<%BANNER%>

Mixture Theory Simulation of Vortex Sand Ripple Dynamics

Permanent Link: http://ufdc.ufl.edu/UFE0042547/00001

Material Information

Title: Mixture Theory Simulation of Vortex Sand Ripple Dynamics
Physical Description: 1 online resource (131 p.)
Language: english
Creator: Penko, Allison
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: mixture, modeling, morphology, numerical, ripples, seabed, theory, vortex
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Coastal and Oceanographic Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The presence of ripples on the seabed affects the turbulent dynamics of the wave bottom boundary layer (WBBL). The difference in the roughness length scales between a planar and rippled sand beds produces quantifiable differences in the turbulent WBBL that affect wave energy dissipation, coastal circulation, and sediment transport. A complete understanding of the effects of sediment and fluid properties on the turbulent wave bottom boundary layer and small-scale bedform evolution are currently unknown. We implement a three-dimensional bottom boundary layer model (SedMix3D) using mixture theory for highly resolved simulations of the coupled interactions between fluid and sediment in domains up to 32 cm x 24 cm x 16 cm. Mixture theory treats the fluid-sediment mixture as a single continuum with effective properties that parameterize the fluid-sediment and sediment-sediment interactions. The grid spacing is on the order of a sediment grain diameter and simulated flows have maximum free stream velocities between 10 and 120 cm/s and periods between 2 and 4 s. Modeled ripple geometries range from a single ripple to multiple ripples with varying heights, lengths, and steepness. Only non-cohesive sediments (0.02 < d < 0.054 cm) are considered. The model predicts ripple heights and lengths that compare reasonably to an existing ripple predictor formula. SedMix3D also predicts the merging and separation of ripples as they transition from an initial state to an equilibrium state. Comparisons of SedMix3D to laboratory measurements of fluid velocity and sediment concentration over rippled sand beds are in excellent agreement. We compare two-dimensional to three-dimensional simulations to find that the vortex dynamics over sand ripples are highly three-dimensional. Two-dimensional flow simulations are inadequate for the numerical modeling of turbulent flow in the WBBL. We also test the model sensitivity to the parameterizations for effective viscosity, particle pressure, and bulk hindered settling velocity. Finally, we demonstrate the capability of SedMix3D to provide detailed information on the dynamics of complex three-dimensional ripple geometry evolution.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Allison Penko.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Slinn, Donald N.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042547:00001

Permanent Link: http://ufdc.ufl.edu/UFE0042547/00001

Material Information

Title: Mixture Theory Simulation of Vortex Sand Ripple Dynamics
Physical Description: 1 online resource (131 p.)
Language: english
Creator: Penko, Allison
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: mixture, modeling, morphology, numerical, ripples, seabed, theory, vortex
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Coastal and Oceanographic Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The presence of ripples on the seabed affects the turbulent dynamics of the wave bottom boundary layer (WBBL). The difference in the roughness length scales between a planar and rippled sand beds produces quantifiable differences in the turbulent WBBL that affect wave energy dissipation, coastal circulation, and sediment transport. A complete understanding of the effects of sediment and fluid properties on the turbulent wave bottom boundary layer and small-scale bedform evolution are currently unknown. We implement a three-dimensional bottom boundary layer model (SedMix3D) using mixture theory for highly resolved simulations of the coupled interactions between fluid and sediment in domains up to 32 cm x 24 cm x 16 cm. Mixture theory treats the fluid-sediment mixture as a single continuum with effective properties that parameterize the fluid-sediment and sediment-sediment interactions. The grid spacing is on the order of a sediment grain diameter and simulated flows have maximum free stream velocities between 10 and 120 cm/s and periods between 2 and 4 s. Modeled ripple geometries range from a single ripple to multiple ripples with varying heights, lengths, and steepness. Only non-cohesive sediments (0.02 < d < 0.054 cm) are considered. The model predicts ripple heights and lengths that compare reasonably to an existing ripple predictor formula. SedMix3D also predicts the merging and separation of ripples as they transition from an initial state to an equilibrium state. Comparisons of SedMix3D to laboratory measurements of fluid velocity and sediment concentration over rippled sand beds are in excellent agreement. We compare two-dimensional to three-dimensional simulations to find that the vortex dynamics over sand ripples are highly three-dimensional. Two-dimensional flow simulations are inadequate for the numerical modeling of turbulent flow in the WBBL. We also test the model sensitivity to the parameterizations for effective viscosity, particle pressure, and bulk hindered settling velocity. Finally, we demonstrate the capability of SedMix3D to provide detailed information on the dynamics of complex three-dimensional ripple geometry evolution.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Allison Penko.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Slinn, Donald N.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042547:00001


