreet al., 2017). Additionally, the sheer volume of oil sands processed in ex-traction plants has resulted in more than 9.8x108 m3 of FFT, making it theworld’s largest deposit of tailings (COSIA, 2014 (retrieved August 3, 2017;Dompierre et al., 2017).As laid out by the Alberta Energy Regulator, land disturbed by surfaceoil sands mining must be returned to an “equivalent capability” (Govern-ment of Alberta, 2016 (retrieved August 3, 2017). However, this mandatedreclamation process is made more complex by several unique features of oilsands tailings. For one, FFT contain measurable concentrations of inor-ganic chemical constituents and organic compounds including residual bitu-men (Dompierre et al., 2017). Additionally, the high water content of FFT,11.1. Study Siteinitially no more than 35% solids by weight, results in low shear strengthswhich, due to the slow settlement and consolidation of the FFT, can persistwell past the lifetime of a mine (COSIA, 2014 (retrieved August 3, 2017). Toincrease FFT shear strength, thereby allowing the FFT to be incorporatedinto terrestrial reclamation landscapes, a number of techniques to speed upsettlement and consolidation rates have been put into practice. These in-clude the addition of flocculants and coagulants, mechanical filtration, andlarge scale centrifugation (COSIA, 2014 (retrieved August 3, 2017). Whilethese techniques are effective at dewatering FFT they are also prohibitivelyexpensive and time consuming.Instead an alternative reclamation strategy for oil sands tailings is tofill a mined out pit with FFT and cap it with a mixture of OSPW andnon-process affected water. This effectively creates what is known as an endpit lake and is an attractive reclamation technique as it does not requirethe treatment of FFT before placement (CEMA, 2012 (retrieved August 3,2017; Lawrence et al., 2016). The goal of an oil sands end pit lake is similarto that of a pit lake in the metal mining industry. They sequester material(FFT) to the bottom and treat process affected water (OSPW) in the watercap. Additionally, given enough time, they can be reincorporated into thenatural hydrologic cycle (Pieters and Lawrence, 2014). However, unlike pitlakes in the metal mining industry, oil sands end pit lakes typically havethin water caps, generally less than 10 m, and the tailings, often FFT, havemuch finer particle sizes. In the future end pit lakes are expected to becomean important aspect of the oil sands closure landscape. Currently there aremore than thirty end pit lakes proposed in oil sands mine closure plans andall will be subject to reclamation requirements (Dompierre et al., 2017).This has motivated a need to understand the water cap physics of end pitlakes as the physical processes present in the water cap have implicationson pit lake water quality and biology.1.1 Study SiteSyncrude’s Base Mine Lake (BML), located 40 km north of Fort McMurrayAlberta, is the first commercial scale demonstration of an oil sands endpit lake (Figure 1.1A). The original mine pit, known as Base Mine, wasdecommissioned in 1994 and divided into an east-in pit and a west-in pit.From 1994 to 2012 the west-in pit was filled with FFT and capped withOSPW. As BML water was used in various mining processes during thisperiod the water cap was maintained between 3 and 5 m thick. In 2012 the21.1. Study Sitefilling of BML was stopped and the end pit lake was commissioned. At thetime of commissioning the surface area of BML was approximately 8 km2,the maximum FFT thickness was near 50 m, and the water cap was increasedto an average depth of 8 m by pumping in non-process affected water fromnearby Beaver Creek Reservoir (Figure 1.1B). Since commissioning the watercap has increased to a maximum depth of 11 m due to dewatering of theFFT. In general the nearshore areas of BML have steep to vertical bed slopes,an artifact of the mine pit. However, along the northern shoreline of BMLa littoral zone, formed when the lake level was raised above the vegetation,is characterized by water depths less than 1.5 m. While this area consistsof flooded vegetation, which naturally acts to reduce wave heights thereforeminimizing sediment transport processes, a breakwater was still considerednecessary. In result a rock breakwater was installed along the edge of thelittoral zone to block surface waves (Figure 1.1B).31.1. Study SiteFigure 1.1: (A) Location of the province of Alberta within Canada. Thelocation of the Syncrude Base Mine Site is indicated by the square in thezoom in of Alberta. (B) Satellite view of Syncrude’s Base Mine with BMLoutlined in yellow. The yellow circle and triangle denote Sandhill Fen Site 3and Beaver Creek Reservoir respectively. The rock breakwater is indicatedby the red line. (C) Bathymetry of BML with the locations of the threeplatforms (P1,P2,P3) and the East Bay (D26) mooring.Currently significant efforts are underway to understand the evolution ofthe physical limnology of BML. As a result, extensive measurements of waterand atmospheric based variables are being taken. On the lake itself threeplatforms (P1, P2, P3) serve as the primary locations for the deployment oftemperature, pressure, and turbidity moorings (Figure 1.1C). Additionally,an instrument mooring is regularly deployed in the East Bay (D26) of BML(Figure 1.1C). Water level measurements are taken at the southwest cornerand surface wind waves are measured along the northeast embankment.Atmospheric variables such as wind speed, direction, and air pressure are41.2. Thermal Stratificationrecorded on the lake at Platform 1 and off-site at Sandhill Fen Site 3 (Figure1.1B,C).1.2 Thermal StratificationLakes in the earth’s mid-latitudes undergo significant temperature fluctua-tions with seasons (Wetzel, 1983). Under summertime heating the surfacewater becomes warmer than the bottom water and the lake becomes ther-mally stratified (Figure 1.2). Additionally, since density decreases with in-creasing temperature the surface water is less dense than the bottom waterand therefore the stratification is stable. As the summer progresses the up-per layers become more uniform in temperature and the thermal gradientsharpens. This area of sharpening is referred to as the thermocline and thewaters above and below are known as the epilimnion and hypolimnion, re-spectively (Figure 1.2). As summer transitions into fall the surface waterbegins to cool and the thermal stratification weakens. Eventually, once thestratification is sufficiently weak, the lake will mix to a uniform tempera-ture and thermal gradients will cease to exist (Figure 1.2). This process ofmixing completely with depth is known as turnover.With the onset of winter the surface water cools faster than the bottomwater and results in a top heavy water column, dense water on top of lessdense water. This thermally unstable stratification will persist until thebottom water reaches 4 oC, the temperature of maximum density. At thatpoint the lake is once again thermally stable and the surface water maycontinue to cool below 4 oC leading to inverse thermal stratification (Figure1.2). In some lakes, such as BML, an ice cover will form and the surfacewater will be kept just above the freezing temperature (Figure 1.2). In springthe surface layers will begin to warm towards the temperature of maximumdensity. Once the surface waters reach 4 oC the lake once again mixescompletely with depth (Figure 1.2). Lakes that experience these turnoverevents twice per year are referred to as dimictic lakes.1.3 Wind Induced ProcessesIn many lakes, including dimictic lakes, wind is the major driver of surfaceand subsurface motions. Initially the wind stress perturbs the lakes surfacecreating small ripples known as capillary waves (Kinsman, 1965). Assum-ing the fetch, speed, and duration of the wind is sufficient these waves willeventually grow into surface wind waves or gravity waves (Kinsman, 1965).51.3. Wind Induced ProcessesFigure 1.2: An idealized annual temperature cycle of a dimictic lake suchas BML. The solid vertical line indicates the temperature profile in eachseason. The dashed horizontal lines denote the location of the epilimnion,thermocline, and hypolimnion. Fall and spring turnover is represented bythe arrow inscribed circle.In most cases the oscillating free surface elevation (η) associated with grav-ity waves is well approximated under linear (Airy) wave theory (Equation1.1)(USACE, 1984).η =H2cos(kx− ωt) (1.1)HereH is wave height, k is wavenumber, and ω is wave angular frequency.This theory, published by George Biddell Airy (1841), treats a prop-agating surface wave as a sinusoid and assumes the fluid is incompressibleand inviscid, the flow is irrotational, and the free surface is uncontaminated.However, as the theory is linear and therefore neglects higher order nonlin-ear terms, its use is generally limited to waves propagating in water depthsmuch greater than their wavelength. Following Airy’s theory a number ofnonlinear wave theories were proposed to account for nonlinear effects ona propagating wave. These include solitary, Stoke’s, cnoidal, and numeri-cal wave theories (Stokes, 1847; Boussinesq, 1871; Wiegel, 1960). Of these,Stokes’ second order nonlinear wave theory has been widely applied to sur-face waves in deep water and has been shown to better reproduce the freesurface elevation of a wave train (USACE, 1984). In this case the oscillatingfree surface is no longer sinusoidal and instead the wave troughs becomeelongated and the crests become compressed (Equation 1.2).η =H2cos(kx−ωt)+(kH216)cosh(kd)sinh3(kd)(2+cosh(2kd)) cos(2kx−2ωt) (1.2)61.3. Wind Induced ProcessesAlong with surface wind waves a wind stress on the free surface cre-ates a surface setup or a piling of water at the downwind end (Figure 1.3A)(Stevens and Lawrence, 1997). In the most basic sense this setup can be rep-resented by a linearly sloped free surface which becomes steeper the greaterthe wind speed (Equation 1.3) (Monismith, 1987; Stevens and Lawrence,1997). Furthermore, if the lake is thermally stratified the surface setup willresult in an opposite setup of the thermocline (Figure 1.3A) (Stevens andLawrence, 1997). However, while the surface setup is generally on the orderof millimeters the magnitude of the internal setup can be a thousand timeslarger (Mortimer, 1952). This is because the density difference across thethermocline is much smaller than the density difference across the air-waterinterface (Equation 1.4)(Stevens and Lawrence, 1997; Mortimer, 1952).dddx=τρ1gd1(1.3)dd1dx=τρ1g′d1(1.4)g′ =ρ2 − ρ1ρ2g (1.5)Where d is fluid depth, τ is wind stress, ρ1 and ρ2 are fluid density aboveand below the thermocline respectively, g is local gravitational acceleration,d1 is depth of upper layer, and g′ is reduced gravity.Once the wind relaxes the surface and internal setups will begin to oscil-late back towards equilibrium (Figure 1.3B). As a result internal waves,gravity waves propagating along the thermocline, are generated. Thesewaves are similar to surface gravity waves, but due to the reduced den-sity gradient across the thermocline their amplitudes are much larger andwave speeds much slower (Mortimer, 1952). The dominant internal wavesoften have wavelengths comparable to or larger than the length of the lake.When this is the case the waves are capable of reflecting back and forthbetween the basin walls without appreciable damping. This oscillation isgenerally referred to as an internal or baroclinic seiche (Mortimer, 1952).These seiche events generate strong horizontal velocities above and belowthe thermocline, a result of large wave amplitudes and wavelengths (Mor-timer, 1952). Additionally the seiche generated velocities are a maximumwhen the deflection of the thermocline from equilibrium is at a minimumand vice versa (Figure 1.3B)(Mortimer, 1952).71.4. Thesis Motivation & ObjectivesFigure 1.3: (A) Idealized surface and internal setup for a two layer lakeresulting from a wind stress. The equilibrium position for the surface andthermocline are indicated by the dashed line. (B) Oscillation of the ther-mocline in the absence of wind. The oscillation of the free surface is quicklydampened and therefore not shown. The direction of the horizontal veloci-ties in the epilimnion and hypolimnion are denoted by arrows.1.4 Thesis Motivation & ObjectivesBoth surface and internal waves play important roles in driving mixing inlakes. Oscillating motions, known as orbital velocities, occur beneath wavecrests and troughs creating localized shear stresses. In nearshore areas sur-face and internal waves break and generate turbulent motions that can ex-tend the depth of the water column. Additionally, internal waves can gener-ate significant circulation patterns at depth and surface waves can enhancenearshore currents as a result of refraction and reflection. At the air waterinterface whitecapping of surface wind waves and upwelling and downwellingassociated with internal waves can enhance the fluxes of gas and heat.81.5. Thesis OutlineThe aim of this research is to provide the first description of the wind andinternal waves in Base Mine Lake through field measurements, laboratoryexperiments, and numerical simulations. The goal is that this initial picturewill help elucidate the impact of wave dependent mixing mechanisms onthe water cap physics and subsequently inform future reclamation decisions.Of particular interest in this study is the consequence of wave generatedbottom orbital velocities on the resuspension of FFT and the effect of surfacehydrocarbons on wind waves.1.5 Thesis OutlineThis thesis is divided into six distinct chapters. Chapter 1 provides an in-troduction to the research along with the motivation for it. This includesan overview of Oil Sands end pit lakes, a description of Base Mine Lake,and a brief literature review on lake stratification, wind waves, and internalwaves. Chapter 2 presents the observed wind waves in Base Mine Lake. Inaddition, the instrument setup is described and the challenges associatedwith measuring wind waves in small lakes is addressed. Chapter 3 discussesthe setup of the SWAN model and displays the model resultant wind waves.The modeled and observed wind wave induced resuspension of FFT is alsodiscussed. Chapter 4 looks to quantify the effect of hydrocarbons on windwaves through field and laboratory experiments. Chapter 5 compares theobserved internal waves to the modeled internal waves from Delft3D Flow.Additionally, the effects of rotation and the parameterization of the winddrag coefficient is examined. Lastly, Chapter 6 provides a concluding sum-mary of the research, some implications of the findings on reclamation ofBML, and suggestions for future work.9Chapter 2Measuring Wind Waves2.1 IntroductionMeasuring the properties of short period wind waves (ω > 0.25 Hz), suchas those found in many inland water bodies, is a non-trivial task. Typi-cally