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Application of a Three-Dimensional Model to Deep-Water Wave Breaking

Permanent Link: http://ufdc.ufl.edu/UFE0011684/00001

Material Information

Title: Application of a Three-Dimensional Model to Deep-Water Wave Breaking
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0011684:00001

Permanent Link: http://ufdc.ufl.edu/UFE0011684/00001

Material Information

Title: Application of a Three-Dimensional Model to Deep-Water Wave Breaking
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0011684:00001


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APPLICATIONOFATHREE-DIMENSIONALMODELTODEEP-WATERWAVEBREAKINGByJENNIFERL.REGISATHESISPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFMASTEROFSCIENCEUNIVERSITYOFFLORIDA2005

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Thisworkisdedicatedtomyfamily.

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ACKNOWLEDGMENTSFirstandforemost,Iwishtothankmyimmediatefamily,especiallymyparents,fortheirinnitededicationandencouragement.Iattributemyaccomplishmentstodatetotheirloveandsupport,andIthankthemforsharinginbothmyvictoriesaswellasmydefeats,andforalwayskeepingmelaughing.Aspecialacknowledgmentgoestomymom,whosecourageandstrengththispastyearhasremindedmewhatlifeisallabout.Myextendedfamilyandfriendsalsodeserverecognitionfortheroleeachofthemtookinmysocialandacademicdevelopment.ManyspecialthanksareofferedtoLieutenantChristopherSteele,forhisunwaveringbeliefinmyabilities,andforhistime,supportandinexhaustibleabilitytomakemesmile,forwhichIameternallygrateful.CreditisdueDr.DonaldSlinn,myacademicadviser,forhisencouragement,ideas,andadvice.IwouldliketoextendmygratitudetoDrs.RobertThiekeandAndrewKennedy,oftheUniversityofFlorida,forthesupportandguidancetheyprovidedasmembersofmysupervisorycommittee.TheremainderofthefacultyandstaffattheUniversityofFlorida,allofwhomhavemadevaluablecontributionstomyexperiencesthepasttwoyears,alsodeservemanythanks.FortheirsignicantcontributionstomyoverallsuccessandhappinessintheCivilandCoastalEngineeringDepartment,myofce-matesdeservemuchcredit.IwouldliketogiveaspecialthankstoBretWebb,towhoseencouragement,patience,andthoughtfulnessIamforeverindebted.FinancialassistanceforthisworkwasprovidedbytheOfceofNavalResearchaswellastheUniversityofFlorida.Inaddition,fundingformuchofthisresearch,aswellasmyeducation,wasadministeredbytheAmericanSocietyforEngineering iii

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EducationASEEintheformofaNationalDefenseScienceandEngineeringNDSEGFellowship,andIamtrulygratefulfortheirconsideration. iv

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TABLEOFCONTENTS page ACKNOWLEDGMENTS ................................ iii LISTOFTABLES ................................... vii LISTOFFIGURES ................................... viii ABSTRACT ....................................... x 1INTRODUCTION ................................ 1 1.1Background ................................ 1 1.2LiteratureSurvey ............................. 4 1.3Organization ................................ 10 2METHODOLOGY ................................ 12 2.1ModelDynamics ............................. 12 2.2AssumptionsandApproximations .................... 13 2.3GoverningEquations ........................... 14 2.4FlowAlgorithm .............................. 15 2.4.1Free-SurfaceTracking ....................... 16 2.4.2VolumeTrackingAlgorithm ................... 18 2.4.3PressureandVelocityFieldEvaluations ............. 19 2.4.4AccelerationTechnique ...................... 21 2.4.5PossibleSourceErrors ...................... 22 2.5CreationofaNumericalWavetankandModelImprovements ..... 23 2.5.1WaveInowBoundaryCondition ................ 23 2.5.2OutowConditions ........................ 26 2.5.3BoundaryConditions ....................... 28 3EXPERIMENTALINVESTIGATIONS ..................... 29 3.1ASISTExperiment ............................ 29 3.2ModelAdaptation ............................. 31 3.2.1NumericalSetup .......................... 31 3.2.2WaveForcingUsingLaboratoryData .............. 33 3.3NumericalSimulations .......................... 35 3.3.1SpecifyingUserInputs ...................... 35 3.3.2ComputationalCost ........................ 36 3.3.3Three-DimensionalEffects .................... 37 v

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4RESULTS ..................................... 39 4.1WaveFocusingandBreakingDynamics ................. 39 4.1.1BreakingVisualizations ...................... 39 4.1.2MeanVelocity ........................... 41 4.1.3RMSVelocity ........................... 44 4.2ComparisontoLaboratoryData ..................... 45 4.2.1HorizontalVelocity ........................ 46 4.2.2VerticalVelocity .......................... 50 4.2.3Free-surfaceDisplacement .................... 51 4.3SensitivitytoUserInputSpecications ................. 54 4.3.1TurbulenceModel ......................... 54 4.3.2IncreasedResolution ....................... 58 4.4Two-PhaseFlowDynamics ........................ 65 5DISCUSSION ................................... 68 5.1Applications ................................ 68 5.2Specications ............................... 69 5.3SummaryofFindings ........................... 70 5.4Recurrence ................................. 73 5.5ConcludingRemarks ........................... 76 APPENDIX:WIND-GENERATEDWAVES ..................... 78 REFERENCES ..................................... 80 BIOGRAPHICALSKETCH .............................. 84 vi

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LISTOFTABLES Table page 3Asummaryofmodeloptionsavailabletotheuserandthosespeciedfornalsimulations ........................... 35 3Five-secondtestsimulationsconductedtoinvestigatethecomputationalcostofimprovedmeshresolution .................... 36 vii

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LISTOFFIGURES Figure page 2AcomputationalcelldepictingthecoordinatesystemandfacecenteredvelocitiescomputedbyTRUCHAS ................... 16 2Theinitializationofadeep-waterpropagatingwavetrainutilizingimprovedinowboundaryconditions ....................... 25 2Aproleviewofoutowconditionsfordeep-waterwavesinthenumericaltank .................................... 27 2Aplotofthepressurewithinthenumericalwavetank .......... 28 3PicturesofMiami'sASISTsetupforthelaboratoryinvestigationofdeep-waterspillingbreakers ....................... 30 3NumericalmeshusedinTRUCHASmodelsimulations ......... 32 3Arepresentationofthenumericalforcinganditscomparisontolaboratoryvalues ................................... 34 33DeffectscapturedbyTRUCHASexperimentalsimulations ...... 38 4AcompositeofPIVimagesforthelaboratoryspillingbreaker ..... 39 4Asnapshotoftheowvisualizationatthecriticalpointinthenumericalsimulation ................................ 40 4Acloserviewofthesteepwaveofinterest ............... 41 4Cross-tankaveragedmeanvelocityeldatthecriticalpointofthesimulation ................................ 42 4Atimeseriesofthehorizontalvelocitiesattheexpectedbreakingpointofthewavetankx=220cm ...................... 43 4Totalrmsdeviationfromthemeanvelocityatthecriticalpointofthesimulation ................................ 44 4AcomparisonofhorizontalvelocitiescalculatedforthelaboratoryexperimentandthosepredictedbyTRUCHAS ............. 47 4ThemeanvelocityeldatlocationB ................... 50 4Atimeseriesofbothlaboratoryandsimulatedverticalvelocities .... 51 viii

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4Atimeseriesofthefree-surfacedisplacementascalculatedbyTRUCHASatlocationBanditscomparisontolaboratorymeasurements .... 53 4HorizontalandverticalvelocityprolesatpointB,3mdownstreamoftheforcingboundary ......................... 55 4Modelresultsformeanvelocityandtotalrmswithoutthealgebraicturbulencemodel ............................. 56 4Modelresultsformeanvelocityandtotalrmswiththealgebraicturbulencemodelinvoked. .............................. 57 4ResultinghorizontalvelocitytimeseriesforanewgridmeshtakenatpointB .................................. 59 4Resultingverticalvelocityproleforanewgridmesh .......... 60 4Acomparisonoffree-surfaceelevationsforRun2andthosecalculatedwiththeoriginalmesh .......................... 60 4Run2resultsformeanvelocityatthecriticalpointofthesimulation .. 61 4Acomparisonofthexandyclusteringschemesutilizedinall3simulations 62 4AcomparisonofthemeanvelocityeldfortheoriginalsimulationandthatofRun3 ............................ 63 4TotalrmsdeviationfromthemeanvelocityfororiginalrunsandthatofRun3 ................................. 65 4Adepictionoftheairowpatternsurroundingawaterwave ...... 67 ASnapshotsofwavesgeneratedbya7m/swindacrossawaterbodyinitiallyatrest .............................. 79 ix

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AbstractofThesisPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofMasterofScienceAPPLICATIONOFATHREE-DIMENSIONALMODELTODEEP-WATERWAVEBREAKINGByJenniferL.RegisAugust2005Chair:DonaldN.SlinnMajorDepartment:CivilandCoastalEngineeringThecomplexdynamicsassociatedwithdeep-waterwavebreakingeventsarecrucialtothedelicatebalancebetweenairandsea.Thewavebreakingprocessisthechiefmeansbywhichgasesareexchangedacrosstheair-seainterface,aswellasthekeymechanismbywhichmomentumisimpartedintothewatercolumnfromwind.Assuch,breakingwavesarethedrivingforcesbehindsuchphenomenaasoceancirculation,Earth'sweatherandclimate,andglobalwarmingtrends.Dynamicalloadingsonshipsandoffshorestructuresattributedtothebreakingofdeep-waterwaveshavebeenanareaofconcernforallwhotravel,build,andliveaboutthesea.SincethepioneeringdaysofLonguet-Higgins,VanDorn,andChuinthe1970s,muchprogresshasbeenmadeinthestudyofthisimportantprocess.Still,thehighlynonlinearnatureofdeep-waterbreakingwavesmakeslaboratoryinvestigationsintothedetailsofthisprocessdifcult.Morerecently,analysisofdeep-waterbreakingeventsbymeansofnumericalmodelinghasbecomemoreaccessible.Still,thismethodofinvestigationisrelativelynew,andthemajorityofthesestudiesinvolve2Dmodels,ofwhichmanyonly x

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effectivelycapturebreakingdetailsuptothepointofoverturningbeforebecomingunstable.Inaddition,agreementastothemosteffectivemeansbywhichtoaddresssuchconcernsasfree-surfaceandboundaryconditionsislacking.Advancesin3Dnumericalmodelinghaveledtocodesthatarereasonablywelladeptatcapturingthebreakingofshallow-waterwavesshoalingoveravaryingbedtopography,buthaveyet,toourknowledge,tobesuccessfullyappliedtodeep-waterbreakingregimes.Thisstudyinvolvesthemodicationofafully3D,volumeofuidmodel,entitledTRUCHAS,andthevalidationofitsapplicationtodeep-waterbreakingwaveevents.Improvedcapabilitiesinherentinthismodelincludethecapacitytosimulateowdynamicsinbothuids,airandwater,upto,during,andpost-breaking.OurnumericalinvestigationhasitsbasisinlaboratoryexperimentsconductedbyourpartnersMarkDonelanandBrianHausattheCenterforAir-SeaInteractionattheUniversityofMiami,inwhichafocuseddeep-waterwavepacketwasgeneratedandallowedtoevolvetobreakingintheAir-SeaInteractionSalt-WaterTankASIST.Vericationofournumericalmodelisattemptedbymeansofcomparisonofmodelresultswiththosemeasuredinthelaboratory.Itisourhopethatthisstudyservesasavaluablecomponentintheongoinginvestigationintothishighlyvariableanddynamicprocess. xi

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CHAPTER1INTRODUCTION1.1BackgroundOverseventypercentoftheEarth'ssurfaceiscoveredbywater.Mankindhaslivedonandaroundgreatbodiesofwaterformostofitsexistence,yetremarkablylittleisunderstoodofthedynamicandcomplexwaysinwhichtheoceansbehave.Themostvividexampleofwavemotionandoceancomplexityisthesea'scapacitytooverturn,orbreak.Inparticular,deep-waterwavebreakingisoneofthemostspectaculareventsthattheseahastooffer,andconsequentlyoneofthemostperplexing.Foragesmankindhasstruggledtogaintheunderstandingneededtoquantifysuchanenergeticandimportantoceanprocess.Thebreakingofwaterwaves,beitsmallscaleorlarge,isavitalcomponentofair-seainteraction.Turbulencegeneratedthroughthebreakingprocessisthedominantmechanismforthemixingofatmosphereandseaconstituents.Assuch,thebreakingprocessiscrucialforthetransferofheatandmomentumbetweenairandsea.Airentrainmentisanelementofwavebreakingresponsibleforthetransmissionofgases,particularlyO2andCO2,acrosstheocean'sfree-surface;aprocessaidedbythelocalincreaseinturbulenceanddissipationaccompanyingbreaking.Thisprocessisnotonlyvitaltothesurvivalofaquaticlifeandthepreservationofgoodwaterquality,butitalsoservesalargerpurposeinsuchphenomenaasEarth'sweatherandclimate.Infact,transferofCO2fromtheatmospheretotheoceaniscentraltotheglobalwarmingdebate.Wavebreakingalsoservestotransfermomentumandenergyfromwindtowaves,andcorrespondinglyfromwavestosea.Inbreaking,waterwavesimpartsomeoftheirmomentumtocurrentsandconsequentlyaidinthegenerationandperpetuation 1

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2 ofoceancirculation.Inaddition,noisegeneratedduringthebreakingprocessmayalsobeharnessedforuseasadiagnostictoolforair-seainteractionstudies.Inthecontextofwaterwavestudies,adeep-waterwaveistypicallydenedsuchthattheratioofthewaterdepthtothewavelengthisgreaterthan0.5 DeanandDalrymple 1991 .Thisimpliesthatthewaterissufcientlydeepsoaseliminateanydirecteffectofvariationsinbottomtopographyonthesurfacewaves.Inthissense,evensmallbodiesofwater,suchaspondsandlakes,cansupportdeep-waterbreakingwaves.Breakingwavesindeepwatermaybetheresultofinstabilitiescreatedbytheconstructiveinterferenceofvaryingwaves,interactionsbetweenwavesandcurrents,and/ortheinuenceofwindontheseasurface.Inadditiontotheimportantissuessurroundinggeneralwavebreaking,deep-waterwavebreakingposesaddedconcernstoscientists,engineers,andlaymenalike.Ofutmostinteresttocommercialandrecreationalsea-goersisthesafetyoftheirvessels.Wavebreakingonboatscanleadtoseveredamageoreventotalloss,andeventhemostmodernshipsaresusceptibletotheintenseforcesassociatedwithsuchbreakingepisodes.Similarly,deep-waterwavebreakingeventscanresultinseveredynamicalloadingsonoffshorestructuresandthusareofgreatconcerntodesignengineers.Thedynamicsregardingdeep-waterwavebreakinghavebeenstudiedinvariouscapacitiesrangingfromobservationaleldstudies,tolaboratoryinvestigations,and,morerecently,tonumericalmodeling.Fieldstudieshaveprovenadifcultmeansbywhichtoquantifydeep-waterwavebreaking.Themostsignicantvisualindicationofwavebreakingiswhite-capping,thevisualevidenceofairentrainmentintotheoverturningwave.Wavebreakingcanoccur,however,oncentimeterscales.Suchbreakersaretypicallyvoidofwhite-caps,renderingitproblematictodistinguishthemamongaseaofwaves.Inaddition,whilethereislittleargumentthatwavesbreakindeepwater,thereisdiscrepancyamonginvestigatorsastowhatconstitutestheonsetofbreaking.Thus,thesestudiescanposeaddedchallengesinthecomparisonofresults

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3 duetobothhumanjudgmentandtheunsteady,nonlinearcomplexitiesinherentinwavebreakingevents.Laboratorystudieshaveprovidedamorecontrolledenvironmentinwhichtoconsiderthisphenomenon.Suchstudieshaveledtomanyadvancesinourunderstandingofwavebreakingindeepwaterandpresentlyserveasthemeansbywhichtoverifynumericalsimulationsofthiscomplexprocess.Still,thebestapproachtoadoptinthegenerationofdeep-waterbreakingwavesinthelaboratoryremainsunsettled,andthesestudiesoftenoverlookorignorecomponentsofthewavegenerationprocess,suchaswindinputandcurrents,whichareundoubtedlypresentinmorerealisticoceanconditions.Inaddition,theextremenonlinearnatureofthesebreakers,includinggenerationofvorticityatthefree-surface,rapidproductionofturbulence,airentrainment,andspraygeneration,makesindividualwavecharacteristicsdifculttomeasure.Similardifcultiesprovetobeahindranceinnumericalsimulations.Thebulkofthesestudiesinvolve2Dmodels,manyofwhichareonlycapableofeffectivelycapturingthedynamicsofbreakingwavesuptothepointofoverturningbeforebecomingnumericallyunstable.Typically,thesemodelsalsohavetheirbasisinpotentialow,andthusapproximateorignoremanyofthenonlinearcharacteristicsofwavebreakingindeepwater.Discussionastothemostefcientmeansbywhichtorepresentthefree-surfaceanddomainboundaryconditionsareongoing.What3Dmodelsdoexistintherealmofwavebreakinghaveexperiencedsomesuccessinthesimulationofshallow-waterwavebreakingoveravaryingbedbuthavenotyet,toourknowledge,beenappliedtosimulatedeep-waterwavebreaking.Wehavemodiedafully3D,nite-difference,time-dependentmodel,entitledTRUCHAS,foruseinthisstudy.Thismodeliscapableofsimulatingnotonlythedynamicsofthewatercolumnupto,during,andafterwavebreaking,butalsotheowofairabovethefree-surfacethroughoutthebreakingprocess.Oursimulationsmirrora

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4 laboratoryexperimentconductedbyourpartnersMarkDonelanandBrianHausattheCenterforAir-SeaInteractionattheUniversityofMiami,whocreatedsuchdeep-waterbreakingwavesintheirAir-SeaInteractionSalt-WaterTankASIST.Resultsfromthelaboratoryexperimentarecomparedwithourmodelresultstoverifythenumericalcomputations.Whilewedonotpretendthatthismodelistheonlyormostefcientwayofcapturingdeep-waterwavebreakingevents,wedohopethatourndingsmayfurtherthescienticandengineeringcommunitiesinthequesttounderstandtheintriguingandcomplexdynamicsofwavebreakinginthedeep-waterrealm.1.2LiteratureSurveyWavebreakingindeepwaterhasbeenasubjectofinterestforquitesometime,anddespitewhatremainstobeclariedofthiscomplexphenomenon,muchhasalreadybeenlearnedaboutwavedynamicsinthisregime. BannerandPeregrine 1993 provideacomprehensiveoverviewofthedeep-waterwavebreakingprocess,fromadenitionofdeep-waterwavestoaphysicaldescriptionofthevarioustypesofbreakingevents.Notonlydoesthisworkprovideasummaryofthemanymethodsimplementedinboththeeldandlaboratoryenvironmentstostudydeep-waterwaves,butitalsoincludesadiscussionofthetheoreticalaspectsemployedinthequesttobetterdescribetheunsteadyprocess.Theworkof Duncan 2001 isanin-depthexaminationofspillingbreakers;thebreakingtypethatourstudyisdesignedtoinvestigate.Drawingfromtheexperimentalandtheoreticalstudiesofothers, Duncan 2001 documentstheevolutionofaspillingbreakerfrominitialdeformationtotheturbulencegeneratedbothduringandpost-breaking.Whileprovidinginformationforspillingbreakersatalldepths,thisstudypaysparticularattentiontounsteadybreakers,withadeep-wateranalysisrelevanttoourstudy.Worksby Longuet-Higgins 1978 YuenandLake 1980 ,and KjeldsenandMyrhaug 1980 examinethemechanismswherebysteepwavesindeepwateraregenerated,alongwithathoroughanalysisofwaveasymmetry,steepness,proleandparticlevelocities,andothernonlinear