This item has the following downloads:


Full Text

PAGE 1

MIXTURETHEORY SIMULATIONOFVORTEXSANDRIPPLEDYNAMICS By ALLISONM.PENKO ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2010

PAGE 2

c r 2010AllisonM. Penko 2

PAGE 3

Form ydad,whoalwaysbelievedinmeandtaughtmetonevergiveup 3

PAGE 4

ACKNOWLEDGMENTS I graciouslythankDr.JoeCalantoniforbeingmyresearchadvisor;Iwouldnotbe thescientist,engineer,orphysicistIamtodaywithouthim.Ialsogreatlyappreciate myacademicadvisor,Dr.DonSlinn,andmycommitteefortheirsupportandguidance throughoutmygraduateschoolexperience.Iamextremelygratefulformymentor, friend,andever-supportive,favoritewomanscientist,Dr.DianeFoster.Shehasalways beenaaneartolistenandagiverofgreatadvice.Iwasprimarilysupportedunder basefundingtotheNavalResearchLaboratoryfromtheOfceofNavalResearch (PE#61153N).PartialsupportwasprovidedbytheDoDNationalDefenseScienceand EngineeringGraduateFellowshipProgramandbytheOfceofNavalResearchCoastal GeosciencesProgramCode322CG.Thisworkwassupportedinpartbyagrantof computertimefromtheDoDHighPerformanceComputingModernizationProgramat theNAVYDSRCandtheERDCDSRC.Iwouldalsoliketoacknowledgethehelpful insightofDr.BretWebbandmyfellowgraduatestudents.Aspecialthankyoutomy partner-in-science,KaceyEdwardsforproofreadingthisdissertation.Lastly,butnot least,Iwouldn'tbewhereIamnowwithouttheloveandsupportfrommywonderful boyfriendandbestfriend,Aaron. 4

PAGE 5

TABLEOF CONTENTS page ACKNOWLEDGMENTS .................................4 LISTOFTABLES ......................................7 LISTOFFIGURES .....................................8 ABSTRACT .........................................11 CHAPTER 1INTRODUCTION ...................................13 2MODELFORMIXTURETHEORYSIMULATIONOFVORTEXSANDRIPPLE DYNAMICS ......................................18 2.1Introduction ...................................18 2.2Methodology ..................................21 2.2.1GoverningEquations ..........................22 2.2.2InitialandBoundaryConditions ....................26 2.3Results .....................................26 2.3.1RippleHeightandLength .......................27 2.3.1.1Varyinginitialrippleheights .................28 2.3.1.2Varyingowconditions ...................28 2.3.1.3Multipleripples ........................29 2.3.2RippleShape ..............................30 2.4Discussion ...................................30 2.4.1RippleHeightandLength .......................30 2.4.2RippleShape ..............................31 2.4.3ComparisonsofTwo-andThree-DimensionalSimulations .....31 2.4.4BedStiffnessFunction .........................32 2.5Conclusions ...................................33 3MODEL-DATACOMPARISONOFATHREE-DIMENSIONALMIXTUREMODEL .............................................42 3.1Introduction ...................................42 3.2Methodology ..................................42 3.2.1SedMix3D ................................42 3.2.2ExperimentalFacilityandConditions .................43 3.3Model-DataComparisonResults .......................44 3.3.1Hydrodynamics .............................44 3.3.2SedimentDynamics ..........................47 3.4Discussion ...................................48 3.4.1Hydrodynamics .............................48 3.4.2SedimentDynamics ..........................50 5

PAGE 6

3.4.3Comparisons ofTwo-andThree-DimensionalSimulations .....50 3.4.4ModelDependenceonSedimentPhaseClosures ..........51 3.5Conclusions ...................................53 4MIXTURETHEORYMODELSENSITIVITYTOEFFECTIVEVISCOSITYIN SIMULATIONSOFSANDYBEDFORMDYNAMICS ...............69 4.1Introduction ...................................69 4.2Methodology ..................................70 4.3Results .....................................73 4.3.1IntrinsicViscosity ............................73 4.3.2EffectiveViscosityFormulations ....................75 4.4Discussion ...................................77 4.4.1IntrinsicViscosity ............................77 4.4.2EffectiveViscosityFormulations ....................79 4.4.3ModelLimitations ............................80 4.5Conclusions ...................................80 5CONTROLLEDSIMULATIONSCOMPARINGEMPIRICALSUBMODELSIN SEDMIX3D ......................................94 5.1Introduction ...................................94 5.2Methodology ..................................95 5.3Results .....................................99 5.4Discussion ...................................100 5.4.1BulkHinderedSettling .........................100 5.4.1.1Dependenceonlocalsedimentconcentration .......100 5.4.1.2Dependenceongrainsize .................101 5.4.2ParticlePressure ............................101 5.5Conclusions ...................................102 6MORPHODYNAMICSOFTHREE-DIMENSIONALRIPPLEGEOMETRIES ..111 6.1Introduction ...................................111 6.2Methodology ..................................113 6.3Results .....................................113 6.3.1LongFlatRippleSimulation ......................113 6.3.2BifurcatedRipples ...........................114 6.3.3RipplesOrientedObliquelytoFlowDirection .............115 6.4Conclusions ...................................115 APPENDIX:MESSAGE-PASSINGINTERFACE(MPI)IMPLEMENTATION ......123 REFERENCES .......................................125 BIOGRAPHICALSKETCH ................................131 6