wave parameters such as wave height and wavelength are estimatedfrom either direct or indirect measurements of the surface elevation. In thecase of direct measurements the real surface elevation is recorded using in-struments such as surface piercing gauges, wave-rider buoys, and ultrasonicprobes. However, as most of these instruments are designed for oceanicenvironments they typically sample too infrequently and have too coarsea spatial resolution to resolve high frequency small amplitude wind waves(Hasselmann et al., 1973). Instruments that measure the surface elevationindirectly, through a related property such as pressure or velocity, are po-tentially capable of sampling fast enough to resolve high frequency waves.Though, unlike direct measurements, indirect measurements require the ap-plication of a transfer function to convert the related property to a surfaceelevation signal (USACE, 1984). This conversion is generally done by ap-plying linear and in some cases nonlinear wave theory (USACE, 1984).Numerous studies have shown that linear wave theory can adequatelytransform pressure to surface elevation for long period (Bishop and Donelan,1987; Townsend and Fenton, 1997; Tsai et al., 2005) and in some cases shortperiod waves (Jones and Monismith, 2007). Additionally, this applicationhas been shown to be successful in the presence (Gabriel and Hedges, 1986;Jones and Monismith, 2007) and absence of a mean flow. However, as thefrequency of the waves increase, the instrument noise can begin to dominatethe signal and lead to inaccurate estimates of a wave’s properties. Attemptsto minimize this error by using higher order nonlinear wave theories havebeen made with marginal success (Townsend and Fenton, 1997; Oliveraset al., 2012). Some studies have even looked into the use of empirically de-rived transfer functions to more accurately ascertain the surface elevationsignal, again with mixed results (Wang et al., 1986; Tsai et al., 2002). In-stead Jones and Monismith (2007) found that by identifying the frequency102.2. Subsurface Wave Propertiesof the waves of interest beforehand, the instrument sampling rate (fs) anddeployment depth could be chosen such that linear wave theory was able toreasonably resolve the surface elevation of small amplitude high frequencywaves.The purpose of this chapter is to examine the use of pressure sensors formeasuring high frequency wind waves in BML. Measurements were collectedusing two pressures sensors, sampling at different rates, during various pe-riods in the fall of 2015 and 2016. First the subsurface wave properties arediscussed, and the equation for subsurface pressure, assuming linear wavetheory, is given. Then the challenges and consequences of applying linearwave theory to convert pressure signals generated by small amplitude highfrequency waves to surface elevations is addressed. Lastly the details of thefield campaign and the first ever observations of wind waves in BML arepresented.2.2 Subsurface Wave PropertiesA common way to classify surface waves is by their relative depth (d/λ), aratio of the depth (d) in which they travel to their wavelength (λ) (Kinsman,1965; USACE, 1984). Shallow-water waves have wavelengths much longerthan the depth (λ > 20d) and subsurface velocities, herein referred to asorbital velocities, that move in elliptical paths (Figure 2.1A). Deep-waterwaves have wavelengths less than twice the depth (λ < 2d) and orbitalvelocities that move in circular paths (Figure 2.1B). In shallow water theorbital velocities decay minimally with depth, while in deep water they decayexponentially with depth and are negligible at the seabed. Similarly, thewave generated subsurface pressure, herein referred to as dynamic pressure,follows the same decay with depth. To better understand the decay inamplitude of dynamic pressure with depth the linear wave theory equationfor subsurface pressure, herein referred to as gauge pressure, is examined.In the presence of surface waves gauge pressure, pg = p − pa, where pis absolute pressure and pa is atmospheric pressure, contains a static anda dynamic component (Equation 2.1). The static component, first term inEquation 2.1, increases linearly with depth. While the dynamic component,second term in Equation 2.1, is a result of the oscillating free surface (Equa-tion 2.2). As the amplitude of the dynamic component, pd, measured at agiven depth, may have decayed, a pressure transfer function, Kz, is neededto retrieve the surface amplitude (Equation 2.3).112.2. Subsurface Wave PropertiesFigure 2.1: Orbital velocities due to the deflection of the free surface fromthe mean water level for (A) shallow-water and (B) deep-water waves. Themagnitude of the velocities becomes negligible in deep water at a distanceof half a wavelength below the free surface (z) (B).pg = −ρgz + ρgηKz (2.1)pd = ρgηKz (2.2)Kz(z) =cosh(2pi(z + d)/λ)cosh(2pid/λ)(2.3)Where z is the distance from the free surface (negative is downwards)and η is the surface elevation.For a constant fluid depth, Kz is a function of wavelength. In shallow-water, when wavelength is much larger than the depth, the value of Kzat any distance below the free surface is approximately 1 (Equation 2.3).This results in dynamic pressure signals at the surface and the seabed thatare equal. In deep water, when depth is much larger than wavelength,the expression for Kz tends to e2pizλ−1 . Therefore, the amplitude of thedynamic pressure decays exponentially with increasing distance below thefree surface. Furthermore, at a distance of half a wavelength below the freesurface, when Kz = e−pi, the amplitude of the dynamic pressure will havedecayed to negligible values (Figure 2.1B). This means that a pressure sensorpositioned deeper than half a wavelength below a deep-water wave wouldsense primarily the hydrostatic pressure.122.2. Subsurface Wave Properties2.2.1 Pressure Transfer FunctionGiven a dynamic pressure signal the surface elevation can be found by rear-ranging Equation 2.2. This can be done in time or frequency space. In timespace the wavelength of each individual wave in the time series of dynamicpressure is found using the zero up-crossing method (USACE, 1984). Thena value of Kz can be determined for each wave in the record and applied toEquation 2.2. This results in an estimate of the surface elevation. However,errors introduced during the zero up-crossing method and an incomplete es-timate of Kz across the wind wave spectrum may be problematic. Instead, apreferred method is to perform a spectral analysis on the dynamic pressuresignal, calculate Kz for a range of frequencies, and transform the dynamicpressure spectrum to a surface elevation spectrum (Equation 2.4). Once thesurface elevation spectrum is known the associated significant wave height(Hs), the mean of the highest one-third of waves, can be determined from thespectral moments (Equation 2.6). Additionally, the surface elevation spec-trum can be transformed into a surface elevation time series by mapping thefrequencies back to time space.Sηη(ω) =Spdpd(ω)K2z(2.4)mn =∫ ∞0ωnSηη(ω)dω (2.5)Hs = 4√m0 (2.6)Where Sηη is the surface elevation spectrum, Spdpd is the dynamic pres-sure spectrum, ω is wave angular frequency, mn is the spectral moments,and m0 is the zeroth spectral moment or variance of the surface elevationsignal.Noise AmplificationThe sources of noise in a subsurface pressure signal can be hard to pin-point. Environmental factors such as turbulence and biofouling, and me-chanical imperfections such as vibrations from the power system lead to anonzero noise floor in all subsurface pressure gauges. At high frequenciesthe dynamic pressure signal approaches the noise floor (W ) and the pres-sure transfer function, Kz, tends towards zero (Figure 2.2A). This means asignificant amount of energy (S) in the dynamic pressure spectrum at high132.2. Subsurface Wave Propertiesfrequencies is due to noise. As a result there is an overamplification of en-ergy in this frequency range via Equation 2.4, and an overestimation of thehigh frequency surface elevations and the significant wave height (Figure2.2B). This is especially apparent during calm periods as the wave energyis concentrated at higher frequencies and decays exponentially with depthso that the dynamic pressure spectrum falls below the noise floor a shortdistance beneath the free surface.A number of techniques have been proposed to deal with the overam-plification of high frequency noise. The simplest solution is to analyze onlystorm events, when the peak in the frequency spectrum is clearly discernibleand centered at low frequencies (Figure 2.2A). However, even then an over-amplification of noise at high frequencies will occur (Figure 2.2B). Anotheroption would be to move the subsurface pressure gauge closer to the freesurface, thereby reducing the amount of decay in the dynamic pressure sig-nal. This would increase resolution in the spectrum at high frequencies,but as the sensor may come out of the water in large waves it would fail tocapture storm events. The best solution would be to use multiple subsur-face pressure gauges, with high sampling rates, positioned at various depths.This way each sensor would resolve a specific frequency band and the arrayas a whole would capture a more complete picture of the dynamic pressurespectrum (Jones and Monismith, 2007).Figure 2.2: Dynamic pressure spectrum (Spdpd) with the pressure transferfunction (Kz) shown as a multiplier and the instrument noise floor (W )indicated (A). The estimated surface elevation spectrum (Sηη) from Equa-tion 2.4 (B). Surface elevation spectrum after removing overamplified noisewith a cutoff frequency (fc) (C).As an array of pressure sensors is generally impractical a more typicalway to deal with overamplified noise is through filtering. One method isto remove the noise floor before applying the pressure transfer function.Though in practice, identifying noise due too environmental sources is ex-142.2. Subsurface Wave Propertiestremely difficult. Instead, a more common technique is to choose a highfrequency cutoff (fc) and apply a low-pass filter. As there is no automatedtechnique for choosing the cutoff frequency, it is typically chosen as a pointwhere the energy from the dynamic pressure signal is well above the noisefloor. This effectively removes the overamplified noise, though it comes atthe cost of losing spectral resolution (Figure 2.2C). However, if the wave en-ergy beyond the cutoff frequency is negligible, such as in a storm event, thenlittle error will be introduced into the estimation of the surface elevationsand significant wave heights.NonlinearityIn applying the pressure transfer function to the dynamic pressure spectrumfor deep-water waves (Kz 6= 1), the resulting wave heights (H) in the surfaceelevation signal are larger than those found in the dynamic pressure signal.However, the wavelengths in the surface elevation signal are identical tothose in the dynamic pressure signal. This consequently leads to an artificialsteepening of the waves towards the breaking limit (Equation 2.7).Hλ>17(2.7)As the waves approach the breaking limit they become more nonlinear.Generally this nonlinearity can be minimized with the choice of the cutofffrequency. Regardless, an assessment of the nonlinearity resulting from theapplication of the pressure transfer function is needed to 1) determine if thereare waves exceeding the breaking limit and 2) quantify the error introducedby using the linear wave theory equation for dynamic pressure instead of anonlinear theory.To accomplish this the height and period of every wave in the surface el-evation time series is extracted using the zero up-crossing method (USACE,1984). The wave field can then be mapped onto the wave validity diagramof Le Me´haute´ and Koh (1967). This provides guidance as to what wavetheory (linear or nonlinear) best explains the measured signal and showsthe percentage of waves that exceed the breaking limit. It is worth notingthat the wave validity diagram provides an approximation as to where linearwave theory ends and nonlinear theories begin as the regime lines are notformal.152.3. Data Collection2.3 Data CollectionMeasurements of the wind waves in BML were collected using two subsurfacepressure sensors from October 6-28 2015 and August 15 to October 19 2016.Each sensor was mounted to a steel piling (2” ND) that was located in 3m of water and positioned 8.2 m from the shoreline (Figure 2.3). Duringthe 2015 campaign a single RBR Duo sampling continuously at 6 Hz waspositioned 2.75 m above the lake bed (Figure 2.4). In 2016 an RBR Solosampling continuously at 16 Hz and positioned 2.9 m above the lake bedwas added (Figure 2.4).The shallow mounting of the instruments meant it was possible for themto come above the free surface during large wave events. As a result theinstruments were oriented downward to reduce the potential for surface con-taminants to become trapped on the sensor faces post event. The publishedaccuracy of both sensors is 0.05% of the full scale and the resolution is bet-ter than 0.001% of the full scale. Every three weeks the instruments wereremoved, serviced, and redeployed in less than twenty-four hours.Post deployment it was found that both sensors had recorded subsurfacepressures to be less than atmospheric. To address this a constant pressureoffset for each instrument was found by taking the average of the differencebetween the recorded out of water pressure and the atmospheric pressureduring a 15 minute period. This offset was found to be +0.36 dbar and+0.40 dbar for the 6 Hz and 16 Hz sensors, respectively. Additionally,a phase shift and a spurious signal, occurring once a minute, in the 6 Hzsensor was corrected. The dynamic pressure signal (Equation 2.2) was foundby removing the atmospheric and hydrostatic pressure components from theraw subsurface pressure (p). All data (pressure, water elevation, etc.) wereoversampled to 16 Hz to aid with post-processing.Spectral analysis of the dynamic pressure was performed by dividing thesignal into rectangular windows and performing a fast Fourier transform.In 2015 only the storm events were analyzed (see section 2.2.1) with thewindow length set to the storm length. However, in 2016, with the additionof better deployment protocols, the signal was split into 10 minute windows.In each window a high-pass filter was applied to remove the baratropicwaves (ω < 0.1Hz) and the average depth of the sensor face below the freesurface was computed. Then the pressure transfer function (Equation 2.3)was calculated for each window.162.3. Data CollectionFigure 2.3: Map of BML with contoured depth in meters and the locationof the steel piling with the mounted RBR sensors inset.Lastly, the dynamic pressure spectrum was transformed into a surfaceelevation spectrum (Equation 2.4) and a low-pass filter with cutoff frequen-cies of 1.3 Hz for