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5 effectsinherentindeep-waterbreakingwaves.Implicationsofdeep-waterwavebreaking,includingthesignicantroleofthisprocessinair-seainteractionandEarth'sclimateandcirculation,arenotedby Csanady 2001 and Melville 1996 .Adetailedlookatthespecicmeansthathavebeenemployedtostudythisphenomenon,bothexperimentallyandnumerically,willprovidethereaderwithanunderstandingofthevisionbehindthemultiplemethodsofinvestigationuponwhichourstudyrelies.Observationaleldstudiesofdeep-waterwavebreaking,suchasthatcarriedoutby HolthuijsenandHerbers 1986 ,areoftenlimitedsolelytotheexaminationofwhite-cappingevents;thisphenomenonbeingthemostreliablemeansbywhichtoidentifyabreakingevent.Suchstudies,however,arehighlysubjective,andillustratethemainmotivationbehindmostphysicalstudiesbeingconductedincontrolledlaboratorysettings. VanDornandPazan 1975 initiatedthepracticeofinvestigatingthebreakingdynamicsofdeep-watersurfacewavesincontrolled,reproduciblelaboratoryconditions.Single-frequency,periodic,deep-waterwavestrainsweregeneratedbyatape-controlledpaddleandmadetoconvergeandbreakinataperedchannel.Whilemuchinformationregardingvelocityandproleevolutionswasascertained,neglectofsuchparametersasrandomnessofwaves,inuenceofwindshear,andthedynamicsofwavetrainsofvaryingfrequenciesestablishthisstudyasintroductoryatbest.Perhapsthemostcomprehensivedeep-waterwavebreakingstudytodateisthatof RappandMelville 1990 ,inwhichtheauthorsusedafocusingtechniquetoensurebreaking.Wave-waveinteractioninducedbreakingresultedfromlinearlydecreasingthewavemakerfrequency,thusincreasingthegroupvelocityofthegeneratedwavesandfocusingwaveenergylongitudinallyatapredeterminedtimeandlocation.Amultitudeofbreakingcharacteristics,includingvelocity,rateandextentofturbulentmixing,andnetlossoftotalmassux,horizontalmomentumux,andenergyuxwereconsidered. RappandMelville 1990 citereectionsduetothenite-lengthchannel,disregardoftheeffectsofwind,anderrorsoccurringinthe

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6 scale-upofresultstoamorerealisticdomainasdisadvantagesofthistechnique.Still,theirworkremainsastapleinthescienticandoceanographiccommunitytowhichtheresultsofmodernstudiesarecompared.Asimilarmethodofwavegenerationwasemployedby Kwayetal. 1998 ,whocorrelatedmanywavebreakingcharacteristicstothespectralslopeofthehigherfrequencycomponentsofthewaveenergy,offeringthisparameterasamorereliabledeterminationofwavebreakingthansteepnessalone.Non-negligibleenergylosswasattributedtodissipationatthechannelwallsandbottomduringthisstudy,andthedeterminationofsurfaceelevationwithinthebreakingregionwascomplicatedbytheentrainmentofair.Afurtherexaminationoftheenergyassociatedwiththenonlinearevolutionandsubsequentbreakingofdeep-waterwavegroupsisprovidedby TulinandWaseda 1999 ,whoattemptedtocorrectforlimitationsinpreviousstudiesbygeneratingwavetrainswitharangeofsteepnessesandbyemployingawiderwavetanktodiminishwalleffects.Still,multiplereectionsbetweenbeachandwavemaker,aswellascross-tankdisturbances,wereseentobiasresultsifmeasurementswerenottakenwithin3-4round-tripsofthewavemaker. Melvilleetal. 2002 alsoutilizedthemethodsdescribedby RappandMelville 1990 toinvestigateapositivemeanvorticitythroughoutthevolumeofuidthatismixeddownwardunderthedeep-waterbreakingwaves,andfoundthatthisindicatedaowinthedirectionofwavepropagationatthesurfacewithareturnownearthebed.ConsistentlynegativeReynoldsstressesfoundduringthisstudyindicatedpositivehorizontalmomentumbeingtransporteddownwardthroughthewatercolumnduringbreaking,andadownstreampropagatingeddygeneratedduringthebreakingprocessisalsoofinterest.Despitetheseintriguingobservations,itisworthytonotethatalthoughtheauthorsdeemtheimportancetrivial,thesemeasurementswereconductedunderconditionsinwhichtheindividualwaveswereofthedeep-watervariety,butwavegroupswereintermediateorevenshallowindepth.

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7 Anearlyinvestigationofair-seainteractionduringbreakingofinteresttoouranalysiswasconductedby Zagustin 1972 ,whosimulatedthedynamicsbetweentwouidsduringbreakingusingamercury-watermodel.Waveswereinitiatedattheinterface,albeitrathercrudely,inthreesectionsbyvaryingthemovementofthebedineachsectionwiththeuseofwheelsofdifferentdiametersconnectedbychains. Zagustin 1972 observedacirculationowpatternaboveeachbreakingwaterwave.Theauthorattributedthetransferofenergyfromairowtothewaterwavetothiscirculationpattern.Thoughonlyexaminedbrieyinthecontextofthiswork,ourmodeldoesverifytheexistenceofthisowpatternintheairsurroundingthebreakingwaves.Suchlaboratoryanalysespavedthewayfortheexplorationofthedeep-waterwavebreakingprocessbynumericalmeans.Two-dimensionalmodels,stillwidelyemployedtoday,wererstappliedtothedeep-waterenvironmentbysuchpioneersas ChuandMei 1971 ,whousednumericalsimulationstoobservethenonlinearevolutionofdeep-waterwavetrains. Longuet-HigginsandCokelet 1976 werethersttoreportcomputationsoftheevolutionuptobreakingoffullynonlinear,unsteadydeep-waterwaves.Thisstudy,however,neglectsbothsurfacetensionandviscosity,andisonlyvaliduntilthebreakingwavereachesoverturning,atwhichpointthemodelbecomesunstable.Similarproblemsareexperiencedinthecomputationsgivenby Hendersonetal. 1999 and Dommermuthetal. 1988 ,wherebyeffectiveanalysisofbreakingishinderedbymodelinstabilitiesapparentasthewaveinitiatesoverturning. Longuet-HigginsandCokelet 1976 alsonotethatineachoftheircomputationssaw-toothedinstabilitiesoccur.Whilethewaveprolecanberenderedsmoothviaasmoothingmechanism,itsoriginisunknown,andtheauthorssuggesttheabsenceofviscositywithintheirmodelcomputationsasaplausibleexplanation. Dommermuthetal. 1988 suggesttheLagrangianmethodofparticletrackingemployedby Longuet-HigginsandCokelet 1976 concentratespointsofthe

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8 free-surfaceinregionsofhighvelocitygradients,wheresmallerrorsinthecomputedvelocitypotentialcanleadtolargeerrorsinparticlevelocities,thusproducingthesaw-toothappearance.Thisinstabilityisavoidedby Dommermuthetal. 1988 byemployingaregriddingmechanism.However,wavereectionfromtheendwallofthecomputationaltankprovidesanewsourceoferrorinthisnumericalapproach.Both BannerandTian 1998 and SongandBanner 2002 examinetheonsetofbreakingfor2Dnonlineardeep-waterwavetrainsviaaboundaryelementmethod. BannerandTian 1998 givessteepnessvalueshigherthanthosetypicallyreportedofdominantoceanwavebreakers,whichmayindicatethatkeyparameterssuchastheinuenceofshearfromtheairand/or3Deffectsnotincludedinthis2Dmodelareofgreatimportanceinthedeep-waterwavebreakingprocess. SongandBanner 2002 employtheboundaryelementmethodtoinvestigatecontrolledbreakingviaachirpedwavepacketsimilartothethosegeneratedby RappandMelville 1990 inthelaboratory;ascenarioverysimilartothatwhichweexamineinourpresentstudy.Again,computationsinthistechniquearelimitedtotherealmuptoandincludingoverturningandarethusincapableofeffectivelyrepresentingtheentirebreakingprocess,duringwhichmanyofthemostimportantelementsaregeneratedorintensiedduringtheturbulentpost-breakingphase.Asasolutiontothesubstantialshortcomingsoftheboundaryelementmethodinexplainingthecomplexbreakingprocess, Miyata 1986 suggeststhenite-differencemethodasthesuperiortechniqueinmodelingwavebreakingscenarios.Therobustnessofthismethodwasveriedby Chenetal. 1999 ,whoemployedapiecewiselinearversionofthevolumeofuidmethod LiuandLin 1997 usingnite-differencestosimulatethebreakingprocessofdeep-waterplungersincludingoverturningandsplash-up.Thoughamuchmorecomprehensivestudythanitspredecessors,thisanalysislacksaturbulencemodel,andconsequentlyisapttomisskeycomponentsofthepost-breakingprocess.Inaddition,the2Dnatureofthemodelitselfisahindrance.Itiswelldocumentedthat2Dturbulenceisless

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9 dissipativethanthatofthreedimensionsandthatsmallscalestructuresgeneratedduringthebreakingprocessdiffergreatlyintwoandthreedimensions,andthusarelikelytoeffectthevorticityeldandenergydissipationindifferentmanners.Recentattemptstoimproveuponthese2Dmodelshavebroughtnewinformationtolightregardingthecomplexnatureofbreakingdeep-waterwaves. SongandSirviente 2004 assessedtheroleofsurfacetensionindeep-waterwavebreaking,aparameterthatuntilthispointhadnotbeenconsideredinmostnumericalmodels.Modelresultsshowthatincludingsurfacetensioninnumericalcomputationsbringsaboutasignicantreductioninjetintensityandairentrainment,andthuscontributessignicantlytothebreakingprocess.Itshouldbenoted,however,thatparametersusedinthistwo-uidstudyarenotalwaysrepresentativeofoceanwaves,butresultsareexpectedtocorrelatewellwithrealisticbreakingevents.Improvementsinthecalculationofvelocityeldsbeneathunsteadywavesaregivenby Donelanetal. 1992 .Theseauthorsaddresstheissuethatpreviouslyemployedtechniques,dependentupontherelationbetweenseasurfaceelevationandvelocitypotentialasgivenbylineartheory,assumeafree-surfaceboundaryconditionthatisappliedatthemeanwaterlevelandnotattheactualfreesurface. Donelanetal. 1992 insteadofferasolutionbasedonthelinearsuperpositionofasumoffreelypropagatingwavetrains.Inthisapproach,thefree-surfaceataparticularlocationisgivenasthelinearcombinationofallofthewavecomponentspresentatthatinstant,andthushasavelocityatthefree-surfacethatisreectiveofthissuperposition.Thismethodisutilizedincalculatingthefree-surfaceelevationandparticlevelocitiesinputintoourmodel. LinandLiu 1999 offeralternatemethodsbywhichtogenerateanynumberofspecicwavetrainsviaaninternalmasssourcefunction.Thisinternalwavemakerdoesnotinterferewithreectedwavesandthusissuitableforuseinlongdurationsimulations.Advancestoincludethethirddimensioninnumericalapproachestostudyingwaterwavebreakinghavemostrecentlybeenmadeby Grilli

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10 etal. 2001 Xueetal. 2001 ,and Viausseretal. 2003 ,eachnotwithoutlimitation. Grillietal. 2001 describeshoalingwavesovercomplexbottomtopographyusingaboundaryelementmethod.Accordingly,thenumericalcomputationsaresubjecttothesameconstraintsoftheir2Dcounterpartsandcanonlybecarriedouttothepointofoverturning. Xueetal. 2001 ,alsooptingtoadopttheboundaryelementmethod,experiencedthesamerestraints,ndingthataccuratesimulationofbreakingisunattainableasbreakersreachlatestagesofoverturning.Bycouplingtheboundaryelementmethodwithavolumeofuidapproachforthepost-overturningstagesofbreaking, Viausseretal. 2003 wereabletogiveresultsforbreakingwavesthroughouttheentirerangeofthebreakingprocess. Viausseretal. 2003 usedthistechniquetoexplorethedynamicsofshoalingwavesonslopingbeaches,andthereforegivenoinsightastothe3Ddetailsofbreakingwavesindeepwater.Theeffectsofsurfacetension,airdynamics,andviscosityarealsoneglectedinthisstudy,leavingneedforamorerobust3Dnumericalmodeltobedeveloped.1.3OrganizationInthesubsequentchapters,weprovideinformationregardinganew3Dmodelanditsabilitytoaccuratelyresolvephysicalcharacteristicsandnonlineardynamicsassociatedwithspillingwavesindeepwater.Chapter 2 iscomprisedofmodelparameters,capacities,andlimitations.Thegoverningequationsanduser-speciedcontrolsusedinthisstudyarepresentedwithinthischapter.AlsoincludedinChapter 2 arethespecicsofourimprovedboundaryconditionforwaveforcingaswellastheoutowconditionsadoptedforthisstudy.AbriefdescriptionofthelaboratoryinvestigationconductedbyDonelanandHaus,informationregardingtheadaptationofourmodeltosimulatethisexperiment,andthephysicalandnumericalspecicationsofoursimulationscanallbefoundinChapter 3 .BothlaboratoryresultsandtheoutcomeofournumericaleffortswillbeexaminedinChapter 4 .Thischapteralsoincludesabriefasideintotheowpatternsintheairsurroundingthewaterwaves.

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11 Ananalysisofournumericalcomputationsandadiscussionoftheimplicationsofourndings,inconjunctionwithconcludingremarksonthecapabilityofthenumericalmodeltoaccuratelydepictwavebreakingindeepwatercanbefoundinChapter 5 .Alsocontainedwithinthischapterisasummaryofnumericalstudiesexperiencingoutcomessimilartothoseobtainedinthisinvestigationandtheimplicationsoftheirndings.Apromisingcapabilityofourmodel,notexaminedwithinthescopeofthisstudy,isitscapacitytosimulatetheowofwindoverthewatersurface,thuscreatingwind-generatedwaves.ThisndingisbrieyexploredintheAppendixonpage 78 ,butthefullpotentialofthisdiscoveryisultimatelylefttoafuturestudy.

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CHAPTER2METHODOLOGY2.1ModelDynamicsCapableofproducingdetailedsimulationsofowregimesinvolvingnumerousuidsofvaryingdensity,TRUCHASisa3D,nitedifference,time-dependentnumericalmodelofgreatcompetence.AsuccessorofsuchcomputationaluiddynamicsCFDmodelsastheSOLA-VOFMethodandRIPPLE,TRUCHASistheresultof40yearsofadvancementdatingbacktothedebutoftheMarker-and-CellMACMethodforincompressiblemultiphaseowsin1965 Team 2004 .InsimilarfashiontotheSOLA-VOFmethodology,TRUCHAScouplesitsalgorithmswithavolumetrackingmethodtoaccuratelyevaluatethefractionofeachuidmaterialwithineverymeshcell.TRUCHASalsoemploystheContinuumSurfaceForceCSFMethod,asurfacetensionmodelutilizedbyRIPPLEinwhichtheeffectsofsurfacetensionareappliedtouidelementslocatedwithinthenumericallyresolvabletransitionregions.Thislocalizedvolumeforceisreadilyincludedintothealgorithmbyapplyinganextrabodyforceintothemomentumequation Kotheetal. 1991 .Advancesinprojectionmethodsandincreasedefciencyinsolvinglinearsystemsofequations,coupledwiththemethodologymentionedabove,haveresultedinTRUCHAS,therobustnumericalmodelconsideredinthiswork.Numerousalgorithmsincludedwithinthethemodel'svastcodeallowforthesolutionandmodelingofsuchphenomenaasheattransferandphasechanges,chemicalreactions,solidmechanics,electromagnetics,anduiddynamics.Wewishtofocusontheuiddynamicsalgorithmofthemodel. 12

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13 2.2AssumptionsandApproximationsTheuiddynamicsalgorithmincludedwithinTRUCHASoperatesonthebasicassumptionthattheuidsareincompressibleunlessdesignatedasvoidspace,denedasanidealizedmaterialhavingzerodensityandthereforeinnitecompressibility.TRUCHASalsoemploystheContinuumHypothesis,asmolecularactivityisaveragedoversmallspatialandtemporalscales.Moreover,TRUCHASassumesthattheowofalluidsincludedwithinthesimulationcanbecapturedandevaluatedonasinglevelocityeldatanygivenpointwithintheowregime.Thus,boundarylayers,oftenofamuchsmallerscalethantheoverallowdimensions,areresolvedbythecomputationalmesh.Inadditiontotheaforementionedassumptions,TRUCHASalsoexploitsmanyapproximationstosimplifyitsgoverningowequations.ThosemostpertinenttothisworkincludetheassumptionthatalluidscanbeconsideredNewtonian.Thus,viscousshearstressisassumedtobealinearfunctionoftheshearrate.TRUCHASalsoapproximatesturbulentowregimesbycalculatingthisviscousstressfromtheaveragedmolecularviscosityineachcell,auidpropertydesignatedbytheuser,andthencouplingthisstresswithasimplealgebraicturbulenceclosuremodel.TheadvectionofmomentumbyTRUCHASisachievedthroughtheuseofarstorderschemethatutilizesoldtimelevelvelocityvalues,butdensitiesconsistentwithupdatedmaterialvolumefractions.TRUCHASoperatesunderasemi-implicittimeschemetoproduceastablesolutionthatis1storderaccurateintime.Thisisaccomplishedbytreatingthepressuregradientimplicitly,whileallowingallotherforcestobetreatedexplicitly Team 2004 .Spatialdiscretizationwithinthemeshisconductedviaacombinationofboth1stand2ndorderaccuratederivations.Advectionterms,however,remain1storderaccurate,asisnecessaryforcomputationsinvolvinginterfacesbetweendifferentuids.Inaddition,owspecicsrelyheavilyontheprecisionofinput