PAGE 7

LISTOFT ABLES Table page 2-1Bed,domain, andowconditions. .........................34 2-2Rangeofparametersforthepresentedsimulationsandresultsfromexisting ripplepredictorformulae. ..............................34 2-3Thepercentageofequilibriumrippleheightreached. ..............35 7

PAGE 8

LISTOFFIGURES Figure page 2-1Effectiv eviscosityformulationsandexperimentaldata. ..............35 2-2Bedstiffnesscoefcientplot. ............................36 2-3Rippleheighttimeseriesforvaryinginitialrippleheightsimulations. ......36 2-4Rippleheighttimeseriesforvaryingowconditionsimulations. .........37 2-5Rippleheighttimeseriesforthehighenergysimulation. .............37 2-6Timeseriesoftherippleprolefor2Dl02a. ....................38 2-7Rippleheighttimeseriesforthemultipleripplesimulations. ...........38 2-8Timeseriesoftherippleprolefor2Dl02b. ....................39 2-9Timeseriesoftherippleprolefor2Dl01. .....................39 2-10Timeseriesoftherippleprolefor2Df01. .....................40 2-11Timeseriesoftherippleproleforthethree-dimensionalsimulation. ......41 3-1FreestreamvelocitymeasuredbytheADV ....................55 3-2Initialmodelbedprole ...............................56 3-3Model-observationvorticityeldcomparisons ...................57 3-4Model-observationswirlingstrengtheldcomparisons ..............58 3-5Time-averageofmodeledandobservedhorizontalvelocity ...........59 3-6Time-averageofmodeledandobservedverticalvelocity .............59 3-7Standarddeviationof u atsevenlocationsalongthebedprole .........60 3-8Standarddeviationof w atvelocationsalongthebedprole ..........61 3-9Ensemble-averaged u velocityproles .......................62 3-10Verticalprolesof u atdifferentxlocations ....................63 3-11Horizontalvelocityphaselead ............................64 3-12Modelconcentrationandobservationimageintensity ...............65 3-13Ensemble-averagedmodeledandobservedbedproles .............66 3-14Ensemble-averaged u velocityprolesfor2Dand3D ...............67 8

PAGE 9

3-15Bede volutioncontoursfor2Dand3Dsimulations ................68 4-1Maximumfreestreamvelocitytimeseriesforawaveperiod. ..........82 4-2Effectiveviscositycurvesfordifferentintrinsicviscosities. ............82 4-3Suspendedsedimentconcentrationeldsforvaryingintrinsicviscositiesat owreversal. .....................................83 4-4Suspendedsedimentconcentrationeldsforvaryingintrinsicviscositiesat maximumowacceleration. .............................84 4-5Suspendedsedimentconcentrationeldsforvaryingintrinsicviscositiesat maximumowdeceleration. .............................85 4-6Timeseriesoftotalsuspendedsedimentabovetherippleprole. ........86 4-7Timeseriesofthesuspendedsedimentconcentrationsovertheripplecrest. .87 4-8Effectiveviscositycurves. ..............................88 4-9Suspendedsedimentconcentrationeldsforvaryingeffectiveviscositycurves atowreversal. ....................................89 4-10Suspendedsedimentconcentrationeldsforvaryingeffectiveviscositycurves atmaximumowacceleration. ...........................90 4-11Suspendedsedimentconcentrationeldsatmaximumowdeceleration. ...91 4-12Timeseriesoftotalsuspendedsedimentabovetherippleprole. ........92 4-13Timeseriesofthesuspendedsedimentovertheripplecrest. ..........93 5-1Effectiveviscosityformulations. ...........................102 5-2Bedstiffnesscoefcientplot. ............................103 5-3Concentrationcontoursduringgravitationalsettlingofasedimentplanefor d = 0.2cm. ......................................104 5-4Contouredtimeseriesofconcentrationfor d = 0.2cm. ..............105 5-5Horizontallyaveragedconcentrationandsettingrateusingtwodifferentaveraging methodsforthe d = 0.2cmsimulation. ......................106 5-6Concentrationcontoursduringgravitationalsettlingofasedimentplanefor d = 0.04cm. .....................................107 5-7Contouredtimeseriesofconcentrationfor d = 0.04cm. .............108 5-8Horizontallyaveragedconcentrationandsettingrateusingtwodifferentaveraging methodsforthe d = 0.04cmsimulation. ......................109 9