the 6 Hz sensor and 2 Hz for the 16 Hz sensor was applied.In addition to reasons discussed in section 2.2.1, these cutoff frequencieswere chosen with the instrument depth below the free surface in mind. Forexample, a 2 Hz wave will have a wavelength of approximately 40 cm. Thismeans that 10 cm below the free surface, the location of the 16 Hz sensor,the dynamic pressure associated with a 2 Hz wave will have decayed by afactor of five (Equation 2.3). Therefore, despite a Nyquist frequency (fs/2)of 8 Hz, the 16 Hz sensor was considered unreliable above 2 Hz based onthe sensor depth alone. After filtering, the surface elevation spectrum wasmapped back into a surface elevation time series by performing an inversefast Fourier transform. The standard deviation of the surface elevation ineach window was then calculated and the significant wave height was com-puted by applying Equation 2.6.172.4. ResultsFigure 2.4: Schematic of the instrument setup. The fluid depth is from thelake bed to the mean water level and instrument heights are from the lakebed to the sensor face.2.4 Results2.4.1 NonlinearityAfter estimating the surface elevation the nonlinearity of the resulting waveswas assessed in order to determine the validity of the measurements (see2.2.1). Figure 2.5 showcases the characteristics of the wave properties fromsix distinct storm events during the 2015 campaign. During these stormsthe waves were primarily deep-water waves and exhibited mostly nonlinearcharacteristics. However, none of the waves during these periods exceededthe breaking limit. Additionally, the ratio of the linear dynamic pressureto the Stokes second order dynamic pressure (USACE, 1984) is shown asa percent error. As expected the closer you get to the breaking limit thesteeper and more nonlinear the waves become and the more error you incurby assuming a linear equation. Despite this the maximum error is 4%, in-dicating that linear theory is a safe assumption even when nonlinear wavesexist. Ultimately this means that the difference between the estimated sur-face elevations using linear and nonlinear theories is also less than 4%.182.4. ResultsFigure 2.5: The wave validity diagram of Le Me´haute´ and Koh (1967) withthe wave properties from six storm events in 2015 shown as dots. Deep-water and transitional-water waves, separated by the vertical dashed line,are divided into linear and nonlinear wave regimes. The breaking limit isindicated by the topmost line. The ratio of the linear dynamic pressureto the Stokes second order nonlinear dynamic pressure (USACE, 1984) isindicated as a percent error.2.4.2 Wave EnvironmentThe observed wind waves and meteorological conditions on BML for the 2015and 2016 campaigns are shown in Figure 2.6 and Figure 2.7, respectively.All dates from this point forward are displayed as day of year (DOY) whereday of year 1.5 is January 1 at noon. During both years, winds greater than5 m/s were predominately from the southwest through northwest quadrant,and to a lesser extent from the north (Figure A.2). The westerly windswere aligned with the longest fetch to the instruments and produced thelargest waves at the sensors (Figure 2.6, 2.7). This was the case even whenthe wind speed during a westerly was slower than non-westerly periods, asshown in box ii of Figure 2.7. The short fetch from the eastern shorelineto the instruments meant that winds from the southeast through northeast192.4. Resultsproduced only small waves at the sensors, regardless of wind speed. This isreadily visible in shaded region i of Figure 2.7.In 2015 there were six distinct storm events (a-f) that produced waveswith a peak period of approximately 2 s and significant wave heights rang-ing from 5 to 38 cm (Figure 2.6). The maximum wave height in the recordoccurred during storm a and was approximately 60 cm which correspondsto a significant wave height of approximately 38 cm (Figure 2.6A). In com-parison the theoretical fetch limited significant wave height and peak period(USACE, 1984), using the maximum observed wind speed of 12 m/s and afetch of 3 km, is 33 cm at 2 s. As described in detail in section 2.2.1 andsection 2.3 only the storm events were analyzed leading to exaggerated calmperiods in the remainder of the record. One feature of particular interest isthe three hour calm period between storms b and c (Figure 2.6A). It is likelythat there was a shift in the wind direction, a relaxation of the wind speed,or both that was too fine to be resolved by hourly average wind parameters.Additionally, this shows that unlike larger bodies of water where wind wavesand swell can exist for days or weeks the waves in BML quickly dissipate.During the 2016 campaign the wind waves had a peak period of 2 s andsignificant wave heights that ranged from 0 to 30 cm with a maximum waveheight of approximately 70 cm (Figure 2.7). Both the 6 Hz and 16 Hz sensorsshowed similar wave heights with only minor variations due primarily todifferences in instrument depths (Figure 2.7A,B). In large wave events, boxi Figure 2.7A, the proximity of the 16 Hz sensor to the free surface meantit came out of the water, notice the wave troughs are much smaller thanthe wave crests. There are also more small amplitude wave events in the2016 record (Figure 2.7A,B) than in the 2015 record (Figure 2.6A). This isan artifact of better data processing and shallower instrument deployments(see section 2.3).202.4. ResultsFigure 2.6: The estimated estimated surface elevation (A) showing six dis-tinct storm events (a-f). Measurements of the hourly average and dailymaximum (·) wind speed (B) and direction (C) at Sandhill Fen Site 3 (seeFigure 1.1)212.4. ResultsFigure 2.7: The estimated surface elevations from the 16 Hz (A) and 6 Hz(B) sensors. Measurements of the hourly average and maximum (·) windspeed (C) and direction (D) at Sandhill Fen Site 3 (see Figure 1.1). The greyboxes indicate features of interest. Notice that the 16 Hz sensor comes outof the water during large wave events (ii). Easterly winds fail to generatewaves at the sensors (i) while westerly winds, even at relatively slower windspeeds, generate the largest waves due to the large fetch (ii).22Chapter 3Modeling Wind Waves3.1 IntroductionIn order to elucidate the role of wind generated surface waves on physicalprocesses, such as sediment resuspension and shoreline erosion, a descrip-tion of the wind wave field beyond a point measurement is critical. Oftenthis is accomplished in one of two ways. The first, and most basic way, isto estimate significant wave heights and associated peak periods with a onedimensional fetch based model. Typically, due to the complexity of the windwave processes, these models are based on semi-empirical relationships (Oz-eren and Wren, 2009). This has resulted in numerous field studies conductedin ocean (Hasselmann et al., 1973) and coastal (Sverdrup and Munk, 1947;Bretschneider and Reid, 1954) environments as well as large (Schwab et al.,1984) and small (Ozeren and Wren, 2009) inland water bodies to determinethe relation between wave growth and the wind. However, as these modelsare a function of only wind speed, duration, and fetch they don’t account forthe effects of shallow water processes and bathymetry on the surface waves.Instead, a more complete picture can be achieved with a third genera-tion wave model. These models simulate the wind wave field by solving thespectral action balance equation allowing the two dimensional wave spec-tra to evolve without constraints on spectrum shape or energy (Tolmanand Chalikov, 1996). Among the many third generation wave models avail-able the most widely used are SWAN (Simulating WAves Nearshore), WAM(WAve Model), and WaveWatch III. SWAN, developed for coastal applica-tions, simulates wave parameters at a high spatial and temporal resolution,accounts for shallow water processes such as diffraction, refraction, shoal-ing, and breaking, and allows for spatially varying winds (Booij et al., 1999).SWAN has been applied and validated in coastal areas (Booij et al., 1999),bays of complex geometry (Lowe et al., 2005; Hoeke et al., 2011) large lakes(Jin and Ji, 2001), and estuaries in the presence and absence of a mean flow(Gorman and Neilson, 1999).While some studies have used SWAN to simulate waves in small bodiesof water (Seibt et al., 2013) it has generally been assumed that one dimen-233.2. Model Setupsional fetch based models are sufficient. However, a recent study by Seibtet al. (2013) showed that SWAN more closely matched the observed wavefield in the nearshore zone of a medium sized lake when compared to a fetchbased model. In the nearshore zone sediment resuspension is heavily influ-enced by surface wave induced motions at the bed (Lawrence et al., 1991;Wiberg and Sherwood, 2008). These motions, known as a waves bottomorbital velocity, are directly proportional to wave height and dependent onwave period (Lawrence et al., 1991; Wiberg and Sherwood, 2008). Whilebottom orbital velocities can be estimated from statistical wave parame-ters, such as significant wave height and peak period, it has been shownthat estimates using the full wave spectrum are more accurate (Wiberg andSherwood, 2008). Therefore, as fetch based models do not resolve the fullwave spectrum and can lead to inaccurate estimates of wave heights in thenearshore zone a third generation wave model such as SWAN is preferredwhen estimating resuspension rates at various depths.In this chapter the wind waves on BML are simulated in SWAN andcompared to the wave observations from the 2015 and 2016 sampling periods.First the model setup is described and then the results of the simulationsare presented. Next, the model predicted sediment resuspension is comparedwith an estimate of resuspension based on the observed wave field. Thenthe model estimated sediment resuspension at all depths in BML during twowave events is shown. Lastly, the general findings and implications of thewind waves on sediment resuspension are discussed.3.2 Model SetupThe SWAN model, incorporated into Delft3D (WL—Delft Hydraulics), wascalibrated to BML during the October 9-23 2015 sampling period and val-idated during the August 16 to October 14 2016 sampling period. In bothperiods the wind waves were simulated on a computational domain coveringthe extent of BML and consisting of a rectangular grid with a resolutionof 50 × 50 m (Figure 3.1). Additionally a nested domain with a resolu-tion of 5 × 5 m extending outwards from the location of the RBR pressuresensors helped resolve the nearshore wave properties (Figure 3.1). Modelbathymetry was interpolated from single beam sonar data with 2 m reso-lution to the computational and nested domains. Since SWAN models thewaves as an evolving two-dimensional wave spectrum the spectral resolutionin frequency and direction space must be predefined. In this study SWANwas prescribed 72 frequency bins ranging from 0.25 to 3 Hz and 36 direc-243.2. Model Setuptional bins with constant 10 degree spacing. This spectral resolution wasfound to provide the best fit in the 2015 calibration period. Additionally, thefrequency resolution extended to higher values compared to other studies asthe wind waves in small lakes have shorter periods than those in coastalenvironments.Figure 3.1: The computational domain for BML with the boundaries of thenested domain denoted by the three sided box and the location of the RBR’sindicated by the black dot. The thick line along the northern boundarydenotes the location of the littoral zone parameterized in SWAN.During the 2015 and 2016 simulations the model was run with a timestep of 60 minutes and forced with hourly average wind speed and directionrecorded at Sandhill Fen Site 3. In both years the computational domainwas prescribed a constant wind field which was justified given the smallsurface area of BML. Additionally, as Sandhill Fen Site 3 is located approxi-mately 1.5 km from the lake a sensitivity analysis between the BML CentralPlatform and the Sandhill Fen site was carried out (Figure A.1). It wasfound that in general there is little difference between the two meteorolog-ical stations. The effects of a littoral zone and a submerged breakwater onthe waves was parameterized in SWAN (Figure 3.1). This was done by pre-scribing a line of grid cells in which the waves would be allowed to transmit253.3. Resultsno more than 50% of their energy across. Additionally, the flux of waveenergy across the boundaries and reflections at the boundaries were consid-ered to be zero. During the 2015 simulation the model value for diffractionwas calibrated while all other parameters were left as default (Table B.1).The model output of significant wave height, peak period, significant bottomorbital velocity, and 1D wave spectra at the location of the RBR pressuresensors was recorded hourly.Computational ModeWithin SWAN a simulation can be performed in the stationary or non-stationary mode. In the stationary mode the time derivatives are droppedfrom the spectral action balance equation and the model solution convergesto a steady state in every time step (SWAN Team et al., 2011). The non-stationary, or quasi-stationary mode, does not ignore the time derivativesso that the model solution at each time step is a function of the previoustime steps solution. In other words a stationary model predicts a wave fieldsimilar to that of a fetch limited model while a quasi-stationary model doesnot.The decision to use the stationary or nonstationary mode depends ona number of factors. One consideration is that if the time needed for awave to propagate through the computational domain is much less thanthe timescale on which the wind changes then the stationary mode can bechosen. It has been found that in general when the domain is less than 100km then the stationary mode assumption is valid (SWAN Team et al., 2011).In all other cases the nonstationary mode is necessary. For this study theSWAN simulations were always performed in the stationary mode.3.3 Results3.3.1 Model CalibrationComparison of the simulated and observed hourly significant wave heightsduring the 2015 sampling period are shown in Figure 3.2A. The SWAN sim-ulation reproduces the timing and height of the observed wind waves duringthe six storm events (a-f) with reasonable accuracy. This is especially truewhen the wave heights during an event have a distinct maximum (Figure3.2A a,d-f). In more complicated events, when there are multiple local max-imums in the wave height, the model begins to deviate from the observations(Figure 3.2A b,c). Notice that the rate of change of the model wave heights263.3. Resultsduring a storm event is nearly identical to the rate of change of the corre-sponding wind speed. For example, the modeled waves in storm a go fromnear 0 cm to above 30 cm and back to near 0 cm at the same rate that thewind goes from 1 m/s to greater than 8 m/s to less than 5 