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14 variables,suchasuiddensities,asdenedbytheuser,inCGSnotation.Amorecomprehensiveevaluationoftheowanalysisanditsdetailsfollows.2.3GoverningEquationsTRUCHASseekstosolvetheIncompressibleNavier-StokesEquationsinitsdeterminationofuidow.SaidequationscanberepresentedasinasingleConservationofMomentumequation,showninEq. 2 .@~u @t+r~u~u=rp+r~+fB+fS+fD where~u=uidvelocity=densityp=pressure~=shearstresstensorfB=bodyforces,i.e.gravityfS=anysurfaceforcesfD=dragforceincludedtodescribeowinthevicinityofasolidoropenboundaryOperatingundertheassumptionsmentionedintheprevioussection,TRUCHAScanfurtherdenetheshearstressrateasafunctionofthedynamicviscosityoftheuid,avariablesetbytheuserattheonsetofthesimulation,asdepictedinEq. 2 .~=r~u+rT~u where=dynamicviscosityT=operationoftransposeSimilarly,TRUCHAScanfurthersimplifythesurfaceforcesterm,fS,ofEq. 2 byrecognizingthattheonlysurfaceforceemployedintheuidowsimulationsissurfacetension.TRUCHASdenesthisconstituentasavolumetricforceatworkonuidelementsinthevicinityofasurface,S,asillustratedinEq. 2 .fS=nSS where

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15 =surfacetensioncoefcient,asspeciedbytheuser=totalcurvatureofaninterfacenS=aunitnormaltoSS=DiracdeltafunctionConservationofmassisthenmaintainedviaEq. 2 .@ @t+r~u=0Despitethepreviously-statedassertionthatalluidsconsideredbyTRUCHASareassumedincompressible,theowalgorithminherentwithinTRUCHASiscapableofhandlingmultipleimmiscibleuids,allofvaryingdensity,withinasingledomain.Assuch,TRUCHASchoosestopreservethetermwithinthebracketedtermsontheleft-hand-sideofEq. 2 Team 2004 .Withinasingleuidmaterial,however,isexpectedtoremainconstantthroughouttime,asrepresentedbyEq. 2 .D Dt=0Utilizingthisconstraint,Eq. 2 canberewrittenastheContinuityEquation,Eq. 2 .r~u=0Initsnalexpression,Eq. 2 issimplyaEulerianformofconservationofmomentum,conditionalontheincompressibilityrequirementimposedbyEq. 2 .Furthermore,Eq. 2 ,initssimplestexplanation,detailsthetransportofvariousuidsthroughoutthesystem Team 2004 .2.4FlowAlgorithmTheowalgorithminherentinTRUCHASreliesheavilyonavolumetrackingmethodtoquantifyandtoadvectmaterialpropertiesthroughoutthenumericaldomain.Morethansimplygeneratingnewvaluesoffractionalvolumeforeachuid,thisstepalsoallowsTRUCHAStonotethevolumesofuidsmovingacrosscellfacesfromonetimesteptothenext.Saidvolumesthenbecomethemeansbywhichall

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16 otherquantitiesareadvectedthroughoutthemesh.ThisactstoensurethatthevariedtransportequationsemployedbyTRUCHASremainconsistent.ThoughTRUCHASiscapableofhandlingvariousdomaintypes,thisworkutilizesasimplerectangularmesh.Atypicalgridcell,includingthecoordinatesystemdesignatedbyTRUCHASandthecorrespondingfacecenteredvelocities,isgiveninFig. 2 .Materialvolumefractionsareevaluatedineachofthesenumericalcellsfor Figure2:AcomputationalcelldepictingthecoordinatesystemandfacecenteredvelocitiescomputedbyTRUCHAS. eachtimestepofthesimulation,andvolumeuxesacrosscellsarealsonoted.Giventhenewvolumefractionsforeachuid,materialpropertiesincludingdensityandviscosityarethenassessedwithineachcell.Suchvaluescanthenbeimplementedintheevaluationofvelocityandpressureeldsthroughoutthedomain.Amoredetailedanalysisofthisinvolvedprocessisoutlinedinthefollowingsubsections.2.4.1Free-SurfaceTrackingTRUCHASinitiatesitsowalgorithmwiththemultidimensionalPiecewiseLinearInterfaceCalculationPLICmethodtodeterminethevolumeofeachuidineachmeshcell.Free-surfacetrackingisaccomplishedwithinTRUCHASbyrepresentingtheuidinterfaceswithvolumefractions,asexplainedby Team 2004 .ThismethodaimstoresolvetheConservationofMassequation,Eq. 2 ,forn+1usingunf.Initiation

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17 ofthisprocessinvolvesthedeningofavolumefraction,fk,asthefractionofacellvolumeVoccupiedbyuidk,asdepictedinEq. 2 .fk=Vk=VCorrelationofcelldensitytoEq. 2 yieldsEq. 2 .=XfkkThis,inreturn,leadstoanewdenitionofEq. 2 ,Eq. 2 .@fkk @t+rfkk~u=0Furthermore,utilizingtheknowledgethatkisconstant,anevolutionequation,Eq. 2 ,canbeascertained.@fk @t+rfk~u=0 where~u=uidvelocityfk=volumefractionofuidkThesolutionoffkrepresentsthepresence,orconverselytheabsence,ofaparticularuidelementwithineachmeshcell.Thus,Eq. 2 isessentiallyanevolutionequationforthelocationofeachuid.Thevolumefractionsofeachuidareboundedwithintherange0fk1asdepictedbelow.fk=8>>>><>>>>:1insideuidk>0;<1attheuidkinterface0outsideuidkAsEq. 2 iscontinuallyresolvedwithinthealgorithm,TRUCHAStracksuidvolumesandmarchesthemforwardintimewitheachsuccessivecalculation.

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18 2.4.2VolumeTrackingAlgorithmThePLICVolumeTrackingAlgorithm,mentionedintheprevioussubsection,allowsforthesolutionofEq. 2 intermsoffn+1k.Thecompleteresolutionofthisalgorithmincludestwoseparatesteps.Theinitialstepconsistsofaplanarreconstructionofuid-uidinterfaceswithineachmeshcell.Workingunderthereconstructedinterfacegeometryassumption,interfacesbetweendifferentuidsareconstructedusingtheuidvolumedatasuchthatthegeometryoftheinterfaceispiecewiselinear,orplanar.Asdetailedby Team 2004 ,thisreconstructioninvolvesanexactcorrelationtofnkaswellastoapproximationsofthelocationsoftheuidinterfacesbasedupongradientsofthefnk.Thesecondphaseofthetrackingalgorithmentailsacomputationofthevolumeuxesofalluidsacrosscellfaces.Viaasimplemultiplicationbyt,thesevolumeuxescanrevealthevolumeofeachuidmaterialcrossingeverycellface.Afteraspatialsmoothingofthefkeldhasbeenimplemented,thisinformationisusedtoupdatethevolumefractionsofeachuidconstituentthroughouteverycellinthemesh,and,shouldtheneedarise,thisinformationmayalsobeutilizedtotrackthetransportofchemicals,temperature,orotherquantitiestheusermaywishtomodel.Forinstance,suchmeshcellattributesasuiddensityandviscosityarecalculatedasaveragesofthevariousuidcomponentswithinthatspeciccell.AnadvantageousqualitycentraltoTRUCHAS'sowalgorithmisitsallowanceofsub-cycling.Thisprocess,bywhichthevolumetrackingalgorithmisallowedtorunmultiplepasseswithinasingletimestep,vastlyimprovestheaccuracyofthesolution.AbenettothisaddedcapacityisthatTRUCHASisabletotrackuidelementsthroughmorethanonemeshcellduringeachtimestep.Thiscapabilityisofgreatvaluethroughoutthedomainwheretheuidinterfacemaybepropagatingatanangletocellfaces.

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19 2.4.3PressureandVelocityFieldEvaluationsHavingdeterminedtheuidpropertiesuniquetoeachmeshcell,TRUCHASembarksupona4-stepevaluationofthenewvelocityandpressureelds.Therststageinthisprocessinvolvesthetimediscretizationofthemomentumequation,Eq. 2 ,inwhichpredeterminedvaluescalculatedasacombinationofvelocity,temperature,andspeciesconcentrationvaluesretainedfromtheprevioustimestepareusedalongwithuidvolumefractionsandmaterialtransfervolumesfromthevolumetrackingsteptoapproximatethenewcellcenteredvelocitiesviaaforwardEulertimestep.Theresultingtime-discretizedmomentumequationcanbedividedintotwoparts,apredictorstepandaprojectionstep.Inthepredictorstep,aninterimpredictedvelocityvalueisintroducedandsolvedfor,asshowninEq. 2 .n+1u)]TJ/F25 11.955 Tf 11.955 0 Td[(nun t=ruun+rn+1ru+rTu+fn+1S+fn+1D)-30(rPn+fnB whereu=aninterimpredictedvelocityOnceavalueforuhasbeenestablished,apressurecorrection,denedasPn+1=Pn+1)]TJ/F25 11.955 Tf 11.955 0 Td[(PnisevaluatedviaEq. 2 .rrPn+1 n+1=ru tThesolutionofEq. 2 forPn+1providesthepressurecorrectionneededtoensurethatthedivergencewithineachmeshcellremainszero,orthatun+1satisescontinuity.Thispressurechangeisthenusedtosolvetheprojectionequation,giveninEq. 2 ,forthecell-centeredvelocityatthenewtime.n+1un+1)]TJ/F25 11.955 Tf 11.955 0 Td[(n+1u t=rPn+1+fn+1B+fnB

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20 Finally,Pn+1=Pn+Pn+1isusedtoestimatethepressureeldforuseinEq. 2 forthenexttimestep.Incorporatedintothisprocessaretheexplicitapproximationsofbodyforces,aswellasimplicitapproximationstoviscousanddragforceswhichacttoaidinthestabilityofthesimulation.Dragforcesaredeterminedfromtheassumptionthattheyareproportionaltothevelocitycomponentspreviouslyestimated.Anyviscousforcesarefoundbyaveragingvelocityvaluesfromtheprevioustimestepwithvelocityvaluesfromtheintermediatetimelevel*,inconjunctionwiththeassigneduidviscosityvaluesinitiallydesignatedbytheuser.Thenetviscousstressforeachmeshcelliscalculatedasasumofthedotproductofthevelocitygradientmultipliedbythefaceareawiththefacenormalvector,asgiveninEq. 2 .~F=XffAf[^nfr~u+rT~u] where~F=viscousstressf=viscosityatthefaceAf=facearea^nf=facenormalvectorAsthevelocitygradientisrstorderaccurate,calculatedviaaleastsquaresmethod,theresultingviscousstresswillhavesecondordererrors.Suchapproximationsasthoseoutlinedaboveresultinthenecessitytosolvealinearsystemofequationsinmostcalculations Team 2004 .Duringthesecondphaseofthisevaluation,TRUCHASdeterminescellfacevelocitiesfromthecellcenteredvelocitiesascertainedinthepreviousstep.Oncecellfacevelocitiesareestablished,bodyforceaccelerationsarethenappliedtothesystem.Thepressureeldisupdatedinthethirdstep,asTRUCHASagainsolvesforthepressureeldcorrectionneededtoeradicatethevelocitydivergenceineverymeshcell.Finally,TRUCHASadjustsitspreviouslydeterminedcellcenteredvelocityeldbyaveragingthechangesinpressureeld,calculatedinstep3,acrosseachcell

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21 face.SuccessfulrealizationofthefouraforementionedstepsachievesnewvelocityandpressureeldsthatarefullyupdatedusingtheforwardEulertimescheme Team 2004 .2.4.4AccelerationTechniqueAs Fletcher 1991 asserts,alliterativetechniquescanbesimplystatedasproceduresforsuccessivelymodifyinganinitialguesssuchthatthesolutionissystematicallyapproached.TRUCHAShasthecapacitytoemploymanysuchpreconditioningalgorithmstoaidinitssolutionofthepressureandvelocityelds.TheaccelerationtechniquesavailabletotheuserincludeaMultistepWeightedJacobimethod,SymmetricSuccessiveOver-RelaxationSOR,IncompleteLUFactorization,LUDecomposition,ConjugateGradientsandaMultigridMethod.Forourpurposes,wefoundtheMultigridMethodtobethemosttimeefcientandaccuratepreconditioningmethod.Accordingly,allresultspresentedinthisworkreectthisaccelerationalgorithm.TheMultigridprocedureismosteasilyexempliedbyassumingagridspacingofhkuponwhichanitedifferenceapproachisusedtosolveLU=F whereL;F=matricesAnewvariable,u,isthenintroducedasanapproximationtotheabovesolutionandisdenedasU=u+v wherev=thecorrectiontouAtthispoint,Eq. 2 canberewrittenasLv=f

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22 wheref=F)]TJ/F25 11.955 Tf 11.955 0 Td[(LuEq. 2 isresolvedonagridwithvaryingcellspacing.Thenalsolution,U,canthenbedeterminedfromEq. 2 oncevhasconvergedtoitsnalsolution PeyretandTaylor 1985 .Theprocedureoutlinedaboveisdescribedby PeyretandTaylor 1985 asastrategyinvolvingthetransformationofanegridsolutiontoacoarsegridsolution,andthenbacktothenegrid. Fletcher 1991 assertsthatitisthisparticularprogressionthatallowstheMultigridMethodtobemoreefcientthanmanyofitscounterpartsiniteratingtoconvergence.Otherrelaxationprocedures,includingJacobi,Gauss-SeidelandSOR,readilyresolvehighfrequencyerrorcomponentsinafewiterations.Thesemethods,however,areill-equippedtoquicklyremovethelowfrequencycomponentsoftheerror.Conversely,theselowfrequencyerrorscommontoanegridaretransformedintohighfrequencycomponentswhenshiftedontoacoarsegridspacing.Assuch,theMultigridMethodactstoeffectivelyutilizethehighfrequencysmoothingintrinsicintherelaxationprocedures.2.4.5PossibleSourceErrorsPlausibleerrorscanbebornfromtheniteresolutionofanycalculation.Theinitialgenerationoftheowgeometryisonesuchinstanceinwhichstatisticalerrorsmaypresentthemselves.SucherrorsaretheresultoftheMonteCarloMethodemployedbyTRUCHAStoevaluatetheinitialfractionofeachuidelementpresentwithineverymeshcell.Thisalgorithmgeneratesanumberoftestpointswithineverymeshcellinarandommanner.Itisthendeterminedinwhichspecicuid'sgeometrytherandompointhappenstolie,andthetestpointislabeledaccordingly.Thevalueofeachmeshcellisthenapproximatedviaanassumptionthatthefractionalvolumeof

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23 thecelloccupiedbyeachspecicuidisequaltothefractionofgeneratedtestpointswithinthecellbearingthatspecicuid'slabel Team 2004 .Inaddition,errorsmayresultfrominterfaceapproximations.Asthesimulationisallowedtoprogress,thelocationandorientationofuid-uidanduid-solidboundariesinsideeachmeshcellareevaluatedsolelyfromvolumefractions.Theinaccuraciesproducedinthisprocesscanbegreatlyreducedbyincreasingtheresolutionofthesimulation.Asmaybeexpected,meshcellscontainingmorethantwouidsrequirethegenerationofmultipleinterfaces.Assuch,thesesituationsincreasethepotentialforerrorwithintheowgeometry.2.5CreationofaNumericalWavetankandModelImprovements2.5.1WaveInowBoundaryConditionAnorthogonalwavetankwithanumericalwavemakerwasdesiredtoaccuratelysimulatethelaboratoryexperimentsconductedbyDonelanandHausattheUniversityofMiami'sASIST.AnewinowboundaryconditionwasaddedtoTRUCHAStoallowforthetime-dependentinuxofwavesintothedomain,effectivelyactingasawavemakerattheinowx=0cmboundaryofourcomputationalmesh.Testingofthisnewboundaryconditionwasaccomplishedona100cmx50cmx60cmxbyybyzmeshwithcellnumberstotaling50x10x60.Equationsdetailingthemotionofthefree-surface,aswellasthekinematicsforwaterparticlesatanygivendepth,werespeciedeverywherewithinthersttenthofacminthex-direction.Takenfrom DeanandDalrymple 1991 ,theselinearequationsEq. 2 ,Eq. 2 ,andEq. 2 aregivenbelow,andrepresentfree-surfacedisplacement,horizontalvelocityu,andverticalvelocityw,respectively.Thecross-tankvelocity,v,wastakenaszeroastherewasassumedtobenegligiblemovementacrossthenumericalmesh.=H 2coskx)]TJ/F25 11.955 Tf 11.955 0 Td[(t

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24 u=H 2coshkh+z sinhkhcoskx)]TJ/F25 11.955 Tf 11.955 0 Td[(tw=H 2sinhkh+z sinhkhsinkx)]TJ/F25 11.955 Tf 11.955 0 Td[(t whereH=waveheightk=wavenumber,denedas2=LwhereListhewavelength=angularwavefrequency,denedas2=TwhereTisthewaveperiodt=timex=horizontalpositionz=verticalposition,takenaszeroatthefree-surfacewithincreasingnegativevaluesfromthefree-surfacetothebedTestrunswereconductedwithawaveheightof8cmand0.7secondperiodwaves.Themeanwaterlevelwassetto45cm,yeildingawavenumberofapproximately0:0823cm)]TJ/F24 7.97 Tf 6.586 0 Td[(1.Suchspecicationsensureddeep-waterconditionsforoursimulations.Thehorizontalandverticalvelocitiesgivenabovewereappliedattheinowboundaryonlyforthosecellsbeneaththefree-surfaceforeachtimestep.Auiddensityof1g=cm3,distinctiveofwater,wasalsospeciedwithinthisregion.Cellsattheboundaryabovethefree-surfaceweredesignatedasair,withadensityof0:001g=cm3andzerohorizontalandverticalinowvelocities.Assuch,anyowintheairabovethefree-surfaceissimplyinresponsetothedynamicsofthewatercolumn.Thedensityofthecellontheboundarycontainingthefree-surfacewasreectiveoftheverticallocationofthefree-surfacewithinthatcell.Thedensityofwaterwasmultipliedbythefractionofthecellbeneaththefree-surface,whiletheremainingfractionofthecellwasweightedbythedensityofair.Thesumofthesetwofractionsgaveagoodestimateofthedensityofthecellcontainingthisinterface.Fig. 2 showstheinitiationofadeep-waterwavesimulationutilizingtheseinowequations.Numericalsimulationsmodeltime-dependentwavetrainswhichareuniformacrossthetank.Thesedeep-waterwavetrainsaredirectedtopropagatealong

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25 thenumericaltank,dissipateonabeach,andexitthecomputationaldomainthroughaconstant-pressureoutowcondition,furtherexaminedinthefollowingsection.Fig. 2 providesavisualdepictionoftheinowofadeep-wateruniformwavetrain Figure2:Theinitializationofadeep-waterpropagatingwavetrainutilizingimprovedinowboundaryconditions.AvisualofthenumericaltankandinowwaveisshowninA,whilevelocitycontoursofBuandCwaredisplayedinaproleviewandillustratethedepth-dependencyofthevelocityequations. withawaveheightof8cmaswellasthehorizontalandverticalvelocitycontoursassociatedwiththeseincomingwaves.Thelinearnatureofthewaveequationsrequiresthatthevelocityprolesdecaywithdepth,apropertythatisclearlydisplayedinthegure.Thus,thisimprovedforcingmechanismallowsforthesuccessfulgeneration

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26 ofdeep-waterwavetrainsasgivenbylineartheory,effectivelyactingasanumericalwavemakerwiththeaddedbenetofdepth-dependency.2.5.2OutowConditionsInordertobothconservemasswithinthesystemaswellastomaintainthemeanwaterlevelataconstantdepth,anoutowmechanism,bywhichexcessmassmayexitthedomain,hasbeenincorporatedintothenumericalscheme.First,abeachwascreatedsoastodissipatewaveenergyandtominimizewavereectionatthefarendofthenumericalwavetank.Thebeachusedintheseinitialstagesisgivenaslopeof35degrees. 1 Thebeachisdesignedtoterminateontheoutowwallx=100cmatthemeanwaterlevel.ItisworthytonotethatthePLICAlgorithm,detailedinSubsection2.4.2,allowsforasmoothbeachface,ratherthanthestaircaseappearanceoftenseeninothernumericalmodels.Aconstant-pressureboundaryconditionwasthenimposedontheendwalleverywhereabovethebeach.Thiseffectivelycreatedanoutowcondition,asuidcanleavethedomainthroughthisambientpressurezone.Fig. 2 showsadeep-waterwavedissipatingenergyonthebeachandthenowingoutofthedomainthroughtheconstant-pressureboundary.Itisimportanttonotethatthisisnotaperiodicboundarycondition.Thus,wavesowingoutofthetankattheoutowboundarydonotreappearattheinowboundary.Instead,thisconditionisameansbywhichtoallowforcingofwavegroupsintothedomainattheinowboundary,whilestillsatisfyingconservationofmassandmaintainingameanwaterlevel.ThepressurethroughoutthedomainisshowninFig. 2 .Asapparentinthisgure,azerogagepressureboundaryconditionhasalsobeenspeciedatthelidofthe 1Beachslopeswerechosenwiththesimpleconstraintofslopingasgentlyaspossiblewithoutextendingmorethanapproximatelyhalfwayalongthebaseofthetanktowardtheinowboundary.