PAGE 10

5-9Angleof reposeforvaryingbedstiffnessfactors. .................110 5-10Heightofthesedimentplanevs.time. .......................110 6-1Longatripplesimulationinitialization .......................117 6-2Longatripplesimulationsnapshots ........................118 6-3Bifurcatedripplesimulationinitialization ......................119 6-4Bifurcatedripplesimulationsnapshots .......................120 6-5Obliqueripplesimulationinitialization .......................121 6-6Obliqueripplesimulationsnapshots ........................122 A-1Parallelizedsimulationspeedup ...........................124 10

PAGE 11

Abstractof DissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy MIXTURETHEORYSIMULATIONOFVORTEXSANDRIPPLEDYNAMICS By AllisonM.Penko December2010 Chair:DonaldN.Slinn Major:CoastalandOceanographicEngineering Thepresenceofripplesontheseabedaffectstheturbulentdynamicsofthewave bottomboundarylayer(WBBL).Thedifferenceintheroughnesslengthscalesbetween aplanarandrippledsandbedsproducesquantiabledifferencesintheturbulentWBBL thataffectwaveenergydissipation,coastalcirculation,andsedimenttransport.A completeunderstandingoftheeffectsofsedimentanduidpropertiesontheturbulent wavebottomboundarylayerandsmall-scalebedformevolutionarecurrentlyunknown. Weimplementathree-dimensionalbottomboundarylayermodel(SedMix3D)using mixturetheoryforhighlyresolvedsimulationsofthecoupledinteractionsbetween uidandsedimentindomainsupto32cmx24cmx16cm.Mixturetheorytreatsthe uid-sedimentmixtureasasinglecontinuumwitheffectivepropertiesthatparameterize theuid-sedimentandsediment-sedimentinteractions.Thegridspacingisonthe orderofasedimentgraindiameterandsimulatedowshavemaximumfreestream velocitiesbetween10and120cm/sandperiodsbetween2and4s.Modeledripple geometriesrangefromasinglerippletomultiplerippleswithvaryingheights,lengths, andsteepness.Onlynon-cohesivesediments(0.02 < d < 0.054cm)areconsidered. Themodelpredictsrippleheightsandlengthsthatcomparereasonablytoanexisting ripplepredictorformula.SedMix3Dalsopredictsthemergingandseparationof ripplesastheytransitionfromaninitialstatetoanequilibriumstate.Comparisonsof SedMix3Dtolaboratorymeasurementsofuidvelocityandsedimentconcentration 11

PAGE 12

over rippledsandbedsareinexcellentagreement.Wecomparetwo-dimensionalto three-dimensionalsimulationstondthatthevortexdynamicsoversandripplesare highlythree-dimensional.Two-dimensionalowsimulationsareinadequateforthe numericalmodelingofturbulentowintheWBBL.Wealsotestthemodelsensitivity totheparameterizationsforeffectiveviscosity,particlepressure,andbulkhindered settlingvelocity.Finally,wedemonstratethecapabilityofSedMix3Dtoprovidedetailed informationonthedynamicsofcomplexthree-dimensionalripplegeometryevolution. 12