m/s. Similarly,the modeled wave heights in storm b go from approximately 10 cm to 20cm at the same rate that the wind increases from approximately 5 m/s to 7m/s. However, the observed waves do not follow this same relationship. Infact in all six storm events the observed wave heights increase from near 0cm to a maximum very quickly, regardless of the rate of change of the windspeed.Outside of the storm events, when the observed waves fall below approx-imately 10 cm, the model generally overestimates the wave heights (Figure3.2). In some cases, such as DOY 284.6, the model overestimates by only afactor of two, but in other times, such as DOY 288.6 and 292.2, the modelpredicts waves when there are none observed. In both DOY 284.6 and 292.2the wind speeds are approximately 2 m/s, but the wind direction is from thesouth and the east respectively. This difference in wind direction explainsthe smaller observed and modeled waves on DOY 292.2 compared to DOY284.6, remembering that the fetch to the RBR pressure sensors is shortestduring an easterly. However, it does not explain the overestimation by themodel during an equivalent time step (see 3.4).To assess the model performance during various events the mean signif-icant wave height and model fit, expressed as the root mean square error(RMSE) and model skill (Willmott, 1982), are presented in Table 3.1. Themodel skill, also known as the index of agreement, yields a value of 1 whenthe observations and model results are in perfect agreement and a value ofzero when they are in complete disagreement. It is worth noting that whilethe dimensionless skill values can be compared between events the RMSEvalues cannot. In five of the six storm events (a,c-f) the model skill was muchgreater than 0.5 indicating that the modeled and observed wave heights weregenerally in good agreement. Moreover, in storm event a the similarity ofthe observed and modeled mean significant wave height along with the highmodel skill and low RMSE value indicate an extremely accurate prediction.This is also seen, to a lesser extent, in storm events d-f. The low modelskill and high RMSE value associated with events less than 10 cm furtherillustrates the models tendency to overestimate small amplitude waves.While the significant wave height provides a rough idea of the statisticaldistribution of wave heights during a given window in time a more completepicture of the wind wave field is achieved with the wave spectrum. In Figure3.3 the observed and modeled wave spectra, with energy spectral densities273.3. ResultsFigure 3.2: Simulated (—) and observed (—) significant wave heights (A)along with daily maximum wind speed (·), hourly average wind speed (B),and direction (C) during the 2015 sampling period. The length of each ofthe six storm events (a-f) is indicated by a thick black line at the top. Thevertical dashed lines from left to right indicate DOY 284.6, 288.6, and 292.2respectivelyTable 3.1: Statistical comparison of the observed and modeled significantwave heights in 2015 during storm events and in calm periods.Hs Mean (m)Event Field Model Hs RMSE (m) Hs Skilla 0.129 0.124 0.054 0.949b 0.188 0.161 0.074 0.538c 0.171 0.142 0.064 0.732d 0.091 0.145 0.062 0.778e 0.105 0.148 0.052 0.758f 0.114 0.151 0.057 0.818≤0.1 m 0.010 0.057 0.055 0.484283.3. Resultsbelow 1.5 × 10−2 m2/Hz removed, is presented. A high value of the energyspectral density represents large wave heights. Additionally, the distributionof energy indicates the wave periods present in an event with the maximumin energy corresponding to the wave field’s dominant period. During thesix storm events (a-f) the phase of the simulated spectra (Figure 3.3B) isinline with the observed spectra (Figure 3.3A) and for the most part thedistribution of energy across periods is comparable. However, as the modeloverestimates small amplitude waves, the simulated wave spectra shows en-ergy outside the storm events that is not present in the observed spectra.Additionally, events b and c, which showed the poorest match in Table 3.1,have much more variability in spectral energy in the observed spectra thanthe modeled spectra. Furthermore, the observed spectra in general indicatesa larger range of wave periods present than the modeled spectra.Figure 3.3: Comparison of the observed (A) and modeled (B) wave spectraduring the 2015 sampling period. All spectral energy below 1.5 × 10−2m2/Hz has been filtered out. High spectral energy indicates larger waveheights than lower spectral energy. The dominant wave period during agiven time interval is associated with the peak in the energy of the wavespectra.3.3.2 Model ValidationThe observed and modeled significant wave heights during a 24 day subsetof the 2016 sampling period are shown in Figure 3.4A. Parallel to what293.3. Resultswas observed in the 2015 model calibration the SWAN model overestimatessmall amplitude waves, but accurately predicts the magnitude and durationof storm events. Furthermore, the influence of the wind direction once againappears to play a large role in the agreement between the modeled andobserved significant wave heights. Notice that when the fetch length is short,such as when the wind is from the southeast through northeast sector, themodeled waves vary the greatest from the observations. Additionally, asseen in the 2015 modeling results, the model skill decreases as the numberof peaks in a storm event increases. For example, notice the near perfect fitof the storm event at DOY 261 compared to the storm event at DOY 277.Figure 3.4: Simulated (—) and observed (—) significant wave heights (A)along with daily maximum wind speed (·), hourly average wind speed (B),and direction (C) during the 2016 sampling period. The vertical dashedlines indicated DOY 261 and 277, respectively.To further address the models tendency to overestimate small amplitudewaves a scatter plot of the observed versus modeled wave heights is shownin Figure 3.5. It is clear that when the observed waves are less than 10 cmthe model overestimates wave heights, and the smaller the observed waveheights are the greater this overestimation is (Figure 3.5). Discussed indetail in section 3.4, this overestimation is likely a result of inaccurate wind303.3. Resultsinputs, poor model resolution at high frequencies, or potentially the modelnot accounting for the dampening effect of hydrocarbons on high frequencywind waves. In contrast, when the observed waves are greater than 10 cmthe model accuracy improves dramatically (Figure 3.5). This point is furtherenforced by the statistics presented in Table 3.2.Figure 3.5: Observed versus modeled significant wave heights during the2016 sampling period. The dashed line indicates a 1:1 ratio or perfect agree-ment of the model.Table 3.2: Statistical comparison of the observed and modeled significantwave heights during the 2016 sampling period.Hs Mean (m)Event Field Model Hs RMSE (m) Hs SkillAll 0.026 0.063 0.040 0.731≤0.1 m 0.014 0.058 0.054 0.479>0.1 m 0.155 0.152 0.029 0.857313.3. Results3.3.3 ResuspensionThe linear wave theory expression for bottom orbital velocity, Ub, is given inEquation 3.1. Although this leads to an adequate estimation a more accu-rate representation of bottom orbital velocity is achieved by applying Equa-tion 3.1 to the surface wave spectrum (Wiberg and Sherwood, 2008). Thissubsequently results in a spectral estimate of the bottom orbital velocity(Equation 3.2). From Equation 3.2 the significant bottom orbital velocity,Ubs, analogous to the significant wave height, can be found (Equation 3.3).Ub =piHT sinh(kd)(3.1)Ub =√2∫ ∞04pi2T 2 sinh2(kd)Sηηdω (3.2)Ubs =√2Ub (3.3)A comparison of the modeled and observed significant bottom orbitalvelocities at the location of the RBR pressure sensors, approximately 3 me-ters deep, during the 2015 and 2016 sampling period are shown in Figure3.6. To asses when resuspension occurred a laboratory determined criticalbottom orbital velocity, UCr, of 5 cm/s for FFT is denoted (Lawrence et al.,1991). In 2015 spikes in the significant bottom orbital velocity were associ-ated with the six storm events (a-f) (Figure 3.6A). However, in the observedorbital velocities only storm event a lead to resuspension and the modelpredicted orbital velocities never exceeded the critical threshold. Notice theunderestimation of the modeled significant orbital velocities in events b andc and recall that the modeled significant wave heights during these eventswere also underestimated. The significant bottom orbital velocities duringa 24 day subset of the 2016 sampling period were on average less than the2015 period (Figure 3.6B). During this time the observed orbital velocitiesexceeded the resuspension threshold in one storm event and the modeledorbital velocities never exceeded 2 cm/s.To gain an idea of the frequency of resuspension events that occur inBML an extreme value analysis was conducted. The observed significantbottom orbital velocities during the 2015 and 2016 sampling periods thatwere greater than 1.5 cm/s were recorded. Then, to assure statistical inde-pendence, only the largest of these recorded events every 6 hours was kept.This is roughly the time for a storm to pass. From this data set a Gumbeldistribution was fit and the expected occurrence or return period, TR, of a323.3. ResultsFigure 3.6: Simulated (—) and observed (—) significant bottom orbitalvelocities (Ubs) during the 2015 (A) and 2016 (B) sampling periods. Thesix storm events (a-f) in 2015 are indicated (B). The critical bottom orbitalvelocity (UCr) required for resuspension of FFT is denoted.given value of Ubs could be extrapolated to future events. Figure 3.7 showsthe return period of a given significant bottom orbital velocity. As expected,since the duration of the 2015 and 2016 sampling period combined was 68days, the largest observed event in this time frame had an expected returnperiod of 68 days. Additionally, the return period of a bottom orbital veloc-ity equal to the resuspension threshold of 5 cm/s is approximately 23 days(Figure 3.7). The dashed line in Figure 3.7 represents the magnitude of theorbital velocities that are statistically possible given enough time. However,given the fetch limited nature of the waves a bottom orbital velocity greaterthan approximately 15 cm/s in 3 meters of water is highly improbable.The modeled significant bottom orbital velocities on the coarse andnested BML SWAN domains for storm event a and the 10 year wind event(17 m/s) are shown in Figure 3.8. During storm event a the bottom orbitalvelocities in the littoral zone and along selected areas of the shoreline ex-ceed the resuspension threshold (Figure 3.8A). A closer look at the nesteddomain shows that resuspension is concentrated to the immediate shorelineand that bottom orbital velocities are weak just offshore (Figure 3.8B). The10 year wind event creates large wave heights which in turn leads to highbottom orbital velocities. In the littoral zone these velocities exceed 35 cm/sand much of the nearshore areas are above 10 cm/s (Figure 3.8C). Addition-ally, the nested domain shows that velocities directly onshore are upwardsof 20 cm/s and that even offshore the velocities are still near the resuspen-333.3. Resultssion threshold. While the 10 year wind event could be considered rare, itsoccurrence would cause significant sediment resuspension and transport.Figure 3.7: Estimates of the return periods for significant bottom orbitalvelocities. The observed data (·) is fit with a Gumbel distribution (—) andextrapolated to more remote occurrences of Ubs (−−).Figure 3.8: Significant bottom orbital velocities on the coarse and nestedSWAN domains for storm event a (A,B) and the 10 year wind event (C,D).343.4. Conclusions3.4 ConclusionsThe SWAN model was used to simulate the wave heights on BML duringthe 2015 and 2016 sampling periods. In both years the model accuratelypredicted the magnitude and duration of the storm events (HS > 10 cm),but consistently overestimated wave heights during calm periods (HS ≤ 10cm). It was found that the modeled wave heights during a storm eventmatched the observations best when the corresponding wind speed had awell-defined and sharp peak, and the direction had minimal variation andwas out of the Southwest. Additionally, the failure of the model to simulatewave height variations within a storm event on the order of a few hoursis potentially a result of the wind speed and direction sampling rate beingtoo slow. In the future inter-hourly wind data would lead to better modelagreement within storm and calm events alike.The overestimation of small amplitude waves by SWAN has been docu-mented in the literature and attributed to a number of factors (Seibt et al.,2013). In this study there are two factors that present themselves as likelyculprits. The first is that since the wind is measured off-site it does not ac-count for the effects of the surrounding lake topography on the wind speedand direction. For example, a wind from the East measured at the watersurface next to the instruments would be greatly diminished by the adjacentlake embankment, while the off-site wind would have no knowledge of thisreduction. Therefore, it is very probable that the when the wind direction isout of the southeast through northeast sector the wind speed, used to forcethe SWAN model, is an overestimation of the wind that generated the ob-served waves. A meteorological station positioned on the shore adjacent tothe instruments or on the instrument post itself would likely lead to betteragreement between the modeled and observed wave heights in calm periods.The second factor contributing to the overestimation is that the presenceof hydrocarbons on BML has been shown to dampen high frequency windwaves (Chapter 4). As the model does not incorporate this dampening effectit could be that the model predicted wave heights during calm periods arewhat would actually be observed in the absence of hydrocarbons, hence theoverestimation.During the 2015 and 2016 sampling periods the observed waves rarelygenerated bottom orbital velocities capable of causing sediment resuspensionat a depth of 3 m. Additionally, it was found that the return period for aresuspension event in 3 m of water was approximately 23 days. The SWANmodel was used to estimate the significant bottom orbital velocities duringtwo storm events at all depths within BML. It was found that during the 10353.4. Conclusionsyear wind event, when the fetch limited significant wave height approached60 cm, the significant bottom orbital velocities caused resuspension in onlythe nearshore areas and at depths less than 4 m. Therefore, as BML is aformer mine pit with steep sidewalls, there are few areas where the waterdepth is shallow enough for sediment resuspension, due to bottom orbitalvelocities, to occur.36Chapter 4Effects of Hydrocarbons onWind Waves4.1 IntroductionA leading challenge in the oil