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27 Figure2:Aproleviewofoutowconditionsfordeep-waterwavesinthenumericaltank,includingabeachandtheconstant-pressureoutowzone.TimeshotsA,B,andCaretakenatconsecutive1/16secondintervals. domain.Thisconditionwasappliedinlieuofthetypicalrigid,free-slipboundaryoftenusedtocharacterizethelidofanumericaltank.Wefoundtherigidlidtooconstrictingtotheowofairabovethewatersurface,as,regardlessoftheheightofthetank,undesirableowpatternsabovethewatersurfaceresultingfromtheowofairintothedomainthroughtheconstant-pressureoutowboundarywereexperienced.Anambientpressure,oropenlid,conditionsignicantlyminimizestheseunfavorablenonphysicalpatterns.

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28 Figure2:Aplotofthepressurewithinthenumericalwavetank.Notethezonesofzero-pressureabovethebeachontheendwallandatthelidofthedomain. 2.5.3BoundaryConditionsWithintheuidowdynamicsinheritinTRUCHAS,eldstowhichboundaryconditionsmaybeappliedarerestrictedtouidvelocityandpressure.TRUCHASiscurrentlyunabletoresolvesuchboundaryconditionsasNeumann,periodic,symmetricandhydrostatic,supplementstobeaddedtofuturemodelversions.Thenumericalmodelis,however,capableofhandlingbothno-slipandfree-slipboundaryconditionsatmeshboundariesandonsolidsurfaces.Inaddition,Dirichletboundaryconditionsmaybeappliedatmeshboundariesforeitherpressureorvelocity.Inconjunctionwiththespecialconditionsmentionedpreviously,itwasnecessaryonlytoutilizetheno-slipandfree-slipboundaryconditionsofTRUCHAStocompleteournumericalwavetank.Ano-slipboundaryconditionwasenforcedatthebottomofthetankaswellasalongtheoorofthebeach.Assuch,nohorizontalvelocitywaspermittedalongthebed.Verticalvelocitycomponentswerealsorequiredtobezeroattheselocations,asmaterialsareforbiddentoowthroughthebottomofthetankorintothenumericalbeach.Free-slipboundaryconditionswerespeciedatthewavetankwalls,allowingowtomovefreelyalongthesetankboundariesandthuskeepingtheowasuniformaspossibleinthecross-tankdirectionandreducingdissipationanddampingeffectsfromthesidewalls.

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CHAPTER3EXPERIMENTALINVESTIGATIONSToevaluatethecompetenceofTRUCHAStosimulatedeep-waterbreakingwaves,areliabledatasetisneededtowhichsimulationscanbecompared.MarkDonelanandBrianHausprovidedsuchdatawithalaboratoryinvestigationconductedattheUniversityofMiami'sCenterforAir-SeaInteraction.DonelanandHausutilizedMiami'sAir-SeaInteractionSalt-WaterTankASISTtoconductacontrolledanddetailedanalysisofspillingbreakersindeepwater.Theircomprehensivedatasetprovidedanattractivemeansbywhichtodeterminethecapacityofourmodeltoaccuratelypredictandsimulatewaveheights,spillingcharacteristics,andturbulentgenerationassociatedwithspillingbreakersinadeep-waterenvironment. 1 3.1ASISTExperimentMiami'sASISTisa15mby1mby1mstainlesssteelandacrylictankwithaprogrammablewavemaker.Photosofthelaboratorysetup,includingsomeoftheinstrumentsusedduringthestudyaredepictedinFig. 3 .Usingthetechniquesof RappandMelville 1990 ,thewavemakerwasprogrammedtoproduceaGaussianwavepacketinwhichwavesweredesignedtocoalesceandbreakataspecicpointinthewavetank.DetailedlaboratorydatacanbecollectedwithinASISTthroughanumberofnon-intrusivemeans.Mostpertinenttothisinvestigation,bothinthemodel 1Itshouldbenotedthatlaboratoryexperiments,andconsequentlynumericalsimulations,wereconductedwithparameterscharacteristicofatransitionalwaveclimate.Inaccordancewith Melvilleetal. 2002 ,itisexpectedthatresultswilllendthemselveswelltodeep-waterenvironments. 29

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30 Figure3:PicturesofMiami'sASISTsetupforthelaboratoryinvestigationofdeep-waterspillingbreakers.Viewsofthetank,includingthePIVcamerasandthecomputerstationaregiven,respectivelyinAandB,whilecamerapositioningtomonitorthefree-surfacedisplacementisdepictedinC. forcingandintheresultscomparisonrealmsofthisstudy,istheaccuratecollectionoffree-surfaceelevationdatathroughouttheexperiment.Measurementsofthefree-surfacedisplacementweretakenattwolocationswithinthetank;locationA,approximately5.5mfromthewavemaker,andlocationB,at8.5mfetch,betweenwhichlocationsaspillingbreakerwasobserved.Acquisitionofthefree-surfaceelevationatthesegivenlocationswasaccomplishedwiththeuseofmultiplelaserelevationgaugesaswellasasurface-focusedcamera,asdepictedinFig. 3 .Whilethecamerakeptavisualrecordofsurfaceelevation,thelasersactedtogiveamoredetaileddepictionoftheinterfacecharacteristics.Inadarkenedsetting,lasersweredirectedstraightdownontothefree-surfacefromasettingatthetopofthewavetank.Thesebeamsofenergywouldthenpartiallyreectoffofthesurfaceofthewatercolumn.Basedontheorientationofthefree-surfaceatanygiveninstant,thereectedreturnsignalwouldhaveavaryingdeectionangle.Thisdancingofthelaserbeams

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31 couldthenbeusedtodeterminethecomponentsoftheslopeofthewatersurfaceatanygiveninstantduringthesimulation.Oncethecharacteristicsofthefree-surfacehadbeenestablished,thedetailsoftheowbeneaththeair-waterinterfacecouldthenbedetermined.Utilizingthemethodsoutlinedby Donelanetal. 1992 ,orbitalvelocitiesatcentimeterincrementsbelowthefree-surfacewerethentabulatedfromtheelevationdataatlocationsAandB.Readingsweretakenevery10milliseconds,andadatalecontainingthetime-seriesoffree-surfaceelevationaswellasuandwvelocitiesatcentimeterincrementsdownthewatercolumnwascreatedforeachofthetwolocations.ThedataleforlocationAservedasthemeansbywhichtoforceourmodelsimulations,asdocumentedinthefollowingsections.3.2ModelAdaptation3.2.1NumericalSetupToaccuratelyrepresenttheexperimentalwavetank,anewnumericaltank,depictedbelowinFig. 3 ,wasgenerated.Thecomputationaldomainwas60cminheightand1mcross-tank.Numericalsimulationsofthefull15mlaboratorytankwereunnecessarytocapturetheimportantbreakingaspectsthatwewishedtostudyandwouldputunreasonablerequirementsonthecomputationaltimeneededtorunsuchsimulations.Consequently,thenumericaltankusedinthesesimulationsisjust4minlength,providinganampledistanceoverwhichforcingandbreakingeventscanoccur.Themeshconsistedof106cellsalongthetankinthex-direction,clusteredwitha1cmresolutionwithinthebreakingregionandcoarser-6cmresolutiontowardtheboundaries.Cross-tankinthey-direction,wemadeuseof24totalcells,alsoadoptingaclusteringmethodwithverycoarse10cmresolutionatthetankwallsningto2cmresolutionatthecenterofthedomain.Uniformgridspacingwasutilizedinthezdirectionwith1cmspacingincrements.Suchgridstructuringallowedforadetailedviewoftheareaofconcern,whilestillkeepingcomputationaltimewithin

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32 Figure3:NumericalmeshusedinTRUCHASmodelsimulations. thereasonablerealmofanapproximateoneweekperiod.AsummaryofthevariousmeshestestedandtheircomputationalcostisgiveninSubsection3.3.2.Asdetailedintheearliersimulations,thenumericaltankwasleftopenbyadoptingtheambient-pressureboundaryconditionatthetopofthedomain,keepingerraticowpatternsfromdevelopingintheairabovethefree-surface.Abeachofslope20degrees,extendingjustshyof1malongthebedandterminatingattheoutowboundaryatthemeanwaterlevelcmwasincludedtodissipatewavesandtoencouragetheowofwavesoutofthesystem.Ahybridboundaryconditionwasadoptedattheoutowboundary:At14cmheightabovethebeach,extendingfromthemeanwaterlevelto50cmheight,aconstant-pressureregionwasenforced,allowingtheowofexcessmassoutofthetank.Alongthesameboundarywallrangingfrom50cmtothe60cmtankheight,amandatoryoutowof0.5cm/swasimposed.Thisconditionwasincludedtominimizetheadversepropagationofairfromtheoutowboundaryintothetankandagainsttheoutwardtravelingwaves.No-slipconditionswereincludedattheoorofthetankandalongthebedofthebeach.Incontrasttothedeep-watertestcasesmentionedinthepreviouschapter,however,no-slipconditions

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33 werealsoenforcedalongthesidewallsofthetankinordertodiscouragetheuniformbehaviorofwavesacrossthetankandtopromote3Deffects,therebymoreaccuratelydepictingthelaboratoryexperiment.3.2.2WaveForcingUsingLaboratoryDataAGaussianwavepacketwasforcedattheinowboundaryasspeciedbythelaboratorydatameasuredatpointAofASISTprovidedbyDonelanandHaus,andvelocitiesoutputbyTRUCHASatthethirdgridpointx=4cmwereexamined.Itwasdesiredthatwavevelocitiesoutputbythemodelatthisalong-tanklocationbeconsistentwiththeestimatedlaboratorywavevelocities.ThewaveforcingcomputationsaddedtoTRUCHASwereintroducedtothecodewithintheprojectionmodule.Astheprojectionmoduleisinvoked,TRUCHASisallowedtoadjustvelocityvaluesaccordinglywhenvelocityvaluesenteringacellaregreaterthanthoseleavingthecell.Hence,thelaboratoryvelocitiesbeingintroducedintothecalculationsviatheprojectionmodulemayexperiencesomesmoothingbeforenalvelocitiesareoutputatthethirdgridpoint,therebygivingwaytoslightlyloweractualvelocitiesversusforcedvelocities.Assuch,itbecamenecessarytoincreasetheforcingamplitudeandcorrespondingvelocitiesforthemodelsothatthevelocitiesoutputbyTRUCHASatthethirdgridpointwouldaccuratelycapturetheexpectedlaboratoryvelocities.Afteranumberoftrials,itwasdeterminedthatmodelinowvelocitiesmostcloselyresembledlaboratorydataatthislocationifTRUCHASsimulationswereforcedwiththevelocities,derivedvia Donelanetal. 1992 'smethods,associatedwithfree-surfaceelevationsscaledupbyafactorof1.1.Fig. 3 depictsthecloserelationshipbetweenmeasuredlaboratoryvelocitiesandTRUCHASvelocityvaluesforbothhorizontalandverticalorbitalvelocities.Itshouldbenotedthatvelocityvaluesshowninthisgureweretakenatacross-tanklocationofy=50cmandataverticalheightof29cmforbothlaboratoryandmodeldata.Thespeciedverticalheightwaschosenasitwasthe

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34 rstverticalgridcellbeneaththemeanwaterlevelthatremainedconsistentlywithinthewaterregimethroughouttime.Assuch,timeseriesprolesremainedcontinuous. Figure3:Arepresentationofthenumericalforcinganditscomparisontolaboratoryvaluesforbothuandwvelocity.Theexpectedbreakingwaveisrepresentedbythecentralwaveformoftheuvelocityplot. Asseeninthegure,modelvelocitiesverycloselyresemblethelaboratorydataandonlydeviateslightlyfromcalculatedvaluesoftheuvelocityatthetroughofthewaves.Suchsmalldifferencescouldbeattributedtoslightlyerroneousestimationsinthemethodsutilizedbylaboratoryinvestigators Donelanetal. 1992 tocalculatetheorbitalvelocitiesbeneaththewaves.Forinstance,aslaboratorywavesreachpointAtheyhavealreadydevelopednonlinearities,oftentimeswhichresultinmorepeakedcrestsandshallowertroughs.Suchnonlinearitiesmaybecompundedasweincreasetheamplitudeofthewavesandthenruntheorbitalvelocitycalculationprogram,therebyexplainingthesmalldiscrepancyinhorizontaltroughvelocitiesbetweentheoriginalandincreasedamplitudetimeseries.Wearecondentthatthemodelisforcingwiththerequestedvalues,astheforcingvelocitiesrepresentedbythegreenlineinFig. 3 verynearlyreplicatethevelocityvaluescomputedbyTRUCHASatthethirdgridpointdepictedasthebluelineinFig. 3 .Thealmostimperceptibledifferences

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35 betweentheforcingvelocitiesandthevelocitiescalculatedattherstgridpointaremostlikelyduetonumericalsmoothingwithinthemodelcomputations.3.3NumericalSimulations3.3.1SpecifyingUserInputsAsalludedtointhepreviouschapter,TRUCHAShasavailabletoitsusermanyoptionstofurtherdictateowdynamics.Suchuser-speciedoptionsincludetheuseofsurfacetensionandalgebraicturbulencemodelsandmoredetailedinformationsuchasmaterialdensitiesanddynamicviscosities.TheseoptionsarepresentedinTable 3 ,alongwiththespeciedinputschosenforthenalnumericalsimulationspresentedbelow.TestcaseswereconductedinwhichtheASISTexperimentwassimulatedboth Table3:Asummaryofmodeloptionsavailabletotheuserandthosespeciedfornalsimulations. UserInputUserOptionsFinalSimulations SurfaceTensionModelOn,OffOffAlgebraicTurbulenceModelOn,OffOffDynamicViscosityDefault*,UserSpecied0:0112g/cm*swater,1:79x10)]TJ/F24 7.97 Tf 6.586 0 Td[(4g/cm*sairDensityUserSpecied1:0g=cm3water,0:001g=cm3air *Defaultvalueofdynamicviscosityforallmaterials=0.0g/cm*s withandwithoutactivationofthesurfacetensionmodel.Resultsindicatedthatanactivesurfacetensionmodelhinderedsimulationspeedbyafactorofapproximately1.5,yettherewasnoapparentbenettousingthismodelinthedevelopmentandevolutionofthedeep-waterwavepackets.Itispossiblethatsurfacetensioneffectsarenegligiblefortheprincipledynamicsatthisscaleofwavelengthsandamplitudes.Thus,thesurfacetensionmodelwasturnedoffforthenalnumericalsimulations.Similarly,runswereconductedtotestthevalidityofthealgebraicturbulencemodel.Althoughruntimesforthetestcasewithoutthealgebraicturbulencemodelwereapproximately1.2timesfasterthanthatwiththeturbulencemodelinvoked,theredidnotappeartobeanydetrimenttoexcludingthealgebraicturbulencemodelfrom

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36 oursimulations.Giventheseresults,nalsimulationswererunwithoutthealgebraicturbulencemodel. 2 Testresultsalsoveriedmorereliableandaccuratemodelresultswhenmaterialpropertiessuchasdensityanddynamicviscositywereappropriatelyspeciedforeachmaterial.Valuesofdynamicviscosityanddensityusedinnalsimulationsweretakenfrom Munsonetal. 2002 .Itshouldbenotedthatthebeach,asdenedbytheuserinthesesimulations,wasgivenadensityof5:0g=cm3andwasdenedasanimmobilesolid,therebyhavingzeroviscosity.3.3.2ComputationalCostAsindicatedpreviously,wefoundthatthemostefcientcomputationalmeshtouseinconductingournumericalexperimentswasaclusteredmesh,ningto1cmby2cmby1cmresolutioninthebreakingregion.Ascanbeexpected,nerresolutionaffordedustheabilitytomoreaccuratelydetailthesmaller-scaleowdynamics.Coarserresolutionatthemeshwalls,however,signicantlyreducedthetimeittooktocompletetheseruns.PresentedinTable 3 areanumberoftestcasesthatwereconductedandthecomputationalexpenseofeach5secondsimulation.As Table3:Five-secondtestsimulationsconductedtoinvestigatethecomputationalcostofimprovedmeshresolution. CellAspectRatioNumberofCellsTankDimensionsComputationalTimex:y:znx;ny;nzx;y;zcmhrs 2:1:150,10,10100,10,104.172:1:0.5100,10,20200,10,10252:1:1200,10,60400,10,601252:2:1200,20,60400,40,60166.672:1:1150,10,100300,10,100457.5 isdetailedinTable 3 ,thecomputationalcostassociatedwithmeshesinvolvingbothanincreasednumberofgridcellsaswellasnerresolutionisadrasticincreasein 2Thedecisiontoomitthealgebraicturbulencemodelisfurtherdiscussedinthefollowingchapter.

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37 thetimeneededtocompleteeachsimulation.Assuch,theclusteredmeshdetailedpreviouslywasadopted.Employingthiscomputationaldomain,modelsimulationsof7secondsarecompletedinapproximately7daysontheSGI-Origin3400computerrunningonasingleprocessor.3.3.3Three-DimensionalEffectsItwashopedthatbyincludingno-slipboundaryconditionsatthesidewallsofthenumericalwavetank,3Deffectswouldbecomeapparentinthecross-tankdimension.Totestthishypothesis,timeaveragesofthemeanvelocityandtotalrootmeansquarermsdeviationfromthemeanvelocitywereperformed.Followingtheexamplesillustratedby Lyons 1991 ,they-averagedu,v,andwvelocitieswerecalculatedbysummingeachvelocityateachpointacrossthetankwithpreviousvaluesanddividingbythenumberofycellsbeingsummedover.Ameanvaluefordensitywasalsoobtainedinthismanner.Thevarianceforeachvelocitywasthentabulatedbysquaringthedifferencebetweenaninstantaneousvelocityandthemeanforeachdirectionanddividingagainbythetotalnumberofycellsbeingsummedover.Itshouldbenotedthatboundarynodeswereexcludedfromthesecalculationstoeliminatetheeffectsoftheno-slipsidewallconditionsonthecross-tankvelocityvariance.Finally,anrmsdeviationfromeachmean,orstandarddeviation,wasestablishedbytakingthesquarerootofthevariance.Thisvaluewasmultipliedbythemeandensitytoeliminatelargedeviationsintheairandtofocusprincipallyonvariationswithinthewatercolumn.Inaddition,therootmeansquaredeviationsforeachvelocitywerethensummedtoobtainatotalrmsvalueinthehopesthatthisvaluewouldbelargeenoughtobeofconsequenceinnumericalsimulations.Across-tankviewofthetotalrmsdeviationfromthemeanvelocityisshowninFig. 3 asthesteepestpointofthefocusedwavepacketcrossestheviewplane.Theskewednatureofthermsvelocityelddoesindicatethattherearesome3Deffectsinplayasthefocusedwavecrossestheplaneofview.Thesignicantlysmallvaluesforrmsvelocity,however,aresomewhat

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38 Figure3:3DeffectscapturedbyTRUCHASexperimentalsimulations,withthetotalrmsdeviationfromthemeanvelocitydisplayedinacross-tankviewatx=220cmalongthetank.Theexclusionofboundarynodesinthevariancecalculationsisevidencedbytheblankedvaluesatthetanksidewalls. disappointinggiventherelativelyhighvaluesofmeanvelocityofcloseto95cm/sfocusedwithinthecrestofthewave.Itisourbeliefthathigherresolutionwouldbettercapturesmallscaleturbulentstructuresandthussignicantlyeffectthesevalues,ahypothesisthatisfurtherexploredinthefollowingchapter.

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CHAPTER4RESULTS4.1WaveFocusingandBreakingDynamicsItwasouraimtoprovideamodelcompetentinthesimulationofrealisticwavebreakingevents.Ideally,thismodelwouldaccuratelycapturethedetailedandcomplexowcharacteristicsinherentinwavegeneration,propagation,focusing,andbreaking.Evenmoreso,asuperlativemodelshouldbeabletorepresentsuchimportantbreakingaspectsasturbulencegenerationandeddyformation.Amorein-depthlookintothemodelsimulationsandcapabilitiesisgiveninthefollowingsubsections.4.1.1BreakingVisualizationsInitialreportsfromthelaboratoryexperimentwestrovetosimulateindicatedthataspillingbreakeroccurredwithinthe3msectionbetweenmeasurementlocationsAandB.AcompositeofParticleImageVelocimetryPIVimagesofthesurfaceofthespillingbreaker,asprovidedbyDonelanandHaus,isgiveninFig. 4 .Successive Figure4:AcompositeofPIVimagesforthelaboratoryspillingbreaker. laboratoryrunsdictatedthisspillingbreakertobehighlyrepeatableunderthesameexperimentalconditions.Subsequently,itwasourhopethatTRUCHASwouldaccuratelycapturethesedetailedbreakingconditions,andthatsuchaspillingbreaker 39

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40 wouldbetherealizationofournumericalefforts.Breaking,unfortunately,doesnotreadilymakeitselfapparentwithinthevisualaspectsofourmodelsimulations.Fig. 4 containsasnapshotofthesteepestwaveproleobtainedforourmodelsimulation,includingacloserviewofthewaveofinterest. 1 Whilethewavepacket Figure4:Asnapshotoftheowvisualizationatthecriticalpointinthenumericalsimulation.AviewoftheentirenumericaltankisgiveninA,withacloserviewofthefocusedwaveatitssteepestpointinB. hassuccessfullyfocusedtocreateasteepwaveformseeminglyonthethresholdofbreaking,thereislittlevisualevidencetosuggestthatthewaveactuallyoverturns.AcloserviewofthewaveofinterestisgiveninFig. 4 .A1:1ratiobetweenxandzaxesismaintainedinthisgure,andthegridhasbeenpartionedtofacilitate 1NotethatthetankproledepictedinAisdrawnwithanexaggeratedz-axissuchthattheprolemightreadilytwithintheviewingwindow.TheplotshowninB,however,retainsa1:1aspectratio.

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41 Figure4:Acloserviewofthesteepwaveofinterest. calculationsofwavesteepness.Theredlinesmarkevery10centimetersinthex-direction,andtheyellowlinesarerepresentativeof4cmspacingintheverticaldirection.Asindicatedin DeanandDalrymple 2002 ,wavesbreakindeepwaterduetoexcessiveenergyinput,resultinginabreakingwavesteepnessofH/L1/7.FromthegriddisplayedinFig. 4 ,wecanestablishawavesteepnessofapproximately0.1.Hence,itwouldappearthatourwaveofinterestdoesnotsteepensufcientlytowarrantabreakingepisode.Still,amorein-depthanalysisofthewavecharacteristicsiswarranted.4.1.2MeanVelocityThevelocityeldunderaprogressivewaveisanimportantfactortoconsiderindeterminingtheaccuracyofamodeltodepictwavedevelopmentandbreaking.ViathemethodsoutlinedinSection3.3.3,ameanvelocityeldwasextractedfromthemodelresults.Fig. 4 isadepictionofthemeanvelocityeldcorrespondingtothecriticalpoint,whenthebreakingwaveisatitssteepestposition.ThemeanvelocityelddepictedinFig. 4 isanencouragingjusticationthatTRUCHASappearstobeperformingwellinpropagatingandfocusingthewavesinarealisticmanner.Asone

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42 Figure4:Cross-tankaveragedmeanvelocityeldatthecriticalpointofthesimulation,correspondingtotimet=4.47seconds. wouldexpectforawaveapproachingthebreakingpoint,velocitiesatthecrestofthesteepeningwavearehigh,withvaluesnearing95cm/s.Theseintensevelocitiesalsoseemtobeimpingingontheforwardfaceofthewavecrest,suggestingawavefrontthatisverynearspilling.Itisalsoencouragingtonotethatthemajorityofthemeanvelocityatthecrestandtroughlocationsisreectiveofhighuvelocitiesinthisregion,whilsttheverticalvelocitiesarenearlyzeroatthispointasonemightexpectforarealisticprogressivewave.Phasespeedestimatesforthecriticalwavewerefoundtobeapproximately90cm/s.Theslightlyhigherhorizontalvelocitiesinthecrestincomparisontothephasespeedofthewaveisapromisingindicationthatthecriticalwaveissteepeningtowardbreaking.Inaddition,agroupvelocityforthewavetraincanbeobtainedviaEq. 4 ,takenfrom DeanandDalrymple 1991 .Cg=nC=C 2+2kh sinhkh whereCg=groupvelocity

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43 C=wavecelerityk=wavenumberh=waterdepthUtilizingthewaveperiodof1secondandawaterdepthof36cm,awavenumberof0:04386cm)]TJ/F24 7.97 Tf 6.586 0 Td[(1isobtained.Thisinformation,inconjuctionwiththephasespeedof90cm/sfoundabove,givesrisetoagroupvelocityof57.1cm/s.Suchvelocityvaluesareinaccordancewithwavegrouptheoryinintermediateanddeepwater,inwhichtheindividualwavestravelfasterthanthewavepacket.Assuch,waveswillpropagatethroughthewavepacketovertime,andtheresultspresentedhereafterwillsubstantiatethisclaim.Fig. 4 showsthetimeseriesforhorizontalvelocitiesatthelocationalong-tankatwhichthecriticalwavereachesitsteepestpoint,x=220cm.Soastoproducea Figure4:Atimeseriesofthehorizontalvelocitiesattheexpectedbreakingpointofthewavetankx=220cm. smoothvelocitytimeseries,velocitycalculationsreectedinthisplotweretakenataverticalheightofz=29cm.Assuch,thehorizontalvelocitiesarenotrepresentativeofthoseatthefree-surfaceandarethereforelowerthanthehighestexpectedvelocitiesatthispoint.Althoughthereisnolaboratorydata,ofyet,withwhichtocompare

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44 Fig. 4 ,itisevidentthatthewaveofinterestretainsthehighesthorizontalvelocitiesasitpassesthecriticalpointandisfollowedbyasubsequentwavewithloweruvelocities.Itisofinteresttonotethat,inaccordancetothegroupandphasevelocitiesoutlinedabove,thecriticalwavehaspropagatedtothefrontofthewavepacketfromitspreviouspositioninthewavegroup,aswasshowninFig. 3 .InsimilarfashiontothehighuvelocitiesshowninthecrestofthewaveinFig. 4 ,thepointsmidwaybetweencrestandtroughrepresentmainlywvelocityvalues,whichcanbeasgreatas40cm/s.Truetolaboratorywavesinintermediateanddeepwater,orbitalvelocitieswithinourmodelwavesalsodiminishwithdepth,ascanbeseeninFig. 4 .SuchresultssubstantiatetheclaimthatTRUCHASisperformingwellonfundamentallevels.4.1.3RMSVelocityAtell-talesignofwavebreakingdynamicsisturbulenceproduction.Onewaytoquantifytheturbulentkineticenergybeingimpartedintothewatercolumnistoviewthetotalrmsdeviationfromthemeanvelocity,asdetailedinSection3.3.3.Greatvariancefromthemeanvelocityintheareaofexpectedbreakingwouldsuggestturbulencegenerationinthisregion,anindicationthatsomeformofbreakingisoccurring.Thetotalrmsdeviationfromthemeanvelocityforoursimulations,averagedacrossthetank,isgiveninFig. 4 Figure4:Totalrmsdeviationfromthemeanvelocityatthecriticalpointofthesimulation.Timeis4.47secondsintothesimulation.

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45 Whilethereisevidenceofavariationinvelocityacrossthetankatthecriticalpoint,thevaluesindicatedinFig. 4 aredisappointinglylow,withtotalrmsvelocityvaluesonlyreaching0.1cm/s.Asexplainedby Pope 2000 ,thelargestturbulenteddiestobeproducedbyasystemarecomparableinlength,velocity,andReynoldsnumbertothatoftheowscale.Accordingtotheenergycascade,theselargeeddiesbecomeunstableandbreakup,impartingtheirenergyintosmallereddies.Thisprocessiscontinueduntilthesmallesteddiesarestableandmolecularviscosityisefcientindissipatingkineticenergy.Consequently,thedisturbinglysmallvaluesobtainedfortotalrmsvelocitydictatethatthereisnotsubstantialturbulenteddyproductionoccurringwithintheowdynamics.Thesevaluesare,infact,overanorderofmagnitudesmallerthanwhatwouldbeconsideredrelevantturbulentvelocities.Asdiscouragingastheseresultsmaybe,notallhopeislostforthepossibilityofabreakingeventinmodelsimulations.Thesmallestresolvableturbulentstructuresthatcanbemodeledinasimulationarethosenolessthan2gridcellswide.Hence,withagridspacingof2cmatitsnestinthecross-tankdirection,wemaybemissingmanyturbulentstructuresthatareindeedinherentinourbreakingwave,indicatingthattherearemanymoreparameterstoconsiderintheanalysisofourmodel'spredictivecapabilities.ModelsimulationsarecomparedtolaboratoryresultsinthefollowingsectiontofurtherdenethecapabilitiesofTRUCHASinpredictingwavebreakingevents.Thepossibilitythatbreakingmaybeoccurringunbeknownsttotheusersduetosuchfactorsasinadequateresolutionarealsoaddressedinsubsequentsections.4.2ComparisontoLaboratoryDataThesuccessfulwavemodelshoulddemonstrateanabilitytoaccuratelyrecreatelaboratoryexperiments,andconsequentlytoprovidetheuserwithresultssimilartothosemeasuredinalaboratoryenvironment.ThevalidationofourmodeltoreadilyandaccuratelydepictwavefocusingandbreakingeventsisdependentuponlaboratoryresultsasprovidedbyourpartnersinMiami.TheresultsprovidedbyDonelanand

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46 Hausserveasacomprehensivemeansbywhichtoverifythesuccessofourmodel.Model-laboratorycomparisonsforavarietyofowparametersareconsideredinthefollowingsubsections.4.2.1HorizontalVelocityAswasdescribedinSection3.1,laboratorymeasurementsofthefree-surfaceelevationsweretakenattwolocationswithintheASIST.Valuesforhorizontalandverticalvelocitiesatevenincrementsbelowthefree-surfacewerethenacquiredviathemethodsoutlinedby Donelanetal. 1992 .Thedataretainedfromtherstlocation,thatoflocationA,wasmanipulatedandusedastheforcingforourmodelsimulations.ThedataobtainedatlocationB,approximately3mfromtheforcingboundaryandafterthebreakingregion,servesasameansbywhichtoevaluatethemodeldataafterbreaking.Fig. 4 showsboththelaboratoryresultsandthosecalculatedbyTRUCHASatpointB.AswiththetimeseriescomparisonsforlocationAgiveninSubsection3.2.2,itshouldbenotedthatdataforbothlaboratoryandmodelvelocitieswascalculatedatacross-tanklocationofy=50cmandaverticallocationofz=29cmtoensureacontinuoustimeseriesplot.Thelaboratoryvaluesforhorizontalvelocitypossessgreateructuationsintheearlystagesbeforethelargerwavesreachthemeasurementlocation.Thiscanbeattributedtothefactthatthefree-surfacelaboratorymeasurements,andcorrespondingvelocitycalculations,weretakenovera20secondinterval.Modelsimulations,ontheotherhand,wereforcedwiththemiddle7secondsofthelaboratorydataset,wherethelargerwaves,andmainconstituentsofthewavepacket,aregeneratedandpropagatetobreaking. 2 Thismethodallowedustosaveon 2Atestsimulationwasalsoconductedutilizingthefull20secondsoflaboratorydata.Visualanalysissuggestednodifferencebetweenrunresultsforthe20secondand7secondsimulations.The7seconddatasetwasthereforeemployedfornalsimulationsduetoitssignicantlysmallercomputationalruntime.

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47 Figure4:AcomparisonofhorizontalvelocitiescalculatedforthelaboratoryexperimentandthosepredictedbyTRUCHAS.Modelmeasurementsaretakenatapproximately3mfromtheforcingboundary.Theearliestwaveformdepictedontheplotisthatofthebreakingwave. computationaltimewhilestillmaintainingthemajorcomponentsofthefocusingwavepacket,andisultimatelyareasonthatmodelvelocitiesaresmallerthanthoserecordedinthelaboratoryfortheearlystagesofwavepropagation.Asthelargerwavespropagatethroughthepointofinterest,itisapparentthatourmodeloverestimatestheuvelocitiesinboththecrestandtroughofthewaveofinterestthatrepresentedbytherstwaveforminFig. 4 bynearly5cm/s.Inaddition,aphasedifferencebetweenthelaboratorydataandthemodeldatabecomesapparentafterthecriticalwavepassestheplaneofview.Theseobservationspointtothevisualclaimsmadeearlierthatthemodelwavedoesnotappeartobreakaswehadinitiallyanticipatedthatitwould.Thefactthatthehorizontalvelocitiesforthemodelwaveareapproximately5cm/shigherthanthoseforthelaboratorywaveindicatethatthemodelwavedidnotbreakinamannersimilartothatrealizedinthelaboratorysetting,asexplainedbelow.

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48 Ithasbeenwell-documentedthatturbulentoweldsproducehighlyvariablevelocityeldsthatcanuctuatesubstantiallyonarapidtimescale.AvelocityeldUx;tcanbedecomposedintoitsmean,anductuating,ux;t,partssuchthatux;tUx;t)]TJ/F25 11.955 Tf 14.484 0 Td[( Pope 2000 .Thisuctuatingvelocitycandriveturbulenteddyformation,aswellasacttohindertheprogressoftheinitialwaveform. Pope 2000 clariesthisphenomenonthroughanexaminationofaformoftheReynoldsEquations,giveninEq. 4 .D Dt=@ @xi[@ @xj+@ @xi)]TJ/F25 11.955 Tf 12.619 0 Td[(

ij)]TJ/F25 11.955 Tf 11.955 0 Td[(] where=meanvelocityeldD Dt=rateofchangeofthemeanvelocityfollowingapointmovingwiththelocalmeanvelocity;alsoknownasthemeansubstantialderivativeofthemeanvelocity=density@ @xj+@ @xi=viscousstressterm)]TJ/F25 11.955 Tf 12.62 0 Td[(

ij=isotropicstressderivedfromthemeanpressureeld)]TJ/F25 11.955 Tf 9.298 0 Td[(=turbulentshearstressarisingfromauctuatingvelocityeldConventionpermitsoftheturbulentshearstressterminEq. 4 tobelabeledtheReynoldsstress.ThisReynoldsstressstemsfrommomentumtransferasaresultoftheuctuatingvelocityeldinherentinturbulentows.As Munsonetal. 2002 pointsout,theturbulentshearstress,)]TJ/F25 11.955 Tf 9.298 0 Td[(takesonapositivevalueforturbulentows,therebycausingagreatershearstressinturbulentowsasopposedtolaminarows.Anaturalincreaseinturbulentkineticenergy,denedas1 2theReynoldsstresstensoror1 2,wouldalsoensue.Theresultingowresponseisadecreaseinthemeanvelocityeldwithaxialdistanceintotheowregime,coupledwithaspreadingout,ormixing,oftheoweld.Wavebreakingbeingaverynonlinearandcertainlyturbulentprocess,wewouldexpectthisresponseinthelaboratorywaves,andresultsseemtovalidatethisassumption.Thephysicallaboratory'ssteepwaveeventhasalreadyresultedina