sands industry is the storage and reclamationof bitumen extraction byproducts such as fluid fine tailings and oil sandsprocess affected water. One potential reclamation strategy is to turn a minedout pit into an end pit lake by backfilling the pit with fluid fine tailings andcapping it with oil sands process affected water (Lawrence et al., 2016).In 2013, Base Mine Lake (BML), became the first full scale demonstrationend pit lake in the oil sands industry. One specific interest in BML is thepresence of hydrocarbons, residual bitumen from the extraction process, onthe lakes surface and their effect on wind waves. It has been observed that,in the presence of hydrocarbons, there is a reduction in surface ripples anda general damping of wind waves. Since wind waves can cause mixing in thewater column, lead to sediment transport and erosion in the nearshore, anddirectly affect the fluxes of gas, momentum, and heat through the air-waterinterface, their modification is key in understanding the reclamation process.While a variety of laboratory studies have been conducted to examine thecalming effect of oil on wind waves (Broecker, 1978; Liu and Lin, 1979), fewfield studies have been performed.In this study we seek to examine the effect of oil on wind waves both inthe laboratory and the field. First a brief history on the effect of oil on wavesis given, then the generation of wind waves on clean and oil contaminatedsurfaces is described, followed by the laboratory and field methods. Theresults of the laboratory and field experiments are then reviewed, and theimplications of a modified wind wave field on physical processes in BML arediscussed.374.2. Historical Background4.2 Historical BackgroundSince ancient times people have been fascinated with the effects of oil onwind waves. Records from the 1st millennium AD describe ships pouring oilon rough seas in order to calm the waves, and over the next 800 years tales ofthe calming effect of oil on water appear sporadically (Fulford, 1968). ThenFranklin et al. published “Of the Stilling of Waves by Means of Oil” whichdrew simple yet important conclusions formed over the course of numerousexperiments, the most famous carried out at a pond in the Clapham districtof South London (Franklin et al., 1774). Franklin, adding only a teaspoonof oil on the windward side of the pond, observed a patch of water, roughlyan acre in size, become still as glass in a short period of time. From thisand other experiments, Franklin concluded that oil prevents the formationof new waves, and reduces the presence of small waves and whitecaps withina swell, but does not affect the height of large waves.During the next century the calming effect of oil on water attracted notonly scientific but commercial interest. Politicians in Britain lobbied forships to carry tanks of oil for discharge in rough weather, and the US Life-Saving Service (the precursor to the US Coast Guard) looked into the use ofoil during rescues (Sparrow, 1883; Giles, 1969). On the scientific side, Aitken(1884) ascertained through laboratory experiments that it is a reduction insurface tension that leads to a diminished number of ripples. Then Pockels(1893) found that while the reduction of surface tension plays a role in wavedamping it cannot be the entire cause. This work ultimately led Reynoldsand Langmuir to postulate that gradients in surface tension are key in thedamping effect of oil on wind waves (Reynolds, 1880; Giles, 1969).4.3 Theoretical BackgroundWhen a wind blows above a critical speed over an undisturbed water surfacesmall ripples known as capillary waves are the first to form (Kinsman, 1965).These waves have wavelengths less than 1 cm and surface tension is thedominant restoring force. As long as the wind continues to blow, and theenergy input from the wind is greater than the rate of energy dissipation, thecapillary waves will grow larger. Once the waves reach a length of 1 cm theybegin to experience the restoring forces of gravity as well as surface tension.Eventually, when the wavelength exceeds 3 cm, the gravity effects dominate,and the waves continue to grow in both length and amplitude until there isa balance between energy input from the wind and energy dissipated.384.3. Theoretical BackgroundAt this point the wind wave field is fully developed and, while the largestwaves cease to grow, new capillary waves form on the wave faces and startthe process anew. This fully developed sea state consists of capillary, gravity-capillary, and gravity waves all with different wavelengths and traveling atdifferent wave speeds. The wave speed, c = ω/k, and wavelength, λ =2pi/k, where ω is wave angular frequency and k is wavenumber, are relatedaccording to the dispersion relation:ω2 =(gk +σk3ρ)tanh(kd) (4.1)where g is local gravitational acceleration, ρ is fluid density, σ is surfacetension, and d is fluid depth. In the case of deep-water waves (d > 0.5λ),the tanh(kd) factor approaches one so that the deep-water wave speed, co,is given as:co =√gk+σkρ(4.2)Using d = 1 m, ρ = 1000 kg/m3 and σ =7.2 × 10−2 N/m, the wavelengthdependence of the wave speed is shown in Figure 4.1. For this case there isa minimum wave speed at a wavelength of 1.73 cm. From this minimum,gravity waves move faster with increasing wavelength, and capillary wavesmove faster with decreasing wavelength.The presence of an oil film does not completely alter the mechanismsof wind wave generation, but does change the energy input and rate ofamplitude dissipation. A reduction in surface tension associated with anoil film increases the critical wind speed needed for wind wave generation(Kawai, 1979). This means that it takes a faster wind to deform the now“smoother” surface and the oil film inhibits the flux of momentum at windspeeds below this critical value. Additionally, the presence of oil leads to anincreased rate of energy dissipation in capillary waves due to a phenomenonknown as the Gibbs-Marangoni effect (Lucassen-Reynders and Lucassen,1970; Behroozi et al., 2007). This results in an enhanced attenuation ofcapillary waves and therefore a shift in the most unstable wavenumber tosmaller wavenumbers. This shift means a developing wind wave field isdominated by waves with longer wavelengths and diminished growth rates(Creamer and Wright, 1992).394.4. Experimental MethodFigure 4.1: The complete dispersion relation for surface water waves. Re-gions A, B, and C refer to the capillary, gravity-capillary, and gravity waveregimes, respectively. The capillary wave regime is defined as surface ten-sion contributing > 75% of the restoring force, and the gravity wave regimeas surface tension contributing < 25% of the restoring force. The minimumphase speed (O) occurs at a wavelength of 1.73 cm4.4 Experimental Method4.4.1 LaboratoryWind waves were generated in an open top rectangular Plexiglas tank (50 x10 x 38 cm) attached at one end to a wind tunnel (50.5 x 10 x 15 cm) fittedwith four flow straighteners (Figure 4.2). The fan produced wind velocitiesof approximately 6 m/s, and the long sides of the trough were raised so thata more uniform wind field could be generated across the water surface. As aresult of the wind, a current moving down the tank at 3 cm/s was observed.The tank was filled with 19 L of tap water and dyed with rhodamine. A smallinflow of water, used to give a continuous overflow, reduced wave reflections404.4. Experimental Methodand prevented the buildup of oil at the downwind end of the tank.Figure 4.2: Diagram of the laboratory setupA green laser was mounted above the tank to illuminate the water surfaceand wave characteristics were measured in the dark by recording the verticaloscillation of the laser light sheet with a Panasonic GH4 camera runningat 90 fps mounted in front of the tank. The pixel location of the recordedinterface was found by identifying the center of mass of light intensity of eachcolumn of pixels (1920 columns). Any remaining noise from the extractedinterface was removed with filtering techniques.To observe the effect of oil on the wind waves, an oil film was createdby injecting extra virgin olive oil (Triolein) from a syringe onto the waterssurface at the upwind end of the tank. This was done after achieving a fullydeveloped wind wave field on a clean water surface. Approximately 5 cm3of oil was injected over 10 s, and dispersed by the wind across the watersurface.4.4.2 FieldTo compare wind wave generation in BML in the presence and absence ofoil, a section of the water surface was isolated from hydrocarbons. A rectan-gular oil boom (4.5 x 6 m), anchored in 4 locations, was deployed around afixed instrument post. The boom arms were constructed with commerciallyavailable foam rods, 7 cm in diameter, and fitted with a weighted plasticskirt that hung 45 cm into the water. During a period when the water sur-face was relatively hydrocarbon free, the boom was deployed and left forthree weeks. The fetch inside the boom was large enough so that capillaryand gravity-capillary waves, both affected by oil, could be generated by the414.4. Experimental Methodwind. Shortwaves generated outside the boom were blocked by the boomarms, but longer waves were able to propagate inside.Figure 4.3: Digital image of the oil boom with analyzed points in the boom(A-C) and outside the boom (D). The wind is from the top right to bottomleft and tree reflections are present in the top of the imageAt intermittent periods throughout the boom deployment, images ofthe water inside and outside the boom were captured with an 8 megapixeldigital camera. Since wave crests and troughs appear as different imagelight intensities, due to differences in light reflection, the wavelengths couldbe determined. It was found that analyzing the waves inside the boomnear the edge of the reflection of a red mooring buoy gave the best contrastand provided more confidence as to the location of the crests and troughs(Figure 4.3). Additionally, in the images, the pixel resolution goes from fineto coarse moving away from the foreground. To correct for this distortion,objects of known length in the foreground and background were chosen andtheir pixel to length ratio were determined. A pixel to length ratio foreach row and column was then assigned through linear interpolation. Each424.5. Resultslocation of the analyzed wave field was chosen far enough away from theboom and instrument station so that wave interference was minimized. Thewind speed and direction during the boom deployment were recorded andthe amount of oil present inside and outside the boom was visually noted inthe images.4.5 Results4.5.1 LaboratoryVisualization of the effect of oil on wind waves generated in the wave flumeis shown in a time-space plot (Figure 4.4a). This figure represents a compi-lation of interface heights observed in 2500 images collected over 28 s (onlythe middle 13 s are shown). During the experiment the wave field under-went four obvious changes in wave characteristics indicated by regions A-D.Initially, before the fan was turned on, the water surface was free of oil andwaves (A). Then, after the fan was started, a developing wind wave field -a wave field that is not yet fetch limited - was observed (B). Since the winddid not impact the water surface for the first 5 cm, and wave reflectionswere present in the last 5 cm, results in these regions were ignored. In ashort time the developing wind wave field transitioned into a fully devel-oped wind wave field and waves propagated with fairly uniform wave speed,wavelength, and amplitude (C). Lastly oil was applied to the water surfaceand immediately the amplitude of the waves decreased at the windward endof the tank (D). After a few seconds, the oil was spread across the tank andthe entire wind wave field was damped out.To better understand the change in wave amplitude during the experi-ment, a time transect at the center of the tank is shown (Figure 4.4b). Noticethe growth of the developing wind waves (A), and that the fully developedwind wave field (C) contains wave packets, a consequence of the dispersionrelation. Upon the addition of oil the wave amplitudes resemble those inthe early stages of a developing wind wave field (D). This is illustrated bythe immediate reduction in amplitude from ±0.15 cm in (C) to ±0.03 cm in(D).To gain further insight into the physical mechanisms at work, 2D wavespectra were computed using the Fast Fourier transform (FFT) function inMATLAB. Comparing Figure 4.5a for the clean surface to Figure 4.5b withan oil film, it is clear that the oil film dampens high frequency waves. This isshown as a reduction in spectral energy above 10 Hz and elimination above20 Hz. In addition, noting that wave energy is proportional to wave ampli-434.5. ResultsFigure 4.4: a) Plot of the deviation of the surface elevation from along thetank with increasing time. The wave characteristics for the (A) calm surface,(B) developing wind wave field, (C) fully developed wind wave field, and (D)wind wave field in the presence of olive oil applied at x = 0 cm and t = 16 s,are shown. Shading represents the wave amplitude with white indicating acrest and black indicating a trough. b) Wave amplitude with time at x = 25cm (−−) (A-D, Figure 4.4a)tude squared, the oil has the effect of diminishing wave amplitudes at allwave numbers. In both Figures 4.5a and 4.5b the theoretical dispersion rela-444.5. Results(a) cleanω(Hz)010203040(b) oil010203040k(cycle/m)0 50 100 150Energy104105(c)Figure 4.5: Spectral analysis of the laboratory generated waves on (a) theclean surface (25-40 cm and 11-15 s from region C, Figure 4.4) and (b) theoil contaminated surface (25-40 cm and 19-23 s from region D, Figure 4.4).Dark colors denote high energy. The dispersion relations (Equation 4.1)using the surface tension of water (-) and olive oil (−−) are overlaid. In(C) the energy at each wavenumber for water (−) and oil (–) surfaces alongwith the peak of the spectrum (*) are showntions on a clean and oil contaminated surface with a 3 cm/s wind generatedflow are shown. The spectral energy in the absence of oil falls remarkablyclose to the theoretical dispersion relation for a clean water surface (Figure4.5a). However, the spectral energy in the presence of oil also seems to fall454.5. Resultscloser to the theoretical dispersion relation for a clean water surface than fora contaminated water surface (Figure 4.5b). This may be because the spec-tral energy in the presence of oil is associated with lower frequency waveswhich are less affected by an oil surface.At each wavenumber in Figure 4.5a and 4.5b the energy was summed overω and plotted in Figure 4.5c. The total energy as a function of wavenumberis plotted in Figure 4.5c. It is clear that all wavenumbers are much lessenergetic in the presence of an oil film. It is also apparent that the peakin the spectrum is shifted from 36 cm−1 (λ = 2.8 cm) on a clean watersurface to 27 cm−1 (λ = 3.7 cm) on oil contaminated surface. This shiftis statistically significant at the 95% confidence level and is qualitativelysimilar to the shift shown in the linear instability analysis of Creamer andWright (Creamer and Wright, 1992). It is somewhat strange that the energyin the longest waves is not the same regardless of the surface contaminationsince oil has little effect on long waves. However, as the waves generatedin the experiment never exceeded a wavelength of 6 cm it is not surprisingthat even the longest waves were still slightly affected by the oil film. If theexperiment were extended to smaller wavenumbers (longer wavelengths) itis likely that these energies would become equal.4.5.2 FieldThe wind wave characteristics at three locations inside the boom (A-C) andone location outside the boom (D) were captured (Figure 4.3). Qualita-tively there were more small ripples inside the boom (A-C) than there wereoutside (D). The wind at this time was blowing from the background to theforeground of the image and so the waves seen at A-C were also propagatingin this direction. At the downwind end of the boom, the image foreground,there was an oil film inside the boom, but not present at A-D (Figure 4.3).This film can also be seen at location D. Looking at a plot of A-D showingnormalized light intensity, it is clear that there are waves inside the boom,but none outside (Figure 4.6). This result matches our visual interpretationof Figure 4.3, and indicates a dampening of the wave field in the presenceof an oil film.To get an idea of the wavelengths present at (A-D) transects in y ofeach plot in Figure 4.6 are shown in Figure 4.7. Inside the boom the wavesexhibit wavelengths ranging from 1.0-1.4 cm (Figure 4.7a-c) which falls tothe left of the minimum in the dispersion relation, indicating that the wavesare governed primarily by surface tension. Outside the boom there are nodiscernible waves and the fluctuations are likely noise (Figure 4.7d).464.5. Results(a)0 2 4y(cm)0510(b)0 2 4(c)0 2 4(d)x(cm)0 5 10 15 20 25 30 35 40 45 5002040Figure 4.6: Plot of light intensity in regions A-D of Figure 4.3. Dark colorsrepresent wave crests and light colors wave troughs. Transects in y (−−)are shown in Figure 4.70 5 10z/z 0-1-0.500.51a0 5 10b0 5 10cy(cm)0 5 10 15 20 25 30 35 40 45 50-1-0.500.51dFigure 4.7: Wavelength transects for Figure 4.6 inside (A,B,C) and out-side (D) the oil boom. Amplitude has been normalized by the maximumamplitude (zo) of transect (a)474.6. Conclusions4.6 ConclusionsThe results of laboratory and field experiments reveal a dramatic changein the observed wind wave field in the presence of an oil film. In bothcases it is likely that the oil film is acting to dampen the flux of momentumthrough the air-water interface, thereby increasing the critical wind speedneeded for wind wave generation as described by theory (Kawai, 1979). Thismeans that to develop a similar wind wave field in BML, as found on a non-contaminated surface, a higher wind speed would be required. The observeddampening of capillary waves suggests that the net flux of momentum acrossthe air-water interface in BML is less than it would otherwise be withoutan oil film. In the laboratory it was found that the addition of oil ontoan already fully developed wind wave field dampened the waves and causecaused a shift in the peak wavenumber to smaller wavenumbers or longerwavelengths.In summary, an oil contaminated surface leads to a wind wave fielddominated by longer wavelength waves that take more time to develop andgrow at a slower rate. Since wind waves are direct drivers of the physicalprocesses in a water body it is postulated that the oil film on BML has notonly decreased the flux of momentum from the wind, but likely affected lakecirculation and the fluxes of gas and heat.48Chapter 5Modeling Internal Waves5.1 IntroductionA large collection of literature exists regarding basin scale internal waves orseiches. However, a vast majority of this work has focused on internal wavesin the open and coastal ocean, bays and fjords, large lakes, and labora-tory environments (Mowbray and Rarity, 1967; Stigebrandt, 1976; Beletskyet al., 1997; Liu et al., 1998). Only a handful of studies have examined in-ternal waves in small and medium sized lakes, such as BML (LaZerte, 1980;Hodges et al., 2000; Pannard et al., 2011). In lakes of this size, where inflowsand outflows are often minimal, basin scale internal waves are in large partresponsible for subsurface motions (Hodges et al., 2000). These motionsimpact the fluxes of gas, heat, and nutrients throughout the water columnand potentially lead to the formation of a turbulent benthic boundary layer(Hodges et al., 2000; Pannard et al., 2011). This turbulent layer can sub-sequently enhance mixing and sediment resuspension in the hypolimnion(Hodges et al., 2000; Pannard et al., 2011). Therefore, in order to param-eterize mixing in a stratified system the internal waves must be correctlymeasured and modeled.The application of 3D numerical models to stratified flows did not be-come practical until the development of turbulence closure schemes in thelate 1970’s (Mellor and Yamada, 1974, 1982). However, these turbulence clo-sure schemes, such as the level 2.5 model of Mellor and Yamada (1982), havein large part been applied to oceanic circulation models. Additionally, it hasbeen shown that in many cases the classical closure schemes underpredictthe depth of the surface mixed layer brought on by wind forcing (Martin,1985). In small and medium sized lakes, where the mixed layer depth di-rectly determines the magnitude of the thermocline setup due to the wind,a wrongful estimation of the surface mixed layer ultimately results in anincorrect prediction of the internal wave amplitudes (Hodges et al., 2000).More recently however, the development of 3D numerical models that moreaccurately determine the mixed layer depth, aptly known as mixed layermodels, have led to increased accuracy in the simulation of internal waves495.2. Model Setup(Hodges et al., 2000). Currently there are a number of 3D mixed layermodels available to simulate internal waves in lakes. Although, only two,the Estuary and Lake Computer Model (ELCOM) and Delft3D Flow, havebeen used with some consistency. In both cases the models have been shownto give similar results in terms of the internal wave amplitudes and periods(Dissanayake et al., 2016).Delft3D Flow (WL–Delft Hydrualics), developed for coastal, river, andestuarine areas, is a multi-dimensional (2D and 3D) hydrodynamic model(Delft Hydraulics, 2006). It calculates non-steady flow in a system resultingfrom tidal and meteorological forcing on a variety of horizontal and verticalgrids. It can be performed in hydrostatic or non-hydrostatic mode, pre-scribed multiple turbulence closure models, and account for the effects ofthe earth’s rotation on flow. It has been used to model storm surges andtsunamis, thermal stratification in lakes, and wave-driven currents amongother things. Additionally, modules for computing sediment transport, wa-ter quality, biological activity, and surface wave formation have been suc-cessfully coupled to Delft3D Flow.In this chapter the internal waves in BML are simulated in Delft3DFlow and compared to internal wave observations from platform 1, 2, andthe D26 mooring during the 2016 sampling period. First the model setupis described and the choice of parameterization for the wind drag coefficientdiscussed. Then the results of the simulations are presented. Next, the effectof rotation on the internal waves in BML is examined. Lastly, the findingsare summarized and the implications of the internal waves on the physicalprocesses in BML is given.5.2 Model SetupDelft3D Flow was applied to BML during a four day period from July 10-142016. The flow was simulated on a horizontal rectilinear grid with a resolu-tion of 50 × 50 m covering the extent of BML (Figure 3.1). A vertical gridwas prescribed using the Z-layer model with 20 layers of resolution vary-ing between approximately 100 cm and 25 cm (Figure 5.1). The resolutionwas finest around the thermocline, free surface, and bed in order to moreaccurately resolve the internal wave amplitudes and shear stresses. Modelbathymetry was interpolated from single beam sonar data with 2 m reso-lution to the horizontal grid. The breakwater implemented in SWAN wasremoved from the flow model for simplicity (see section 3.2).A vertically varying temperature profile taken from platform 3 (P3),505.2. Model Setupand applied uniformly in the horizontal, was used to initialize the model.The model was run with a time step of 30 s and forced with wind speedand direction recorded at Sandhill Fen Site 3. A k- turbulence closurescheme with a background horizontal eddy viscosity and diffusivity of 0.01m2/s and a background vertical eddy viscosity and diffusivity of zero wasused. It was assumed that the effects of heat flux and surface waves on themixed layer depth was negligible. This was deemed reasonable given theshort simulation period and small amplitude of the wind waves. The modeloutput of temperature, a proxy for internal waves, and horizontal velocitywas recorded at platform 2, 3, and the D26 mooring every 2 minutes and forthe entire domain every 5 minutes. A complete list of the model parametersis found in Table B.2.Figure 5.1: Idealized discretization of the vertical flow grid.5.2.1 Wind Drag CoefficientWithin Delft3D Flow a non-uniform wind drag coefficient (Cd) can be pre-scribed based on wind speed. However, choosing wind drag coefficient valuesthat are dissimilar to the empirical values of the system can result in over orunderprediction of the mixed layer depth. Therefore, the wind drag coeffi-cient values at various wind speeds on BML were calculated using measure-ments of the wind speed (U) and the momentum flux across the air-waterinterface (U∗) (Equation 5.1).515.2. Model SetupCd =U∗2U2(5.1)U∗ =√τρa(5.2)Where τ is wind stress and ρa is density of air.Additionally, the observed wind drag coefficient values for BML werecompared to values from the literature for small and medium sized lakes(Figure 5.2). It can be seen in Figure 5.2 that the wind drag coefficient atdifferent wind speeds is generally in good agreement with the literature. Thedisagreement at higher wind speeds is most likely due to the rarity of thoseevents on BML. The model wind drag coefficients were chosen to closelyfollow the observed coefficients while obeying the constraints of Delft3DFlow that no more than 3 slope values can be used (Figure 5.2).Figure 5.2: Observed wind drag coefficient (—) for BML compared toliterature reported values for small lakes indicated by the circles and squares(Wu¨est and Lorke, 2003). The parameterized value of Cd used in Delft3DFlow (—).525.3. Results5.3 ResultsSince internal seiches are simply waves propagating along a density inter-face, specifically the thermocline, their amplitude is equal to the amplitudeof the oscillations of the thermocline. Therefore, isotherms are used to de-pict internal wave height and period. A comparison of the observed andsimulated isotherms in BML is shown in Figure 5.3. During this period thethermocline oscillates between approximately 3 m and 6 m with platform2 exhibiting the largest internal wave amplitudes (Figure 5.3). In general,the periodicity of the simulated internal waves matches that of the observedinternal waves (Figure 5.3). The simulated internal wave amplitudes arein good agreement with the observed amplitudes at platform 3 and D26mooring, but underestimate the amplitude of the wave crests at platform 2(Figure 5.3). Additionally, at platform 3 and D26 the gradient in the ther-mocline present during a wave crest and trough is on average larger thanthe gradient predicted in the simulations (Figure 5.3B,C). This is largelya result of too much mixing in the model which leads to discrepancies inthe mixed layer depth. Notice the apparent increase in surface mixing ordeepening of the mixed layer in the simulation at platform 2 (Figure 5.3D).Table 5.1: Statistical comparison of the observed and modeled isothermsin 2016 using root mean square error (RMSE) and the model skill score ofWillmott (1982).Location Isotherm RMSE (oC) SkillP2 15 0.68 0.7117 0.87 0.6519 1.08 0.72P3 15 0.60 0.7517 0.65 0.7819 1.44 0.59D26 15 0.55 0.8217 0.63 0.8119 0.84 0.75535.3.ResultsFigure 5.3: Observed (A-C) and simulated (D-F) isotherms for platform 2 (A,D), platform 3 (B,E), and D26mooring (C,F). The contour closest to the surface is 21 oC and the contour interval is 1 oC.545.3. ResultsTo more systematically assess the model performance the root meansquare error (RMSE) and model skill score of Willmott (1982) are computed.The skill score or “index of agreement” takes on a value of 1 when thereis perfect agreement between the model and observed data and less than1 when there is disagreement. From the statistics it is evident that thesimulations perform best at D26 and poorest at platform 2 (Table 5.1). Inaddition, the model performs well at platform 3 in deep water but begins todeviate from the observations near the surface (Table 5.1). This deviationis also seen in Figure 5.3B,E.A closer examination of the simulated and observed thermocline is achievedby analyzing an isotherm near the thermoclines center, in this case the 17oC isotherm is chosen (Figure 5.4). At all stations the observed internalwaves achieve a maximum wave height greater than 2 m and at platform2 the waves exceed 3 m. The amplitude and period of the simulated in-ternal waves at platform 3 and D26 are nearly identical to the observedinternal waves (Figure 5.4B,C). At platform 2 the simulated internal wavesare in phase with the observed waves and match the amplitude of the wavetroughs, but underestimate the wave crests (Figure 5.4A). In all 3 locationsthe deviation of the simulated waves from the observed waves increases intime. This is likely attributable to a buildup of numerical error that resultsfrom poor estimates of mixing and a lack of modeled heat flux.Figure 5.4: Simulated (—) and observed (—) 17 oC isotherm at platform2 (A) platform 3 (B) and D26 mooring (C)555.3. Results5.3.1 Rotational EffectsThe effect of the earth’s rotation on flow becomes important when theRossby radius of deformation (LR), a ratio of the wave speed to the Coriolisparameter, is of order or smaller than the length scale of the lake (Equation5.3). In small and medium sized lakes surface gravity waves propagate toquickly to be affected by the earth’s rotation. However, since internal wavespropagate much slower, a consequence of a reduced gravity, their Rossbyradius of deformation is much smaller.LR =√g′df(5.3)f = 2Ωsinθ (5.4)Where g′ is reduced gravity, d is fluid depth, f is Coriolis parameter, Ωis earth’s rotation rate, and θ is latitude.In BML the Rossby radius of deformation is approximately 2.5 