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49 spillingbreakeronceitreachespointB.Thus,muchofthekineticenergyassociatedwiththewavehasgoneintoturbulenceandeddyformation,andtheuctuatingvelocityeldisgreatlyincreased.TheresultinghighReynoldsstressesacttodecreasevelocitiesinthelaboratorywaveform,thusallowingthesubsequentwavestoovertakethiswave.Asaresult,thereisaninitialphaselagbetweenthemodelandlaboratorywaves,asthelaboratorywaveexperiencesaslowingduetoturbulenceproduction.However,asthesubsequentwavesovertakethebreakinglaboratorywave,energymaybefedintothesewaves,andtheirvelocitiesincreased.Theinitialmodelwaveretainsthemajorityofitsenergyanddoesnotseemuchturbulentdissipation.AswasindicatedinFig. 3 ofChap.3,modelvelocityeldsshowlittlevariabilityinthecross-tankdirection.Consequently,thereislittleinthewayofauctuatingvelocityeldtoincursubstantialReynoldsstressvaluesandslowthewaveform.Subsequentmodelwaves,therefore,arenotaffordedtheopportunitytoovercomeandfeedoffofthiswave.Assuch,velocitiesinthewavesfollowingthebreakerarelowerthanthoseinthelaboratory,andthemodelwavesarethenseentolagthelaboratorywavesforwaveformsfollowingtheinitialbreaker.Havingreceivedlessenergyfromtheprecedingwaves,modelwavesarecontinuallydampedbythenumericalsmoothing,anddonotseethesameincreaseinenergyandvelocityexperiencedbythelaboratorywaves.AviewofthemeanvelocityeldatpointBisgiveninFig. 4 .IncontrasttoFig. 4 ,whichdepictslargevelocitiesinthecrestatthesteepestpointinthewaveevolution,Fig. 4 showsmuchsmallercrestvelocitiesatpointB,nearingonly30cm/s.Thisplotisincludedasvericationthatthehorizontalvelocitieswithinthewaveofinteresthavebeensignicantlyreducedfromthoseseenatthesteepestpointinthesimulation,andthattherstwaveforminFig. 4 isindeedthecriticalmodelwavethatwasexpectedtobreak.Thereaderisreminded,however,thatvelocitiesdisplayed

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50 Figure4:ThemeanvelocityeldatlocationB,ascalculatedbyTRUCHAS. inFig. 4 areslightlylowerthanthehighestexpectedcrestvalues,asthecalculationsareconductedataverticalheightof29cmabovethebedandnotatthefree-surface.4.2.2VerticalVelocityAsimilarpatternasthatreportedaboveforhorizontalvelocityisseenwithinmodel-laboratorycomparisonforverticalvelocities.AsshowninFig. 4 ,increasedverticalvelocitiesofcloseto5cm/saredepictedinthebreakingwavesimulatedbyTRUCHAS,ascomparedtothelaboratorybreaker.Verticalvelocitiesinthemodelwavepacketarethenseentounderestimatelaboratorycalculationsforthesubsequentwavebyover5cm/s,withadrasticunderestimationofthenegativeverticalvelocitiesofapproximately15cm/s.Asillustratedintheprevioussubsection,areasonableexplanationforthisdissimilarityagainseemstofallupontothefailureofthemodeltosuccessfullyproduceaspillingbreaker.Giventhesubstantialevidencesupportingtheuctuatingvelocityeldinherentinturbulentows,itseemslikelythatthespillingbreakerproducedinthelaboratorysettingwouldimpartmuchofitskineticenergyandmomentumintothewatercolumn,spawningturbulenteddies.Theincreaseinturbulent

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51 Figure4:Atimeseriesofbothlaboratoryandsimulatedverticalvelocities.ModelmeasurementsaretakenatpointB,approximately3mfromtheforcingboundary.Thewaveofinterestisrepresentedbythepreliminarywaveform. kineticenergy,withacorrespondingincreaseinReynoldsstress,wouldthenacttodeterthespeedofthewave,allowingsubsequentwavestoovertakethebreaker,thussteepeningthewaveformsandintensifyingwavecharacteristics.Thephaselagexperiencedbythelaboratorybreakerbutnotthemodelwaveofinterestisfurtherevidencetothisend,anexplanationforitsoccurrencebeingdetailedpreviously.AlthoughdiscouragingthatthemodelresultsdiffersignicantlyfromthosefoundinASIST,itishearteningtoseethattheuandwvelocityprolesforTRUCHASwavesshowsimilarcharacteristicsandtrends.ThisindicatesthatthetendencyawayfrombreakingofthesemodelwavesistheresultofsomeunderlyingdynamicsbeingexperiencedbyTRUCHASwaves,andnotnecessarilybyerrorswithinindividualvelocitycalculations.Furthervericationofthisndingcanbefoundinthecomparisonofthefree-surfacedisplacement,analyzedintheSubsection4.2.3.4.2.3Free-surfaceDisplacementModelresultsforfree-surfacedisplacementfollowthesametrendseeninthetimeseriesforhorizontalandverticalvelocities,examinedabove.Thefree-surfaceelevation

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52 forthemodelwascalculatedfromthepressureeldatlocationBasgeneratedduringaTRUCHASsimulation.Ashortprogramwasdevelopedtoextracttheverticalcelllocationcontainingthefree-surfaceforeachtimestepatlocationB,basedonthepressurevaluesforeachcell,asshowninEq. 4 ,takenfrom DeanandDalrymple 1991 .P=)]TJ/F25 11.955 Tf 9.299 0 Td[(gz+gkpz whereP=pressure=densityz=verticalposition,takenaszeroatthefree-surface=free-surfaceelevationkpz=coshkh+z coshkhThus,thepressureeldcalculatedbyTRUCHAScanbemanipulatedtoobtainavalueforatlocationBforeverytimestepofthesimulation,whichcanthenbecorrelatedtomeasurementstakenduringlaboratoryexperiments.Fig. 4 showsthetimeseriesoffree-surfacedisplacement,,atlocationBforbothmodelandlaboratoryresults,themeanwaterlevelhavingbeenremoved.ThecontinuouspressureeldmodeledbyTRUCHASproducesthesmoothfree-surfaceelevationtimeseriesshowninFig. 4 .Incontrast,thelasermethodusedinthelaboratorysettingisseentoproduceaverydetailedplot,withtheASIST'sfree-surfaceelevationexhibitingacomplexandvariedsignature.Itisalsoworthwhiletoremindthereaderthatmodelsimulationswereforcedwiththemiddle1 3ofthelaboratorydataforlocationA,thusearlymodelcalculationsfordonotreectthesamevariability,andthesmall-scaleuctuationspresentinthelaboratorydataduringthistimeperiodaresubsequentlynotcapturedinthemodel.Toverifythefree-surfaceelevationobtainedfromthemodel'spressureeld,aprogramwaswritteninwhichthevolumeofuidVOFeldwasusedtocalcuatethefree-surfaceelevation.TheVOFeldwasutilizedtodeterminetheverticallocationofthewatersurfaceateachtimestep,andthemeanwaterlevelwasremovedtoproducefree-surfacesaccuratetowithin1centimeter.As

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53 Figure4:Atimeseriesofthefree-surfacedisplacementascalculatedbyTRUCHASatlocationBanditscomparisontolaboratorymeasurements.Free-surfaceelevationisreportedincmwithmeanwaterdepthremoved.Theinitialwaveformrepresentsthebreakingwaveofinterest. theVOFeldisnotcontinuousbutratherisaseriesofpoint-valuescalculatedwithineachgridcell,theresultingfree-surfaceelevationtimeserieswasgivenaratherchoppyappearance.Theoverallplot,however,verycloselymatchedthatobtainedviathepressureeldmethod.InconcurrencewiththepatternnotedinFigs. 4 and 4 ,Fig. 4 depictsatallerwaveofinterestinmodelresultsthanthatmeasuredinthelaboratory.Thehighercrestelevationoftheinitialwaveformagaingivescredencetothehypothesisthatthemodelwavesteepensbutdoesnotundergobreaking,ratherdevolvingbackintoamorestablewaveform.Inaddition,TRUCHAS,onceagainsignicantlyunderpredictsthecharacteristicsofthesubsequentwave,missingthepeakelevationbyamagnitudeinexcessof6cmandthetroughbynearly3cm.Ofinteresttonoteisthenearlyidenticalfree-surfaceelevationsattributedtoboththemodelwaveofinterestandthatofthefollowingwave.Thisgivestheappearanceofamoreuniformwavetrain,andseemstosuggestthatinlieuofbreaking,thesteepwaveeventhasinsteadreceded

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54 toformamorestable,uniformwavepacketconguration.ThisimplicationwillberevisitedinSection5.4ofourdiscussion.Asalludedtointheprevioussection,thecomparisonillustratedinFig. 4 servestofurthervalidatetheadoptedhypothesisthatthemodelwavesdonotrespondinthesamemannerasthoseproducedinASIST.Thecorrelationbetweenhighfree-surfaceelevationandhighvelocitiesintheinitialwaveform,followedbyadrasticdecreaseinelevationandvelocitiesinthesecondwaveformisencouraging,indicatingthattheunderlyingfactorpreventingthespillingofthemodelwavesismanifestedinalloftheoweldsproducedbyTRUCHAS,fromVOFtopressuretovelocities.Inaddition,thesamephaselagsbetweenmodelandlaboratorymeasurementsarepresentinallofthevelocityandplotspresented.Assuch,itdoesnotappearasthoughthereisadistinctproblemwiththeforcingmechanismforTRUCHAS,createdbytheauthorsofthisstudy,butratheratendencytowardnonlinearitiesinherentintheowcomputationsofthemodelthatareproducingsucharesult.Still,thedependenceonuserinputtosuccessfullymodelbreakinghasnotbeencloselyexamined.Thesubsequentsectionisdedicatedtothisanalysis.4.3SensitivitytoUserInputSpecicationsGiventhatthemodelresultsarenotasclosetothelaboratoryresultsaswewouldhavehoped,webegantoquestionthemodel'ssensitivitytouser-speciedowdynamics.Questionsaroseastothebenetsofsuchspecicationsastheturbulencemodelandincreasedgridresolutioninmoreaccuratelyresolvingtheturbulentstructureswehadexpectedtoreproduce.Toascertainthevalidityoftheseoptions,testcaseswereconductedtoexamineeachuserinputindividually.4.3.1TurbulenceModelAswasmentionedinChap.3,initialtestcasesseemedtosuggestthatthealgebraicturbulencemodelwasunnecessaryinsuccessfullysimulatingthelaboratoryinvestigation.TheinabilityoftheTRUCHASmodeltoresolvesmall-scaleturbulent

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55 structures,however,causedustoreconsiderthestancepreviouslytaken.Assuch,anewsimulationwasdesignedtomirrorthesimulationsspeciedabove,withthesimplechangeofactivatingthealgebraicturbulencemodel,detailedbelow.Fig. 4 showstheuandwvelocitiesgivenafterbreakingforbothruns,withandwithouttheturbulencemodel.ThevelocityprolesshowninFig. 4 arenearlyidentical, Figure4:HorizontalandverticalvelocityprolesatpointB,3mdownstreamoftheforcingboundary. indicatingthattheorbitalvelocitiesseemtobelittleaffectedbythepresenceorabsenceoftheturbulencemodel.ThisresultisconsistentwiththendingsmentionedinChap.3,whereitwasdeemedthatthealgebraicturbulencemodeldidlittletoimprovethedynamicsoftheoweld.AmoredetailedcomparisonisprovidedinFig. 4 andFig. 4 ,whichshowthedifferencesintheresultsofthisnewrunandmodelresultswithouttheturbulencemodelinvoked.Consistentwiththendingsmentionedabove,thecomparisonofFigs. 4 and 4 indicatethatthemeanvelocityeldsforbothrunsarealmostidentical.Assuch,thelargescaledynamicsassociatedwiththegenerationandfocusingofthewavepacketarenearlyindistinguishableforbothcases.

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56 Figure4:Modelresultsformeanvelocityandtotalrmswithoutthealgebraicturbulencemodel.ThemeanvelocityispresentedinA,whilealong-tankandcross-tankdepictionoftotalrmsaregiveninBandC,respectively.Snapshotsaretakenatthecriticalpointinthesimulation,correspondingto4.47seconds. However,uponcloserexaminationofthebreakingregion,detailedinBandCofFigs. 4 and 4 ,wedondslightdiscrepanciesbetweensimulations.Inthestudyinvolvingthealgebraicturbulencemodel,wendslightlysmallertotalrmsvalueswithinthewavecrest,aswellaslessvariationinthecross-tankdirection.Totalrmsvaluesforbothsimulations,however,arestillverysmall.Thus,thereseemstobenodistinctadvantage,savecomputationaltime,tousingonemethodovertheother.Infact,itseemsmostttinginordertofacilitateincreasedturbulentproductioninthesimulationstoneglectthealgebraicturbulencemodel,asthisactsonlytofurtherdampenanyeddystructuresthatmaybeforming.ThesimplicityofthealgebraicturbulencemodelincludedinTRUCHASmaybeanunderlyingreasonbehindthepoornumericalresultsgivenwhenthismodelis

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57 Figure4:Modelresultsformeanvelocityandtotalrmswiththealgebraicturbulencemodelinvoked.Again,meanvelocityisshowninA,whileplaneandcross-sectionviewsoftotalrmsareprovidedinBandC,respectively.Snapshotsaretakenatthecriticalpointinthesimulation,correspondingto4.47seconds. invoked.ThisturbulenceclosuremodelinvolvesthesimplecalculationofturbulentdiffusivityasoutlinedinEq. 4 .T=Clmr 1 2KU2 whereT=turbulentdiffusivityC=proportionalityconstantbetweentheturbulentdiffusivityandtheproductoftheturbulentlengthandvelocityscaleslm=mixinglength,chosentorepresentthesizeoftheturbulenteddiesK=fractionofmeanowkineticenergythatisassumedtogiverisetotheturbulentkineticenergyU=meanowvelocityTheeffectivenessofthealgebraicturbulencemodelreliesoncompleteknowledgeoftheowgeometry,asC,lm,andKarealltermsspeciedbytheuserattheonset

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58 ofthesimulation. 3 Pope 2000 warnsthatforcomplexowsforwhichturbulentmixinglengthsarevariableorunknown,theuserspecicationoftheseparametersismainlyguesswork,andcanleadtoerroneousresults.Hence,thedefaultvaluesthatwereusedinoursimulationsmaybeproblematic,andaseparateinvestigationintothemosteffectiveconstantsforthissimulationiswarrantedbeforeadenitivestatementastotheeffectivenessofthemodel'salgebraicturbulencemodelcanbemade.4.3.2IncreasedResolutionArguablythemostimportantfeaturetoconsiderwhentryingtoresolvesmallturbulentstructuresisthemeshgridspacing.Asmentionedpreviously,thesmallestresolvableturbulenteddiesarethosenosmallerthan2gridcellsinlength.Accordingly,wehaveconcernthatthe2cmgridresolutionusedinthecross-tank,ory-direction,maybealimitingfactorinsuccessfullymodelingthesmaller-scaleturbulencewewouldexpecttoseewithinthebreakingregion.Atestcasewasthereforesetupinwhichthegridresolutionwasincreasedto1cmby1cmby1cmgridspacingwithinthebreakingregion.Thesimulation,henceforthreferredtoasRun2,wasconductedasthoseexaminedabove,withouttheutilizationofthealgebraicturbulencemodel,andresultswerecomparedtothoseobtainedinthepreviousruns.Surprisingly,resultsforRun2werepoorerthanthoseobtainedwiththeoriginalmesh.Casualobservanceofthefocusedwavepacketindicatesaless-steepwaveeventthanthosepreviouslynoted.Fig. 4 showsadecreasedhorizontalvelocityincomparisonwithvelocitiescorrespondingtotheoldmeshatpointB.ThoughuvelocitiesforthewaveofinterestcorrespondingtoRun2stilloverpredictthatofthelaboratorydata,atrstglancethereappearstobebetteragreementbetweenthetwo. 3Theproportionalityconstant,turbulentmixinglength,andkineticenergyfractiondesignatedinoursimulationswerethemodeldefaultvaluesof0.05,0.0254,and0.1,respectively.

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59 Figure4:ResultinghorizontalvelocitytimeseriesforanewgridmeshtakenatpointB. ThephaselagthatisapparentearlyoninRun2velocities,andthatremainswithinthetimeseriesassubsequentwavescrosstheplaneofview,however,givescauseforalarm.Despitetheslightlyhigheruatthecrestandtroughofthewaveofinterest,thephaselagbetweenthelaboratorydataandthemodeldataafterthepassingoftherstcrest,prevalentintheoldrunprole,doesnotexistinthenewmeshprole.Instead,theuvelocityproleforRun2suggeststhattheinitialhighervelocitiesforthemodelwaveallowtheproletobrieycapturethelaboratoryresults,butthenimmediatelybeginacontinuouslagbehindlaboratorydata.Plotsofverticalvelocityandfree-surfaceelevation,Fig. 4 and 4 respectively,forRun2showsimilarresults.Thiswouldsuggestthatvelocitiesinthenewmeshprolearelowerthanthatoftheoldnotbecauseofbreaking,butratherarelowerthroughouttheowsimulationinitsentirety.ThelowervelocitiesforthewaveofinterestinRun2mayalsoexplaintheslightlyhighervaluesforvelocitiesandfree-surfaceelevationinthecrestandtroughofthesecondarywave.Thehighvelocitiesoftherstwaveformintheoldmeshareevidentofasteeper,fasterwave

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60 Figure4:Resultingverticalvelocityproleforanewgridmesh. Figure4:Acomparisonoffree-surfaceelevationsforRun2andthosecalculatedwiththeoriginalmesh. passingtheplaneofview.LowervelocitiesinRun2prolesareindicativeofthelesssteep,slowerwavepassingthrough.Thisslowermovingwavemaybeslightlyovertakenbysubsequentwaveforms,feedingthemenergy,andhenceslightlyincreasingtheirvelocitiesandfree-surfacedisplacements.

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61 Thus,itappearsthatthecriticalwavegeneratedinRun2hasvelocitieseverywhereinthedomainlessthanthatoftheoldmesh.ThisconclusionisveriedinFig. 4 ,whichshowsthatthemeanvelocityatthecriticalpointofthesimulation,thesamepointexaminedearlierinFig. 4 ,isdrasticallylowerthanthatofpreviousruns,amountingtoamere48.5cm/s.Thelowerorbitalvelocities,andhencethe Figure4:Run2resultsformeanvelocityatthecriticalpointofthesimulation. poorerresults,ofthenewmeshsimulationcanbeeasilyexplained.Whilegridresolutionwasimprovedinthecenterofthemeshto1cmgridspacingineverydimension,gridcellshadtoberemovedfromthelong-tank,orx,directiontosaveoncomputationaltime.Thus,gridresolutionwithinthepropagatingregionofthewaveformswasreducedtoascoarseas9.6cmgridspacing.Althoughnotdeemedacriticalchangeatthetime,itisnotsurprisingthatsuchcoarsegridspacingwouldcompromisetheaccurateresolutionofthevelocityeldwithinthisregion.Athirdandnalmeshwasthereforecreatedtoalleviatethisproblemandtoprovidemoreaccurateresultswithwhichtoassesstheeffectofresolutiononturbulenceproduction.Keepingthesamescenarioasutilizedintheaboveruns,asimulationwasperformedwithathirdmeshandwillbedeemedRun3.Resolution

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62 waskeptto1cmgridspacingineverydimensionforthecenterofthebreakingregion,insimilarfashiontothatofRun2.Gridcellswereaddedtothexdimension,however,suchthatgridspacingwithinthepropagationregionwas4cmresolution.Thisisanimprovementovereventhemainrunsfocusedoninthisstudy,whichcontainedagridresolutionof6cminthepropagationregion.Asacricewasconsequentlymadeinthepost-breakingrealmofthedomaininthatgridcellshadtoberemovedfromthisregioninordertoincreaseresolutioninthepropagationregionandstillcompletesimulationsinjustoveraweek.Thus,gridspacinginthelong-tankdirectioninthisregionwasreducedtocloseto9cmresolution.Acomparisonofthealong-tankandcross-tankclusteringschemesusedintheorginalrunaswellasRun2andRun3isgiveninFig. 4 Figure4:Acomparisonofthexandyclusteringschemesutilizedinall3simulations.

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63 AsevidentinFig. 4 ,theaddedgridcellsinthepropagationregionofthecomputationaldomaindidservetoimprovethevelocityeldoverthatofRun2.ThoughmeanvelocityvaluesforRun3donotreachthemagnitudescomputedwithin Figure4:AcomparisonofthemeanvelocityeldfortheoriginalsimulationandthatofRun3.MeanvelocityfororiginalsimulationsisgiveninA,andthatpertainingtoRun3isshowninB.Bothprolesaretakenatthecriticalpointinthesimulationst=4.47seconds,whenwavevelocitiesandsteepnessesaregreatest. originalsimulations,meanvelocitiesof70cm/sarecapturedwithinthecrestofthecriticalwaveform.Thenon-negligibleincreaseinmeanvelocityvaluesfromRun2toRun3signifytheimportanceofgoodresolutionthroughoutthecomputationalmesh.TheadditionofgridcellswithinthepropagationregionbetweenRun2andRun3resultedinmeanvelocityvaluesdifferingbyover20cm/s.Asisevidentbytheseresults,notonlycansmallstructuresbeeasilyoverlookedinagridlackingsufcient

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64 cells,buterroneousoweldsmayresultfrompoorresolution,lendingeasilytoawedinterpretationsandinvalidconclusions.AlsoofinterestinFig. 4 istheformtakenbyeachsteepwaveevent.Whilethecriticalwaveproducedinoriginalsimulationshasahighlynonlinearprolewithasteepverticalfaceseeminglyonthecuspofbreaking,thecriticalwaveofRun3hasamoreuniformappearance.Thegentleforwardfaceofthiscriticalwaveagainseemstoindicateamovementawayfrombreakingandtowardamorestableconguration.Thisresultissurprising,asitwasexpectedthatthemorenelyresolvedbreakingregionofthemeshutilizedinRun3wouldprovideabetterindicationofbreakingthanthoseofpreviousruns.DespitetheinclinationofthecriticalwaveawayfrombreakingassubstantiatedbythemeanvelocityeldgeneratedinRun3,improvementswereseenwithinthissimulationinthetotalrmsdeviationfromthemeanvelocitymeasurements.Fig. 4 depictsthetotalrmseldobtainedviathemethodsoutlinedinChap.3fortheRun3simulationincomparisonwiththatoftheoriginalruns.Asindicatedinthegure,totalrmsvelocitiesmorethandoubled,toavalueof0.25cm/sinthecrest,forRun3.Whilesuchvaluesarestilltooslighttoimplyabreakingevent,itisencouragingtonotethatasmallincreaseinresolution,accomplishedviatheadditionofonly5cellstothecross-tankdimension,signicantlyimprovesthequalityofourresults.Evidentwithinthiscomponentofourinvestigationistheneedtomoreefcientlyresolvemodelcomputationsinregardstocomputationaltime.Thoughmanytestcaseswereconductedearlyinthestudytodeterminethemosteffectivecombinationofsuchnumericalparametersascourantnumber,convergencecriterion,relaxationparameter,preconditioningsteps,andmaximumnumberofiterations,acloserexaminationofthesedetailsiswarrantedatthispointinthemodelformulation.Anytimethatcanbesavedinthereductionoftheseparameters,whilestillaccuratelyresolvingowdynamics,correspondstogridcellsthatcanbeaddedtoourdomainwithoutthe

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65 Figure4:TotalrmsdeviationfromthemeanvelocityfororiginalrunsandthatofRun3.ThetotalrmsvelocityeldfororiginalrunsisgiveninA,whiletotalrmsvaluesobtainedwiththemorenelyresolvedmeshofRun3isshowninB.Measurementsaretakenatthecriticalpointofthesimulation,correspondingtot=4.47seconds expenseofincreasedsimulationtime.ThemanipulationofTRUCHAStoruninparallel,whichthusfarhasprovenunsuccessfulonouravailablemachines,willmarkanotherhugestepinthemoreaccurateportrayalofthenumericalwavepacket.Theeliminationoftheheavyrestrictionongridresolutionduetocomputationalexpense,whichatthispointisthelimitingfactorinournumericalmodel,wouldgivewaytomoredetailedowsimulations,possiblyrevealingowdynamicsthatarepresentwithinoursimulationsbuthaveyettoberealized.4.4Two-PhaseFlowDynamicsAsmentionedinChap.2,abenettomodelingusingTRUCHASisitsabilitytohandlemultiphaseowsystems.Assuch,detailedowdynamicscanbecapturedinboththeairandwaterregimes,anadvantagethatmanynumericalmodelstodate

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66 arelacking.Theapplicationsassociatedwiththiscapabilityaresubstantial,aslittleisknownastotheowintheairaroundawaterwaveattributedtothedifcultyassociatedwithstudyingsuchdynamicsinalaboratorysetting.Onelaboratorystudy,outlinedinChap.1,wasdedicatedsolelytotheinvestigationofairowsurroundingawave.Throughtheuseofamercury-watermodel, Zagustin 1972 observedacirculationowpatternaboveeachbreakingwaterwave.Hereasonedthatitwasthisowpatternthatwasresponsibleforthetransferofenergyfromairtosea.Thoughrudimentaryindesign,andobviouslyusingauidotherthanair, Zagustin 1972 'sinvestigationwastherstlookintotheroleofairowinthecomplexinteractionbetweenairandsea.Thoughnotdirectlypertinenttothescopeofthisstudy,itisinterestingtocommentontheairowpatterngeneratedbyTRUCHASinrelationtothatexploredby Zagustin 1972 .Fig. 4 isadepictionoftheairowsurroundingthewaveofinterestatthecriticalpointinthenumericalsimulations.Asisexempliedinthisgure,TRUCHASdoesindeedpredictacircularowbehaviorintheairsurroundingthesteepwaveevent.TheabilityofTRUCHAStocapturesuchowdetailsillustratesjustoneofthemanydiverseandrobustcapabilitiesofthismodel.Thedetailedowdynamicsthatcanbecapturedintheairbythismodelcertainlywarrantfurtherscrutiny;atask,however,thatisleftforafuturestudy.

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67 Figure4:Adepictionoftheairowpatternsurroundingawaterwave.

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CHAPTER5DISCUSSION5.1ApplicationsTheapplicationsofamodelasrobustasTRUCHASareendless.Numerousalgorithmsincludedwithinthethemodel'svastcodeallowforthenumericalcomputationandsimulationofsuchphenomenaasheattransferandphasechanges,chemicalreactions,solidmechanics,electromagnetics,anduiddynamics.Manipulationofthebasicuserinputlesarestraightforward,makingthevastexpansesofthiscodeaccessibletoeventheinexperiencedmodeler.Manipulationofthenumericalalgorithmsthemselves,however,provideamuchmorechallengingtask,asthemodel'snumerousmodulesareintricatelylinked.Thus,evenmoreexperiencedmodelersmayencounterchallengeswhentryingtonavigateortoadjusttheinnerworkingsofTRUCHAS.Additionally,thecomplexityofthismassivemodelcomesatacomputationalcost,andthelargesimulationtimerequiredtoresolvenegridmeshesmaybediscouragingtosomemodelersworkingonmodestcomputationalplatforms.Still,thevirtuesofamodelsuchasTRUCHASoftenoutweighthecost.Evenwithintheuiddynamicsrealm,thisfully3Dmodelhasalargerangeofcapabilities.Onedistinctadvantageofthismodelovermanyothersisitsabilitytohandlemultiphaseowsystems.Simpleadditionstotheinputlesallowforthemodelingofair,water,and/oranyothermaterialvitaltotheproblemathand.Assuch,withrelativelylittleeffortTRUCHASwouldprovideagoodmeansbywhichtoexamineowaroundstructures,scour,orsedimenttransportproblems.Arguablythegreatestattributeofthis3Dmodelisthattheuserisprovidedwiththecapabilitytobothcontrolandaccuratelysimulatetheowofairoverthewatersurface.Thisfeatureiscrucialinanyinvestigationofair-seainteraction. 68

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69 Iflefttoitsowndevices,themodelwillsimulatetheairowinresponsetoanydisturbanceswithinthewatercolumn.Conversely,theuseralsohastheoptionofforcingaspeciedairowwithinthedomain.Consequently,anin-depthnumericalstudyofwind-generatedwavesmaybeaccomplished;adetailedinvestigationwhich,totheauthors'knowledge,hasyettobesuccessfullyundertaken.Thewealthofknowledgethatcouldberealizedregardingsuchair-seainteractionsasmomentumandenergytransferacrosstheinterfacefromsuchaninvestigationisimmense.Itwouldseem,therefore,thatthisstudyhasonlyscratchedthesurfaceofthemanyenvironmentalinvestigationstowhichTRUCHAScanbeapplied.5.2SpecicationsTRUCHASreliesheavilyonuserinputtoaccuratelydepictowconditionswithinanumericalsimulation.CaremustbetakentocorrectlyspecifymaterialpropertiesinthisNavier-Stokesmodel.AstherearenodimensionalconstantswithinTRUCHAS,savethegasconstant,theusermayspecifyanyunitsystemtohisliking.Thisrequires,however,acarefulreviewofallinputvariables,asuidpropertieswithdifferingunitsystemswillprovideerrorsthatareimpossibletodebug.Thus,theuserholdsmuchcontroloverhisnumericalstudy,andmusttakegreatcautionandresponsibilityinrepresentingthenaturalphenomenoninquestionascompletelyasispossible.Thesimplisticnatureofthealgebraicturbulencemodelincludedinsucharobustandhearty3Dmodelisunfortunate.Infact,theTellurideTeam,creatorsofTRUCHAS,citethisadditionasaweaklinkinthecode,andvowtoupdateandimproveupontheturbulencemodelinTRUCHASversionstocome.Applicationofthealgebraicturbulencemodeltoourstudydidlittletoimprovetheoutcomeofoursimulations.Rather,turbulentuctuationsseemedtobemoreaccuratelycapturedwhenthealgebraicmodelwasnotactivated.Questionsariseastothecorrectmixinglengththatneedbespeciedinordertoaccuratelyapplythealgebraicturbulenceschemetoastudysuchastheoneconductedinthiswork.Hence,lackofasoundturbulencemodel

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70 couldbeahindrancetobreakingwavestudiesusingthisversionofTRUCHAS,andtheimplementationofanewturbulencemodelmayallowfutureversionsofthiscodetobemoresuccessfulinendeavorssimilartothoseattemptedinthisstudy.ThesensitivityofTRUCHAStothecellaspectratioisunfortunate,giventhecomputationalexpenseassociatedwithpoweringsuchaninvolvedmodel.Thebenetsofimprovedresolution,however,mayproveinvaluableintheaccuraterepresentationofturbulentstructuresandotherbreakingcharacteristics,andthusremainsanimportantissuetobefurtheraddressedinthevalidityofTRUCHASinitsapplicationtothisrealmofscienticexploration.Improvementsmadeinthecombinationofnumericalparametersemployedinsimulations,includingcourantnumber,convergencecriterion,relaxationparameter,preconditioningsteps,andmaximumnumberofiterations,maysaveoncomputationaltime,therebyallowingforincreasedresolutionatnoaddedcomputationalcost.Similarly,themodicationofTRUCHAStoruninparallelwilleffectivelyremovetherestrictiononmeshresolutioncurrentlyinplace,asruntimeswillseesignicantreductions.Asisthecasewithanynumericalmodel,TRUCHASuserswoulddowelltorecognizeboththelimitationsaswellastheplausiblebenetsassociatedwitheachspecicationoptedforinanygivennumericalsimulation.5.3SummaryofFindingsThequestionssurroundingdeep-waterwavebreakingeventsandtheirroleinair-seainteractionaremanifold.Atpresent,afully3Dmodelcapableofpreciselysimulatingallofthecomplexdynamicsassociatedwiththisphenomenonremainstobedeveloped.Suchanumericalcodecouldremainelusiveforsometimetocome.Still,signicantadvancesintheaccuratenumericaldepictionoftheairandseaduringbreakingeventsarebeingmadecontinuously.Itisourhopethatthisworkmaybeonesuchstepinthequesttounderstandoneofthemostcommoneventsweencounterinnature.

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71 TheobjectiveofthisinvestigationwastomodifytheowdynamicsofTRUCHAStohandleafocusingwavetechnique,andthentoverifytheabilityofthemodeltoaccuratelypredicttheresultingdeep-waterbreakingwaveevents.LaboratoryexperimentsconductedbyMarkDonelanandBrianHausattheUniversityofMiamiprovidedthemeansbywhichtoforcethemodelaswellastovalidatemodelpredictions.NumericalforcingofaGaussianwavepacketwasaccomplishedbyimplementingthefree-surfaceelevationandorbitalvelocitiesobtainedinthecontrolledlaboratorysetting.Focusingofthewavepackettranspired,andthemodel'sresultinganduandwprolescouldthenbecomparedtolaboratoryresultsatapointdownstreamofthebreakingregion.Numerouscomputationalrunswereconductedinwhichspecicationsincludingsurfacetensionmodels,turbulencemodels,andvariouscellaspectratioswereindependentlyinvestigated.Finalsimulationswereconductedwithwhatwasdeemedthemostcomprehensive,yetcomputationallyefcientscheme.Theresultsofthisundertaking,thoughsomewhatdisappointing,gavegreatinsightintothecapabilitiesofthisvolumeofuidmodel.Aqualitativeanalysisofthebreakingregionyieldednodenitiveevidenceofaspillingeventwithinthenumericalsimulations.Visualobservationsofthefree-surfaceorientationcomputedduringmodelrunsdidnotindicateoverturningorsignicantdisruptionoftheuidinterface.Thoughmeanvelocitymeasurementswerehighinthecrestofthewaveofinterest,totalrmsdeviationfromthemeanvelocitywassmallwithinthislocation,indicatinglittleturbulenceproductionthatwouldhaveindicatedbreakingactivity.Bothhorizontalandverticalvelocitycomponents,aswellasfree-surfaceelevations,atlocationBdemonstratedincreasedvaluesincomparisontolaboratorymeasurements.Inaddition,aphaselagofthelaboratorydatawasseentooccurjustafterthepassingofthecriticalwavecrest.Itisexpectedthatturbulenceproducedbythespillinglaboratorybreakerwouldspawneddiesandacttohindertheadvancementofthewaveform,inaccordancewiththeliterature.Thisslowingofthebreaking

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72 wavecouldthusintroducethephaselagseeninthedata.Similarly,theenergyrequiredtocreatetheturbulenceassociatedwithbreakingwouldcomefromthekineticenergyoftheinitialwave,thusaccountingfordiminishedlaboratoryvelocitiesincomparisontomodeldata.Themodelwave,however,havingnotundergoneasignicantbreakingevent,didnotexperiencetheseeffects,andthusretaineditshighervelocityandfree-surfacevaluesdownstreamofthebreakingzone.Asthesecondarywavepassedtheplaneofinterest,however,therewasareversalinthedatatrends.Thesubsequentlaboratorywaveshadampleopportunitytoovertaketheturbulent,slowly-propagatingbreaker.Thus,thevelocitieswithinthesesteepeningwaveswereincreased,correspondingwithhigherfree-surfacedisplacements.Thewavealsoseemedtopropagatefasterintimeasthephaselagexperiencedbythespillingbreakerwasnotrealizedinthesubsequentwaves.Conversely,thesecondarymodelwavesneverfullyovertookthecriticalwave.Assuch,lesssteepeningoccurredandtheirvelocitiescontinuedtodiminish,thusproducingwhatappearstobeaphaselaginthemodeldataincomparisontothelaboratoryprolesforthesubsequentwaves.Theresultsofthenumericalinvestigationinferthefailureofthefocusedwavepackettoreproduceaspillingbreakeratthesegridresolutions.Instead,modelresultssuggestamovementofthesteepwaveeventawayfrombreakingandtowardamorestableconguration.Thefree-surfaceelevationproleatlocationBgeneratedbyTRUCHASisnoteworthyinitsseeminglymoreuniformappearance.Theseresultsseemtoindicatethatnonlinearitieswithintheowdynamicstriggerthesteepenedwavetodevolveintoamorestable,regularwavepacketformation.Inresearchingthisphenomenon,itwasdiscoveredthatothercomputationalcodeshaveexperiencedsimilarresults.Aninvestigationintotheplausibleexplanationsforsuchanoccurrenceisprovidedisthefollowingsection.

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73 5.4RecurrenceAlthoughunfortunate,itdoesnotappearthatthefailureofTRUCHAStoproduceaspillingbreakerisanuncommonproblem.Thenatureoftheevolutiontobreakingofdeep-waterwaveshasbeenanareaofintensescrutinyforquitesometime.Suchinvestigationshaveledtowell-documentedinstabilitiesknowntodevelopwithindeep-waterwavetrains,producingnonlinearmodulations. BenjaminandFeir 1967 wereoneofthersttodocumentsuchinstabilities,showinganalyticallythatniteamplitudedeep-waterprogressivewavesarefundamentallyunstable.Theirndings,whichhavecometobeknownastheBenjamin-FeirInstability,illustratethataperiodicprogressivewavewithafundamentalfrequencyhasalsopresentresidualwavemotionsatsidebandfrequenciesthatcanincreaseexponentiallyaswaveevolutionprogresses.Theresultingwaveformcanbecomehighlyirregularfarfromitsorigin,andsuchwavetrainswillacttosubsideifgivenamplespace.Laboratoryinvestigationsperformedby Melville 1982 conrmedtheBenjamin-FeirInstabilitytobepresentinexperimentaldeep-waterwaves.Asecondinstabilitywasdiscoveredby Tanaka 1986 atthecrestofregularwaves.Hisinvestigationunearthedaninstabilityatthewavesteepnesscorrespondingtothemaximumtotalenergyofthewaveform.TheTanakaInstability,asitisnowreferred,occursonlyatthesteepestwavecrests,andhasbeenproventobealocalresponsetodisturbanceswithinthewavecrest,therebynotbeingaffectedbythedynamicsofthewavetraininitsentirety.Aninterestingconclusiondrawnfromthisinvestigation,andmostpertinenttoourstudy,isthattheevolutionoftheTanakaInstabilitycanleadtooneoftwoplausibleoutcomesintheprogressionofthewaveform.Thoughnotwellunderstoodastoexactlywhyawavewilladvancetowardoneextremeortheother,waveformsexaminedwithinthecontextofthisstudyeitherprogressontobreaking,orelseundergowhatisreferredtoasrecurrence,wherebythewavedemodulatesbacktoclosetoitsinitialform,thusbecomingmorestable.