km, onthe same order as the long fetch distance of the lake. Therefore, the basinscale internal waves may take the form of rotationally modified gravity wavessuch as Kelvin and Poincare´ waves. The oscillatory motions of Poincare´waves are often indistinguishable from those of a linear seiche. And differonly in that the horizontal velocities associated with Poincare´ waves rotateclockwise with time. Kelvin waves, on the other hand, are boundary trappedwaves that rotate counterclockwise in the northern hemisphere and have awave crest that is located along the boundary and decays exponentiallytowards the center of the basin.Figure 5.5 shows the simulated internal waves and associated horizontalvelocities at a depth 5 m in BML during the period July 10 20:00 to July 1108:00 2016. Initially there is a strong impulse of wind out of the southwestthat leads to a setup of the thermocline, upwelling and downwelling of waterin the southwest and northeast corners respectively, and creates horizontalvelocities indicative of a linear seiche (Figure 5.5A). Once the wind relaxesthe thermocline begins to oscillate back towards equilibrium in the form ofPoincare´ and Kelvin waves. Examining Figure 5.5B-E the internal wavetrough, indicated by the cold water, appears to hug the lake boundary androtate in a counterclockwise direction through time. This is a Kelvin wave.While the internal wave crest also rotates in a counter clockwise direction,indicating a Kelvin wave, it’s amplitude decays faster making it harder todiscern (Figure 5.5B-E). Additionally, the horizontal velocities rotate clock-wise in time and suggest that the basin scale seiche is in the form of Poincare´565.3. Resultswaves (Figure 5.5B-E).In order to better understand the effect of rotation on the internal wavesin BML, simulations with and without the influence of the Coriolis forcewere performed. Figure 5.6 shows the maximum temperature differencethat occurred between the two simulations at a depth of 5 m during theperiod July 10 to July 14 2016. Ignoring the Coriolis force produces largetemperature differences, in some cases 5oC, along the boundaries of BML(Figure 5.6). This is inline with the fact that Kelvin waves, present onlywith the influence of rotation, decay towards the basins center. Therefore,temperature deviations are smaller in the deeper areas of BML where theFigure 5.5: Simulated internal waves and horizontal velocities at a depthof 5 m in BML during the period July 10 20:00 to July 11 08:00 2016. Thetime starts at 0 hours (A) and steps forward in 3 hour increments (B-E).An impulse of wind (UA) at time 0 leads to a setup of the thermocline (A).Once the wind relaxes a Kelvin wave, most easily visualized as the cold(blue) water, begins rotating counterclockwise around the basin (B-E). Ad-ditionally, the horizontal velocities rotate clockwise through time indicatinga basin scale seiche in the form of Poincare´ waves.575.4. Conclusionsinstrument moorings are located (Figure 5.6).Figure 5.6: Effects of rotation on the simulated internal waves at a depthof 5 m in BML during the period July 10 to July 14 2016. The maximumdifference in temperature between the simulations with and without Coriolisforce is expressed in the heat map. The location of the three platforms(P1,P2,P3) and the D26 mooring are shown as grey circles.5.4 ConclusionsDelft3D Flow was used to simulate the internal waves in BML during a fourday period from July 10 to July 14 2016. A comparison of the observed andsimulated isotherms throughout the water column at three locations (P2,P3, D26) showed that the model accurately predicted the periodicity and inmost cases the amplitude of the internal waves. At platform 2 the magnitudeof the observed wave crests along the 17 oC isotherm was significantly largerthan the corresponding wave troughs. In other words the internal wavesat platform 2 were less sinusoidal than the waves at platform 3 and D26.This resulted in the model underestimating the internal wave amplitude atplatform 2.585.4. ConclusionsThe model estimates of the internal wave amplitudes became less ac-curate with time at all locations. This is likely a result of the simulatedmixed layer depth becoming less accurate at each time step and thereforeintroducing numerical error into the following time step. It is plausible thatif heat flux was incorporated into the model the buildup of numerical errorwith time would be reduced. Additionally, empirically determined values ofthe background horizontal and vertical eddy diffusivity and viscosity wouldlikely lead to better estimates of the thermocline thickness and location aswell as the surface mixed layer depth.Typically 3D circulation models use a uniform value for the wind drag.However, it was shown that using a single value to define the wind dragcoefficient is not an accurate parameterization and could result in inaccurateestimates of the surface mixing. Instead, the wind drag coefficient shouldbe varied with wind speed and made to match either some observed valuesor a general function. In the case of BML the observed wind drag valueswere highest at low wind speeds, decreased to a minimum at approximately5 m/s, and increased again at higher wind speeds.Since BML is at a high latitude the impact of the earth’s rotation oninternal wave motions is not negligible. Both Poincare´ and Kelvin waves,forms of rotationally modified gravity waves, were observed in the simula-tions. This was seen as a clockwise rotation of the horizontal velocity field( Poincare´ waves) and a counterclockwise propagation of the internal waveswith their crests and troughs being largest along the lake boundary (Kelvinwaves). Both the rotating wave induced velocities and large nearshore waveamplitudes could potentially cause an increase in shear stress at the bed andtherefore lead to higher rates of sediment resuspension. Therefore, incorpo-rating the earth’s rotation into even small hydrodynamic models is necessaryfor an accurate representation of the internal waves and subsequent circula-tions. In summary the internal waves and circulation in BML are far fromlinear and display complex patterns that are strongly influenced by rotation.59Chapter 6Conclusions6.1 SummaryThe aim of this research was to provide the first description of the wind andinternal waves in Base Mine Lake through field measurements, laboratoryexperiments, and numerical simulations. The goal is that this initial picturewill help elucidate the impact of wave dependent mixing mechanisms onthe water cap physics and subsequently inform reclamation decisions. Ofparticular interest in this study was the consequence of wave generated bot-tom orbital velocities on the resuspension of FFT and the effect of surfacehydrocarbons on wind wave formation and growth.In Chapter 2 the first ever measurements of surface wind waves on BMLwere presented. The data was collected using two subsurface pressure gaugesset up at the northeast end of BML after fall turnover in 2015 and 2016.Post deployment the subsurface pressures were transformed into surfacewind wave amplitudes through the application of linear wave theory. How-ever, due to the short period of the wind waves on BML and the fact thatwave properties, such as pressure, decay exponentially with depth, a largeamount of measured wave energy existed at frequencies contaminated bynoise. Therefore, a cutoff frequency acting as a low pass filter was necessaryto avoid the overamplification of noise which would lead to an overestima-tion of surface wind wave amplitudes. A general procedure for deriving waveamplitudes from subsurface pressures is as follows:1. Find the dynamic pressure signal by removing the atmospheric and hy-drostatic pressure components from the raw signal.2. Calculate the dynamic pressure spectrum by splitting the data into seg-ments of equal length and applying a fast Fourier transform to each window.3. Determine the linear wave theory transfer function, identical across win-dows if the segment length is equal, and apply it to the spectral estimate ofdynamic pressure in each window. This results in a spectral estimate of the606.1. Summarysurface elevation.4. Define a cutoff frequency in which to apply a low-pass filter. In Jonesand Monismith (2007) the suggested cutoff frequency is 12 times the noisefloor. The study at hand chose the cutoff frequency as the frequency of awave that has exponentially decayed by a factor of 5 at the sensor face.5. Map the surface elevation spectrum into a surface elevation time se-ries by performing an inverse fast Fourier transform.The data presented in Chapter 2 revealed that significant wave heights inBML were as large as 40 cm during wind events. Additionally, as the windwaves propagate across the lake in a matter of minutes there is little rampup or down time associated with a storm. Lastly, for preceding reasons, thechoice of sensor sampling frequency and deployment depth is dependent onthe waves of interest and in some cases multiple sensors deployed at variousdepths may be necessary.Chapter 3 attempted to simulate the observed wind waves in BML usingthe SWAN model. In addition, the modeled bottom orbital velocities wereused to determine the potential for resuspension of FFT. The model wascalibrated over a three week period in 2015 and validated to observationsof the surface wind waves during a 2 month period in 2016. In general,the predicted significant wave heights were coincident with and of the samemagnitude as the observed wave heights. However, the model invariablyoverestimated wave heights when the observations dropped below 10 cm. Itis thought that this could be attributed to inaccuracies in the input winds,numerical challenges of simulating high frequency waves, or potentially thedampening of small waves due to hydrocarbons on BML. The latter wouldmean that, because SWAN does not incorporate hydrocarbons, the estimatesof small amplitude waves would not be dampened and therefore be largerthan the observations.Given the small surface area of BML the waves present, outside theimmediate shoreline, are typically deep-water waves and therefore do notfeel the bottom. It was shown that both the simulated and observed bottomorbital velocities rarely reach the critical value needed for resuspension ofFFT. Even in the 10 year wind event the wave heights are so limited bythe fetch of the lake that the corresponding bottom orbital velocities do notcause significant resuspension. In fact this finding is driven home further bythe point that FFT is generally concentrated in deeper areas (>4 m) of thelake.616.1. SummaryIn Chapter 4 the effects of hydrocarbons on wind waves in BML wereexamined in the laboratory and field. This chapter is, to the best of myknowledge, the first attempt to quantify the impact of hydrocarbons onwind waves in a mine pit lake. It is also one of only a few studies to exam-ine the impact of hydrocarbons on wind waves using both laboratory andfield methods. The observed damping of high frequency waves, known ascapillary waves, in the presence of an oil film, olive oil in the laboratory andhydrocarbons in the field, suggested that the net flux of momentum acrossthe air water interface in BML is diminished. Additionally, since capillarywaves are necessary for the development of gravity waves it is expected thatthe gravity wave field in BML takes more time to develop and grows at aslower rate. These findings are made more robust by the similarities of thelaboratory and field results. In both cases the waves being dampened werenear the wavelength at which the minimum phase speed occurs (≈1.7 cm)and where the restoring forces of surface tension and gravity are equivalent.This work helps to explain the observed differences in the wave field betweenBML and a water body without a hydrocarbon film.Lastly, Chapter 5 simulated the internal waves in BML using Delft3DFlow. The simulations were performed during summer stratification andspanned a 4 day period. Results of the simulations at 3 thermistor chains inBML accurately matched the phase and in most cases the amplitude of theobserved internal waves. However, the model consistently underestimatedthe wave crests at platform 2 and deviated from the observed amplitudesat all stations with the addition of time. Contrary to most 3D simulationsof internal waves a non-uniform wind drag coefficient was implemented andbased off observations from BML. It was found that this had a non-negligibleimpact on the mixed layer depth and hence the internal wave amplitudes.Perhaps the most stunning finding of this chapter was the impact of theearth’s rotation on the internal waves in a small lake such as BML. Withoutthe incorporation of the Coriolis force the model produced wrongful esti-mates of the wave amplitudes throughout the domain, but especially alongthe boundaries of the lake. With the Coriolis force the simulated internalwaves took the form of Poincare´ and Kelvin waves. It is likely that theserotationally modified gravity waves not only complicate the lake circulation,but lead to increased rates of mixing throughout the lake.626.2. Impacts on Reclamation6.2 Impacts on ReclamationThe impacts of surface and internal waves on a lakes physical processes aresignificant. They cause sediment resuspension and transport, mixing acrossthe thermocline and air-water interface, and drive local and lake wide circu-lation among other things. Within BML high levels of turbidity throughoutthe water column and near the bed, along with anoxic like conditions duringstratification, present major challenges for reclamation. A short list sum-marizing the potential consequences of waves to reclamation is as follows:1. Given the small amplitudes of the surface waves on BML it is unlikelythat they cause resuspension of FFT. In fact most of the lake during a ma-jority of the time will not feel the surface waves at all due to the completedecay of wave properties before the bed.2. The internal waves in BML are on the order of meters and thereforequite possibly create circulation patterns and near bed orbital velocitiesthat are capable of resuspending FFT.3. Surface waves are important in driving the flux of gases, such as oxygen,across the air-water interface. Therefore, the dampening of wind waves byhydrocarbons is likely affecting the oxygen concentration in the epilimnionand subsequently the hypolimnion.4. The internal waves in BML are rotationally modified and therefore takethe form of Poincare´ and Kelvin waves. In the case of Kelvin waves thereis potential for subsurface wave breaking and upwelling and downwelling inthe nearshore areas of BML. This could lead to increases in turbidity andpotentially resuspension of nearshore FFT.6.3 Future WorkThe findings presented in this thesis have created a strong first descriptionof the surface and internal waves in Base Mine Lake. However, a number ofimprovements to the current work should be made in order to further ourunderstanding of the wave processes. In addition the findings have raisednew research questions that could motivate future research directions.As this was the first attempt to measure the surface wind waves in BMLa few changes to the field design could be made. First, a more complete636.3. Future Workpicture of the wind wave field could be achieved by deploying instrumentsat both ends of the lake. Additionally, instrumentation capable of resolvingwave direction, such as Acoustic Doppler Current Profilers and AcousticDoppler Velocimeters, should be considered. As a consequence of the de-cay of deep-water wave properties with depth a single pressure sensor is notcapable of resolving the entire wave field. Therefore, future setups should in-clude multiple pressure sensors sampling in the same location but at varyingdepths.It was found that SWAN consistently overestimated small wave heights.One reason could be that wind inputs from directions other than the westand southwest, the long fetch directions, are not an accurate representa-tion of the wind present at the pressure sensors. This is likely because thepressure sensors are sheltered by the topography when the winds are fromthe northeast through south sectors. Instead a wind sensor mounted at thelocation of the pressure sensors would provide a more accurate wind fieldand help to determine if the model overestimation of small wave heights isdue to inaccurate wind inputs. Another possibility for the overestimationis that SWAN does not account for reduced surface tension from hydrocar-bons. Therefore, a parameterization of the hydrocarbons impact on windwaves could be implemented in SWAN. In general future work should focuson improving the model estimates of small wave heights by determining thereasons for the overestimation.In the laboratory the effect of hydrocarbons on wind waves should beinvestigated further. Particularly the critical wind speed needed for windwave generation should be determined. This would involve first creating anoil film and then testing a range of wind speeds. In addition, the effect ofhydrocarbons on whitecapping and wave breaking should be examined asthis impacts the fluxes of gas, heat, and momentum through the air-waterinterface. A more robust field experiment should be conducted using pres-sure sensors to measure high frequency waves in the presence and absence ofhydrocarbons. Additionally, time-lapse photographs of the water’s surfacewould help indicate when an oil sheen is present and assist in estimating thecritical wind speed on BML. Lastly, there should also be some quantificationof how thick the hydrocarbon layer is at the time of the measurements. Thiscould be done using optical methods such as laser light absorption.The internal waves in BML were simulated for 4 days. A longer simu-lation covering the entire period of stratification, approximately mid-Maythrough August, should be performed. 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Recurrent internal waves in a small lake: Potential ecological con-sequences for metalimnetic phytoplankton populations. Limnology andOceanography: Fluids and Environments, 1(1):91–109, 2011.R. Pieters and G. A. Lawrence. Physical processes and meromixis in pitlakes subject to ice cover. Canadian Journal of Civil Engineering, 41(6):569–578, 2014.69BibliographyA. Pockels. Relations between the surface tension and relative contaminationof water surfaces. Nature, 48:152, 1893.O. Reynolds. On the effect of oil in destroying waves on the surface of water.Brit. Assoc. Rept. Papers, 50:489–490, 1880.D. J. Schwab, J. R. Bennett, P. C. Liu, and M. A. Donelan. Applicationof a simple numerical wave prediction model to lake erie. Journal ofGeophysical Research: Oceans, 89(C3):3586–3592, 1984.C. Seibt, F. Peeters, M. Graf, M. Sprenger, and H. Hofmann. Modelingwind waves and wave exposure of nearshore zones in medium-sized lakes.Limnology and Oceanography, 58(1):23–36, 2013.B. Sparrow. Annual report of the united states life-saving service. Reportsof Comittees, 427(1), 1883.C. L. Stevens and G. A. Lawrence. Estimation of wind-forced internal se-iche amplitudes in lakes and reservoirs, with data from british columbia,canada. Aquatic Sciences-Research Across Boundaries, 59(2):115–134,1997.A. Stigebrandt. Vertical diffusion driven by internal waves in a sill fjord.Journal of Physical Oceanography, 6(4):486–495, 1976.G. G. Stokes. On the theory of oscillatory waves. Trans Cambridge PhilosSoc, 8:441–473, 1847.O. P. Strausz and E. M. Lown. The chemistry of Alberta oil sands, bitu-mens and heavy oils. Alberta Energy Research Institute Calgary, Alberta,Canada, 2003.Suncor. Process, 2016 (retrieved August 3, 2017). URL http://www.suncor.com.H. U. Sverdrup and W. H. Munk. Wind, sea, and swell: theory of relationsfor forecasting. 1947.SWAN Team et al. swan cycle iii, version 40.85: Scientific and techni-cal documentation. Delft, The Netherlands: Delft University of Tech-nology, digital version available in http://www. fluidmechanics. tudelft.nl/swan/index. htm, 2011.H. L. Tolman and D. Chalikov. Source terms in a third-generation windwave model. Journal of Physical Oceanography, 26(11):2497–2518, 1996.70BibliographyM. Townsend and J. D. Fenton. A comparison of analysis methods for wavepressure data. pages 575–588, 1997.C.-H. Tsai, F.-J. Young, Y.-C. Lin, and H.-W. Li. Comparison of methodsfor recovering surface waves from pressure transducers. In Ocean WaveMeasurement and Analysis (2001), pages 347–356. 2002.C.-H. Tsai, M.-C. Huang, F.-J. Young, Y.-C. Lin, and H.-W. Li. On therecovery of surface wave by pressure transfer function. Ocean Engineering,32(10):1247–1259, 2005.U. A. C. o. E. USACE. Shore protection manual. Coastal EngineeringResearch Center, Vicksburg, MS., 1, 1984.H. Wang, D.-Y. Lee, and A. Garcia. Time series surface-wave recovery frompressure gage. Coastal engineering, 10(4):379–393, 1986.R. Wetzel. Limnology. Saunders Company, 1983.P. L. Wiberg and C. R. Sherwood. Calculating wave-generated bottom or-bital velocities from surface-wave parameters. Computers & Geosciences,34(10):1243–1262, 2008.R. Wiegel. A presentation of cnoidal wave theory for practical application.Journal of Fluid Mechanics, 7(2):273–286, 1960.C. J. Willmott. Some comments on the evaluation of model performance.Bulletin of the American Meteorological Society, 63(11):1309–1313, 1982.A. Wu¨est and A. Lorke. Small-scale hydrodynamics in lakes. Annual Reviewof fluid mechanics, 35(1):373–412, 2003.71AppendicesAppendix AThe wind speed and direction recorded at Sandhill Fen Site 3 was comparedwith the values recorded at the BML Central Platform during a one yearperiod (Figure A.1). In general the wind speed at Sandhill Fen Site 3 is rep-resentative of the wind speed at the BML Central Platform (Figure A.1A).However, at high wind speeds the Central Platform values are greater thanthe Sandhill Fen values. This is likely because the Central Platform is overwater and therefore the wind drag coefficient, Cd, is reduced. The winddirection at the Sandhill Fen also agrees well with the wind direction at theCentral Platform during much of the year (Figure A.1B).Figure A.1: Comparison of the wind speed (A) and direction (B) recordedat Sandhill Fen Site 3 and the BML Central Platform. The dashed linerepresents the 1:1 ratio. Notice that a direction of 360o is identical to adirection of zero.To get an understanding of the direction that the wind speed came from72Appendix Aduring the 2015 and 2016 sampling periods a compass plot is shown in FigureA.2. During both sampling periods the wind was primarily out of either theSouthwest, Southeast, or North (Figure A.2A,C). Furthermore, wind speedsin excess of 5 m/s were largely from the Southwest through North sector.This is inline with the long fetch of BML.Figure A.2: The observed hourly average wind direction and speed at Sand-hill Fen Site 3 for the 2015 and 2016 campaigns. The total record for the2015 (A) and 2016 (C) campaigns along with winds greater than 5 m/s for2015 (B) and 2016 (D). The inner radius represents 6 m/s and the outerrepresents 12 m/s. The wind direction is the direction in which the wind isfrom.73Appendix BAppendix BTable B.1: SWAN model parameters after calibration to the 2015 observedwave heights.Model Parameters Parameter Value# Frequency Bins 72Min Frequency 0.25 HzMax Frequency 3 Hz# Direction Bins 36Direction Range 360oDensity of Water 1001 kg/m3Depth Induce Breaking TrueBreaking Alpha 1.00Breaking Gamma 0.73Bed Friction Type JONSWAPBed Friction Coefficient 0.067 m2/s3Diffraction TrueDiffraction Coefficient 0.15Whitecapping KomenWave-wave Interactions TrueRefraction TrueWave Energy Dissipation 3D74Appendix BTable B.2: Delft3D Flow model parameters.Model Parameters Parameter ValueLatitude 58o N∆t 30 s# Z layers 20Density of Water 1001 kg/m3Air Density 1 kg/m3Salinity 31 pptCd (0-1.75 m/s) 0.04Cd (1.75-5 m/s) 0.002Cd (5+ m/s) 0.0012Chezy Roughness (U/V) 130Slip Condition FreeHorizontal Eddy Viscosity 0.01 m2/sHorizontal Eddy Diffusivity 0.01 m2/sVertical Eddy Viscosity 0.00 m2/sVertical Eddy Diffusivity 0.00 m2/sTurbulent Closure Scheme k-Heat Flux None75Appendix CAppendix CThis script converts a time series of absolute subsurface pressure (p) intoa time series of surface elevation (η) following the procedures layed outin Chapter 2, Jones and Monismith (2007), and Wiberg and Sherwood(2008). All variables in the code are inline with the variables presented inthe thesis. The script should only be used for deep-water waves as it calcu-lates the pressure transfer function (Kz) using the deep-water wavenumber((4pi2)(gT 2)−1). Along with surface elevation the following variables areoutput:Hs Significant wave heightTm02 Average zero crossing periodTm01 Mean wave periodUb Bottom orbital velocity1 %% #################### HEADER ######################2 %3 % DISCLAIMER:4 % The f o l l o w i n g code i s provided5 % ” as i s ” with no assurance o f i t s accuracy ,6 % e f f e c i e n c y , or use in any c i rcumstance .7 %8 % Addit iona l ly , whi l e t h i s code makes p r o c e s s i n g9 % subsur f a ce p r e s su r e s i g n a l s to s u r f a c e e l e v a t i o n10 % s i g n a l s e a s i e r i t s t i l l r e q u i r e s at l e a s t a ba s i c11 % understanding o f l i n e a r wave theory and a working12 % knowledge o f the instrument ( i e . understanding13 % deep water vs . sha l low water waves ) .14 %15 %∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗16 %17 % FILENAME: Press2Waves .m18 %19 % AUTHOR: David Hurley20 % CREATED: July 31 , 201721 % CONTACT: dlhurley@ncsu . edu22 %23 %∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗24 %76Appendix C25 % DESCRIPTION:26 % Converts an abso lu t e p r e s su r e s i g n a l i n to a27 % s u r f a c e e l e v a t i o n s i g n a l and computes28 % correspond ing oceanographic v a r i a b l e s .29 %30 % INPUT PARAMETERS:31 % p : Absolute p r e s su r e ( dbar )32 % pa : Atmospheric p r e s su r e ( dbar )33 % rho : Density o f water ( kg/mˆ3)34 % g : Grav i t a t i ona l a c c e l e r a t i o n (m/ s ˆ2)35 % z : Depth o f instrument (m, negat ive down)36 % Fs : Instrument sampling ra t e (Hz)37 % Fc : Cutof f f requency (Hz)38 % d : Water depth at instrument (m)39 % N: # of samples in moving window40 % ( Fs = 16Hz then N = 9600 i s 10 min )41 %42 % OUTPUT PARAMETERS:43 % pd : Dynamic Pressure (m)44 % Eta : Sur face e l e v a t i o n s i g n a l (m)45 % Hs : S i g n i f i c a n t wave he ight (m)46 % Tm02 : Average zero c r o s s i n g wave per iod ( s )47 % Tm01 : Mean wave per iod ( s )48 % Ubr : Bottom o r b i t a l v e l o c i t y (m/ s )49 %50 % REFERENCES:51 % 1) D. Hurley . Wind waves and i n t e r n a l waves in52 % Base Mine Lake . Un ive r s i ty o f B r i t i s h Columbia ,53 % 2017 .54 %55 % 2) N. Jones and S . Monismith . Measuring short−56 % per iod wind waves in a t i d a l l y f o r c ed57 % environment with a subsur f a c e p r e s su r e gauge .58 % Limnology and Oceanography Methods , 5:317−327 ,59 % 2007 .60 %61 % 3) P. Wiberg and C. Sherwood . Ca l cu l a t ing wave−62 % generated bottom o r b i t a l v e l o c i t i e s from63 % sur face−wave parameters . Computers &64 % Geosc iences , 34(10) :1243−1259 , 2005 .77Appendix C65 %66 % #################### HEADER END #################6768 %% #################### SCRIPT START ##############6970 c l e a r ;71 c l o s e ;7273 load Inputs7475 % 1) Convert abso lu t e p r e s su r e to gauge pr e s su r e76 pg = p − pa ;7778 % 2) Convert gauge p r e s su r e to dynamic p r e s su r e79 % by removing h y d r o s t a t i c p r e s su r e .80 % ∗∗∗ change dbar −−−> meters o f water ∗∗∗ .81 pd = ( pg .∗10000) / ( rho∗g ) + z ;8283 % 3) Create f requency vec to r f o r f a s t Four i e rtrans form .84 F = Fs ∗ [ 0 : 1 / (N−1) : 1 ] ’ ;8586 % 4) Ca lcu la te p r e s su r e t r a n s f e r func t i on .87 Kz = cosh ((4∗ pi ˆ2) . / ( g ∗ ( 1 . /F) . ˆ 2 ) ∗ . . .88 ( z+d) ) . / cosh ( (4∗ pi ˆ2) . / ( g ∗ ( 1 . /F) . ˆ 2 ) ∗d) ;8990 Kz( f i n d ( i snan (Kz)==1)) =0; % NaN == 091 Kz = [ Kz ( 1 :N/2) ; Kz(N/2:−1:1) ] ; % Mirror Kz9293 % 5) Ca lcu la te s u r f a c e e l e v a t i o n s i g n a l and94 % oceanographic parameters .95 f o r i = 1 :N: l ength (p)−(N+1)9697 % Dynamic p r e s su r e spectrum98 Spd = f f t (pd( i : i +(N−1) ) ) ;99100 % Sur face e l e v a t i o n spectrum101 Seta = Spd . /Kz ;102103 % Make a l l energy above c u t o f f f requency zero78Appendix C104 Seta ( f i n d (F>Fc & F<Fs−Fc ) ) = 0 ;105106 % Convert s u r f a c e e l e v a t i o n spectrum into s u r f a c e107 % e l e v a t i o n time s i g n a l108 Eta{ i } = r e a l ( i f f t ( Seta ) ) ;109110 % Calcu la te s p e c t r a l moments111 % ( Jones and Monismith (2007) )112 M0 = sum(2∗ abs ( Seta ( 1 :N/2) ) . ˆ2 ) . /Nˆ2 ;113 M1 = sum(2∗F( 1 :N/2) .∗ abs ( Seta ( 1 :N/2) ) . ˆ 2 ) . /Nˆ2 ;114 M2 = sum(2∗F( 1 :N/2) . ˆ 2 . ∗ abs ( Seta ( 1 :N/2) ) . ˆ 2 ) . /Nˆ2 ;115116 % Calcu la te s i g n i f i c a n t wave he ight117 % ( Shore Protec t i on Manual (1984) )118 Hs{ i } = 4∗(M0) ˆ 0 . 5 ;119120 % Calcu la te wave pe r i od s (SWAN User Manual (2011) )121 Tm01{ i } = M0/M1;122 Tm02{ i } = (M0/M2) ˆ 0 . 5 ;123124 % Calcu la te bottom o r b i t a l v e l o c i t y125 % ( Wiberg and Sherwood (2008) )126 Ubr{ i } = (2∗nansum ( ( ( 4∗ pi ˆ2) . / ( ( 1 . / F( 1 :N/2) ) . . .127 . ˆ 2 . ∗ s inh ( ( ( 4∗ pi ˆ2) . / ( g . ∗ ( 1 . / F( 1 :N/2) ) . ˆ 2 ) ) . . .128 .∗d) . ˆ 2 ) ) . ∗ 2 . ∗ abs ( Seta ( 1 :N/2) ) . ˆ 2 ) . /Nˆ2) . ˆ 0 . 5 ;129 end130131 % 6) Concatenate output parameters132 Eta = cat (1 , Eta { :} ) ;133 Hs = cat (1 , Hs { :} ) ;134 Tm01 = cat (1 ,Tm01{ :} ) ;135 Tm02 = cat (1 ,Tm02{ :} ) ;136 Ubr = cat (1 , Ubr { :} ) ;137138 save Output Eta Hs Tm01 Tm02 Ubr pd139140 %% #################### END ######################79

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