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74 Thediscoveryofthesenonlinearmodulationshaveprovidedsomeinsightintothebreakingandrecurrencephenomenonexperiencedbymanyinthenumericalinvestigationsofwavebreaking.Still,theunderlyingtriggerthatwouldcausesuchunstablewavestoproceedtowardeitherbreakingorrecurrenceremainselusiveandhasspawnedanintenseexaminationintothenatureofnumericalbreaking.Manyattemptshavebeenmadetoquantifyinsomeuniversalconstantthelikelihoodthatagivensteepwaveeventwithinawavetrainwilleitherundergobreakingorratherrecurrencebacktoitsinitialsignature. BannerandTian 1998 performedanin-depthanalysisofaperiodic,2Dwavetraintodetailtheonsetofbreakingorrecurrence.Theauthorsutilizedacodeconstructedby DoldandPeregrine 1985 inwhichaCauchytheoremboundaryintegralisusediterativelytosolvedLaplace'sEquationthroughtheevaluationofmultipletimederivativesofthesurfacemotion. BannerandTian 1998 thenaddedtheirowninteriorcodetothemodeltocomputetheinterioroweldfromthefree-surfaceorientationateverytimeduringthesimulationusingaspectralmethod.Theirinvestigationsuggestedthattheonsetofbreakingorrecurrencewasdictatedbythenonlinearbehaviorofthewavegroup,andcouldbedeterminedbytherelativegrowthratesofthemeanmomentumandenergydensities.Findingsindicatedthatbreakingoccurredwhenthemeanmomentumandenergygrowthratessurpassedacertainthresholdvalue.Incontrast,steepwavescouldbeexpectedtoundergorecurrencewithoutbreakingifthesegrowthratesreachthethresholdvalueandimmediatelybegantodecline. Hendersonetal. 1999 ,focusingmainlyonthenonlinearmodulationof2Dperiodicwavetrainsoverseveralthousandwaveperiods,observedsimilarresults.Similarto BannerandTian 1998 Hendersonetal. 1999 alsoadoptedthecodeof DoldandPeregrine 1985 .Capableofsimulating2Doweldsuptooverturningwithaslightsmoothingscheme,thismodelhasbeenprovenaccurateinthesimulationofuniform,irrotational,periodicwavetrains. Hendersonetal. 1999 didnotinclude

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75 aninteriorcode.Rather,theirfocuswasonthebehaviorofadeep-waterwavetrainwithvaryinginitialsteepnessesandthenumberofwavespertrain.Theauthorsnotedthatenergybecomesfocusedintoashortgroupofsteepwaves,oftenthatpossessawavesteepenoughtobreak.Occasionally,however,thewavegroupseemstoreachamaximummodulationandthenproceedstodemodulate,andrecurrencetranspiresuntilanalmostuniformwavetrainisrecovered.Asimilaroutcomeseemstobesuggestedbytheresultsofourstudy:Fig. 4 ,depictingfree-surfacedisplacementatlocationB,showssimilarvaluesforatthecrestofboththewaveofinterest,orthepreliminarywaveformintheplot,andthesubsequentwaveform.Althoughthesewavesarenotperiodicinnature,asthoseexaminedby Hendersonetal. 1999 ,ourmodelresultsseemtoillustratethetendencyofasteepwaveeventhavingundergonerecurrencetodevolveintoanearlyuniform,stablewavetrain.Ofparticularinteresttoourinvestigation, SongandBanner 2002 conductedastudyintotheonsetofbreakingfordeep-waterwavetrainsofvaryingcomplexity.Amongthewavetrainssimulated,theauthorsincludedaclassofwavetrainsdeemedchirpedwavepackets,inwhichasteepwaveresultsfromthefocusingofawavepacket,verysimilartothemethodusedby RappandMelville 1990 inthelaboratory,andanalogoustothewavepacketsutilizedinourstudy.The2Dnumericalmodelemployedby SongandBanner 2002 solvesthefullynonlinear,irrotationalfree-surfaceboundaryvalueproblemwithaboundaryelementmethod.Apistonwavemakerisincludedatoneendofthenumericaldomain,withanenergy-absorbingbeachattheotherend.Initialconditionswerethatofastillwatertank,andsimulationswerecarriedoutpastthepointofoverturning.Intheirinvestigation, SongandBanner 2002 disprovedthetheorythatinstabilitieswithinsteepwaveeventsarecontingentuponthenumberofwaves,N,withinawavepacket,ashadbeensuggestedinpreviousstudies.Instead,theauthors'ndingssupportthoseof BannerandTian 1998 ,citingtheaveragegrowthrateof

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76 adimensionlessenergyparametertobethedeterminingfactorintheevolutionofawaterwavetorecurrenceorbreaking.Withineachclassofwavetrainsstudied,itwasdeterminedthatadimensionlessgrowthratethresholdexisteddeningthebreakingandrecurrenceregimes.Shouldtheenergygrowthrateofthewaveexceedthisthreshold,thewavewasfoundtobreak.Conversely,ifthemaximumvaluesoftheenergygrowthrateremainedbelowthisthresholdvalue,recurrencewasundergone.Thresholdvalues,however,variedsignicantlybetweenwavetrainclasses.Thusaunique,universalbreakingthresholdcouldnotbeascertained.Thoughthereisstillmuchtobeuncoveredastotheexactnonlinearitiesthattriggertheenergygrowthrateofwavestoreachthresholdvalues,muchhasbeenlearnedabouttheinstabilitiesundergonebydeep-waterwavetrains.Thefactthatourstudyandthoseaboveallvaryintheapproachofthesimulation,yetallexperiencethesamerecurrencephenomenonisindicativeofanonlinearproblemnotuniquetoTRUCHAS.Theadded3Dnonlinearitiescertaintoexistinourmodel,incomparisonwiththosediscussedabove,mayonlycompoundtheconditionsleadingtorecurrenceinTRUCHAS.Thoughthereisnoconclusiveevidenceofyetastothespecicnonlinearitiesdictatingtherecurrenceofourmodelwaves,thestudiesmentionedabovehaveprovidedthebeginningsofanexplanationintothecomplexdynamicsobservedinthesesimulations.Asmorestudiesareconductedintothevastandhighlycomplexnonlinearnatureofdeep-waterwaves,itishopedthatconclusionswillbedrawnastothedetailssurroundingtheonsetofwavebreaking.Surelytofollow,then,willbeamorethoroughandpreciseillustrationofthenumericalattributestriggeringeachtypeofbreakingresponse,andimprovementscanbemadetomoreaccuratelymodelthedesiredbreakingregime.5.5ConcludingRemarksDespitetheinabilityofTRUCHAS,giventhenumericalspecications,toproduceaspillingbreaker,muchwaslearnedregardingthevariedcapabilitiesofthisrobust

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77 model.Itisnotimpliedthatthefailureofthisstudytoresultinadenitivebreakerissuggestiveofacompleteinabilityofthemodeltoaccuratelysimulatespillingevents.Muchtothecontrary,simulationsinvolvingincreasedamplitudewaveswereconductedinwhichspillingbreakersoccurredearlyinthesimulations.Unfortunately,thesebreakingepisodestranspiredwithinthepropagationregionofthenumericaldomain,andthusdidnotaccuratelysimulatethelaboratoryexperiment.Assuch,thesecaseswerenotpresentedinthiswork.Itistheopinionoftheauthorsthatincreasedresolutionmaysignicantlyimprovetheperformanceofthecode,andmayrevealowcharacteristics,suchasturbulentstructures,thatarenotreadilyobservablegiventhespecicationssetforthinthisnumericalinvestigation.OngoingresearchinvolvingTRUCHASiscurrentlybeingconductedtofurthervalidatethemodel'sabilitytoaccuratelyreproducespillingeventsexperiencedinlaboratorysettings.Currentsimulationsinvolvesignicantincreasesingridresolutionaswellastheadditionofacross-tankperturbationinthehorizontalvelocityeld.Itistheauthors'hopethatsuchimprovementswillnotonlyprovidetheinstabilitiesneededtoensureabreakingeventwilloccur,butalsowillallowforthesimulationofsmall-scaleturbulenceandotherbreakingcharacteristics.Still,TRUCHAShasprovenaworthynumericaltoolintheinvestigationofair-seainteractionsandisfoundtohavecapabilitiescertaintoproveusefulinfutureinvestigationsintobreakingeventsandwind-generatedwaves.TheexplorationintotheadvancesthatcanbeaccomplishedthroughtheuseofTRUCHASisstillyoung,andwiththecorrectcombinationofresolutionanduserinputs,itislikelythatTRUCHASwillbeavaluableassettotheengineeringworld.

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APPENDIXWIND-GENERATEDWAVESThecapabilitiesofamodelsuchasTRUCHASaremanifold,andamagnitudeofresearchcanbeconductedwithsuchatool.AsmentionedbrieyinChap.1,adiscoverywasmadeduringthisstudysuggestingthepossibilitythatTRUCHAScanbeusedtosimulatethedevelopmentandevolutionofwind-generatedwaves.Thoughoutsideofthescopeofthisstudy,abriefexaminationwasconductedinanattempttoverifythishypothesis.Asimpleorthogonalmeshwasgeneratedspanning1minlength,0.5minwidth,and0.6minheight.Gridresolutionremainedfairlycoarsetoallowforfasterconvergence.Thecorrespondingcellaspectratio,x:y:z,was4:5:2.Themeanwaterlevelforthegivenscenariowas30cm,withfree-slipboundaryconditionsonthesidewallsandalongtheclosedtopofthetank.Abovethemeanwaterlevel,aconstant-pressure,openboundaryconditionwasenforcedattheendwalltoallowtheunobstructedowofairoutofthenumericaltank.A7m/sapproximately15.7mphwindwasthenblownoverthewaterbody,whichwasinitiallyatrest.Themodelwaspermittedtorunforashort3secondtimespanandqualitativeresultsweredocumented.Fig. A showstwotimeshotsofthesimulation.PlotA,takenattime0.48seconds,depictstheinitialformationofwind-generatedwavescausedbytheshearstressimpartedontheinitiallystillwatercolumnbythemovementoftheair.Amorefully-developedwaveeldhasevolvedbythesecondtimeshot,B,takenat2.61secondsintothesimulation.Inaddition,interestingowdynamicsappeartobehappeningattheinowboundary,withthepossibilityofairentrapmentbeneaththewatersurfaceatthislocation.Withoutargument,amoredetailedinvestigationofthis 78

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79 FigureA:Snapshotsofwavesgeneratedbya7m/swindacrossawaterbodyinitiallyatrest.Initialwavegeneration,at0.48s,isshowninA,whileadepictionofamorefully-developedwaveeld,at2.61s,ispresentedinB. scenario,requiringamorenely-resolvedmeshandimprovedboundaryconditions,isneededtoquantitativelygivesoundevidenceofthephenomenoninquestion.Toourknowledge,afully3Dnumericalstudyhasyettobeconductedillustratingowdynamicsinboththeairandseaassociatedwiththecomplicateddevelopmentofwind-generatedwaves.Mostnumericalmodels,tothispoint,areunabletofullyresolvethevelocitiesinbothuidsandareeitheridealized,orfocusentirelyonthedynamicsofthewatercolumn.Itwouldseemthat,thoughthisstudywasbriefandrudimentaryatbest,ourndingswarrantacloserlookintothecapabilitiesofthisvastmodel.

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82 MIYATA,H.1986Finite-differencesimulationofbreakingwaves.J.Comp.Phys.65,179. 1.2 MUNSON,B.R.,YOUNG,D.F.&OKIISHI,T.H.2002FundamentalsofFluidMechanics.JohnWileyandSons,Inc.,Hoboken,NewJersey. 3 5 PEYRET,R.&TAYLOR,T.D.1985ComputationalMethodsforFluidFlow.Springer-Verlag,NewYork,NewYork. 2.4.4 POPE,S.B.2000TurbulentFlows.CambridgeUniversityPress,NewYork,NewYork. 4.1.3 5 6 RAPP,R.J.&MELVILLE,W.K.1990Laboratorymeasurementsofdeep-waterbreakingwaves.Phil.Trans.R.Soc.Lond.A331,735. 1.2 3.1 5.4 SONG,C.&SIRVIENTE,A.I.2004Anumericalstudyofbreakingwaves.Phys.ofFluids16,2649. 1.2 SONG,J.-B.&BANNER,M.L.2002Ondeterminingtheonsetandstrengthofbreakingfordeepwaterwaves,PartI:Unforcedirrotationalwavegroups.J.Phys.Oceanography32,2541. 1.2 5.4 TANAKA,M.1986Thestabilityofsteepgravitywaves.J.FluidMech.156,281. 5.4 TEAM,T.T.2004TRUCHAS,Version2.0,LA-UR-03-9109edn.LosAlamosScienticLaboratoryoftheUniversityofCalifornia. 2.1 2.2 2.3 2.3 2.4.1 2.4.2 2.4.3 2.4.5 TULIN,M.P.&WASEDA,T.1999Laboratoryobservationsofwavegroupevolution,includingbreakingeffects.J.FluidMech.378,197. 1.2 VANDORN,W.G.&PAZAN,S.E.1975LaboratoryInvestigationofWaveBreaking,PartII:DeepWaterWaves,Tech.Rep.ScriptsInst.ofOceanography,SanDiego,California. 1.2 VIAUSSER,B.,GRILLI,S.T.&FRAUNIE,P.2003Numericalsimulationsofthree-dimensionalwavebreakingbycouplingofavofmethodandaboundaryelementmethod.InProc.13thInter.OffshoreandPolarEng.Conf.,pp.333.Inter.Soc.ofOffshoreandPolarEng.,Honolulu,Hawaii. 1.2 XUE,M.,XU,H.,LIU,Y.&YUE,D.K.P.2001Computationsoffullynonlinearthree-dimensionalwave-waveandwave-bodyinteractions,PartI:Dynamicsofsteepthree-dimensionalwaves.J.FluidMech.438,11. 1.2 YUEN,H.C.&LAKE,B.M.1980Instabilitiesofwavesondeepwater.Annu.Rev.FluidMech.12,303. 1.2

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83 ZAGUSTIN,K.1972Energytransfermechanismforniteamplitudewaves.InProc.13thConf.CoastalEng.,pp.523.Vancouver,B.C.,Canada. 1.2 4.4

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BIOGRAPHICALSKETCHIspentmychildhoodinthesmalltownofNorthBillerica,Massachusetts,justashortridefromBoston.IhavemanyfondmemoriesofthewonderfultimesthatIspentwithclosefriendsandatightly-knitfamilyduringthoseyears,manyofwhichinvolvethewater.Iwassplashinginourin-groundpoolbeforeIhadeverconsideredtakingastep,andnotasummerdaywentbythatmybrothersandIwerenotinventingnewpoolgamesorlearningtowaterski,tube,wakeboard,andboatatourlakesidecabininMaine.IknewbythetimethatIwasenteringgradeschoolthatIwouldneverbehappyansweringphonesortypingmemosforaliving;Iwasmeanttobeonthesea.ItwasonourrstbigfamilytriptoFloridawhenIwasin5thgradethatIpinpointedexactlywhatIwasgoingtodowithmylife:IwasgoingtotrainthedolphinsatSeaWorld.IheldontothatdreamthroughouttheremainderofmytimeinBillerica.UpongraduatingfromBillericaMemorialHighSchoolin1999,Isetouttobecomeamarinebiologist.MydreamtookmetoSt.Petersburg,Florida,whereImadeoneofthegreatestdecisionsofmylifetoattendEckerdCollege.Thesmall,intimatesettingatEckerdwasexactlywhatIneededduringmyrstextendedperiodoftimeawayfrommyfamily.Smallclasssizes,multiplelaboratorystudies,andtheschool'son-siteresearchvesselsandwaterfrontpropertymadethestudyofmarinesciencebothexcitingandveryaccessible.Isoonlearned,however,thattherewasmuchmoreunderthesurfaceoftheoceanthansimplymarinemammals.AftertakingmyrstmarineinvertebrateclassandrealizingtheextenttowhichIwouldhavetostudysuchcritters,aswelikedtorefertothem,beforeIwouldeventuallygettothegoodstuff,orthemammals,Ibegantoseriouslyquestionmychoiceinconcentrations.ItwasatthattimethatI 84

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85 tookmyrstmarinegeologyclass,andIimmediatelyfellinlove.Bymysophomoreyear,IhaddecidedtoshiftmyfocustomarinegeophysicsandwenttoworkforDr.GreggBrooks,mymarinegeologyprofessorandasedimentologist.TheexperienceIgainedfromthatresearchassistantship,bothinthelaboratoryaswellasintheeld,hasbeeninvaluable.Duringthistime,Ispentsummersonboardresearchcruisescollectingunderwaysedimentsamples,sidescanandseismicsonardata,andsedimentcores.IalsoobtainedmySCUBAcertication,andhadtheamazingopportunitiestostudygeologyandvolcanologyabroad,inbothEcuadorandtheGalapagosIslandsaswellasinTanzania,EastAfrica.IcontinuetobeamazedattheopportunitiesmadeavailabletomeatEckerdCollege,andIamunbelievablyhappytohavemadesuchanastoundingchoiceinschools.ItwasduringaseniorresearchstudyatEckerdCollegethatIworkedwithDr.DavidDuncan,ofbothEckerdCollegeandtheUniversityofSouthFlorida,inthecollectionofseismicCHIRPdata.Duringthistime,IlearnedhowtocollectandtoanalyzeCHIRPdata,andIpresentedaposterattheGulfofMexicoEstuariesIntegratedScience:TampaBayPilotStudy2002PosterSeriesinwhichIcorrelatedCHIRPdatawithsedimentcorestakeninSafetyHarbor,TampaBay.Havingbecomeextremelyinterestedinseismicsonarstudies,Ibegantothinkthatagraduateprogramincoastaloroceanographicengineeringmightbeaninterestingsupplementtomyundergraduateexperience.Thus,uponcompletionofmyBachelorofSciencedegreeinmarinescience,withaconcentrationinmarinegeophysicsandaminorinmathematics,inMayof2003,IenrolledintheUniversityofFlorida'scoastalengineeringprogram.IwasdrawntotheUniversityofFloridabyawonderfulofferfromDr.DonSlinntobecomearesearchassistant.Thoughsometimesdifcultandsomewhatfrustrating,IhavebeenverygratefulfortheexperiencesthatIhavehadintheCivilandCoastalEngineeringDepartment.NotonlyhaveImetsomewonderfulpeopleandmadesomelifelongfriends,butIhavehadmanyeducationalexperiencesthatIneverwouldhave

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86 imaginedIwouldbeinvolvedinjustafewshortyearsago.Ihavelearnedanothersidetoscienticresearch,theworldofcomputermodeling.ThoughthiseldisnotnecessarilywhereIfeelmostathome,myacquiredskillsinCFDhavegivenmeanothertooltouseinmyresearchandhavemademeamorediverseandskilledscientistandengineer.Combinedwithmyundergraduateexperiences,mytimespentintheCivilandCoastalEngineeringGraduateProgramattheUniversityofFloridahasmadememorecapableandcondentinmyscienticendeavors,andhasprovidedmewiththeknowledgeandexperienceIneedtoembarkonanexcitingcareeron,in,andaroundtheocean.