PAGE 13

CHAPTER1 INTRODUCTION Our lackofunderstandingoftheevolutionofseabedroughness(e.g.,sand ripples)insandycoastalregionsinhibitsourabilitytoaccuratelyforecastwavesand currentsandultimatelylarge-scalemorphodynamics.Mostwaveandcirculationmodels inputaconstantbottomroughnessvalue(i.e.,frictionfactor)orxedbedprolethat parameterizestheeffectsofseabedroughness,ignoringanytemporalorspatial responseofthebedtochangingwaveandsedimentconditions.However,seabed roughnesslengthscalesmayspanupthreeordersofmagnitude(e.g.,fromgrain-scale variationstosandripples),causingsignicantdifferencesinboundarylayerturbulence, waveenergydissipation,coastalcirculation,andsedimenttransport.Theconstant evolutionoftheseabedalsohassignicantimplicationsfornavaloperations(e.g.,ocean acoustics,minehuntingmissions,littoralnavigation)andcommercialactivities(e.g., coastalerosion/restoration,designofcoastalinfrastructure). Allbathymetricchangeultimatelyresultsfromsedimententrainmentanddeposition occurringattheuid-sedimentinterfaceinsidethewavebottomboundarylayer(WBBL). Despitetheapparentaccessibilityofthephenomena,highlyturbulent,sediment-laden owremainspoorlyunderstoodanddifculttoquantifymainlybecauseofourfailure tounderstandthefundamentalinteractionforcesdrivingsedimenttransport.However, withrecentadvancesinhighperformancecomputing,itisnowpossibletoperform highly-resolvedsimulationsofuid-sedimentdynamicsintheWBBLtodeterminethe effectsofsedimentanduidparametersonseabedevolution. Herewefocusonthedevelopment,implementation,andanalysisofathree-dimensional mixturetheorymodel(SedMix3D)tosimulatetheformation,migration,anddecay ofvortexsandripples.SedMix3DsolvestheunlteredNavier-Stokesequationsfor theuid-sedimentmixturewithanadditionalequationdescribingsedimentuxto simulatesandripplemorphologyindomainscoveringupto 1 m 2 oftheseabed. 13

PAGE 14

Mixturetheory treatstheuid-sedimentmixtureasasinglecontinuumwitheffective propertiesthatparameterizetheuid-sedimentandsediment-sedimentinteractions usingavariablemixtureviscosity,abulkhinderedsettlingvelocity,aparticlepressure, andashear-induced,empiricallycalibrated,mixturediffusionterm.SedMix3Dpredicts thetimedependentsedimentconcentrationandthree-componentvelocityeldunder varyingwaveconditions.Withgridspacingontheorderofasedimentdiameterand timestepsnearlyfourordersofmagnitudelessthanthesmallestturbulentuidtemporal scale,SedMix3Dprovidesadetailedthree-dimensionalpictureoftheuid-sediment WBBL. SedMix3Dwasoriginallywritteninserialandemployedasasheetowmodel. UsingtheMessage-PassingInterface,theexisting,computationallyexpensive serialversionwasparallelizedtorunonupto512processorsonHighPerformance Computing(HPC)architectures(seeAppendix).Theserialversionofthecodetook approximatelyoneweekofwallclocktimetogenerate1secondofrealtimesimulation fortheowoverasingle,three-dimensionalripplewavelength.Thedevelopmentand optimizationoftheparallelizedSedMix3Dandtheanalysispresentedherehasutilized over1.5millionCPUhoursandover5TBofstoragespacethroughtheDoDHigh PerformanceComputingandModernizationPrograminthepasttwoyears.Parallelizing SedMix3Dhasresultedinabouta15timesspeedupfromtheserialcode. Thesimulationspresentedhererepresentbottomboundarylayerowsunder varyingwaveconditionsandsedimentsizesandtypes.Flowswithoscillatoryboundary layerReyoldsnumbersrangingfrom10 2 to10 6 withsedimentsizesrangingfrom0.02 cmto0.054cmarepresentedhere.Onlynon-cohesivesedimentsareconsidered. Thegridsarerectangularwithheightsontheorderofasedimentparticlediameter. Domainsizesrangefrom8cm 0.12cm 10cmupto32cm 24cm 16cmwith gridpointtotalsrangingfromapproximately10 4 to10 7 .Forsmallsimulations( O (10 4 ) gridpoints)approximately2hoursofwallclockCPUtimeper1secondofrealtime 14

PAGE 15

isrequiredwhen runningon128processors.Largesimulations( O (10 7 )gridpoints) takeupto2.5daysofwallclocktimeper1secondofrealtimeon256processors.The simulationsareinitializedwithvaryingbedgeometriesfromoneripplewavelengthto multipleintersectingripples. Followingtheintroductorychapter,thisworkisorganizedasacollectionofpapers eitherpublishedorsoon-to-be-submittedforpublicationandanappendixdescribing theparallelizationmethod.Chapter 2 containsacompletedescriptionofthemodeland simulationsusingtheserialcode.Assuch,mostofthesimulationswereperformedin two-dimensionaldomains.Predictedequilibriumrippleheightsandlengthscompared reasonablytoanexistingempiricalripplepredictor.Analysisofatwo-dimensionaland anequivalentthree-dimensionalsimulationrevealedanincreaseinshearstresson thecrestoftherippleinthetwo-dimensionalsimulationthatresultedinadecreased equilibriumrippleheight.Weconcludethatthree-dimensionalsimulationsarenecessary tocapturethethree-dimensionalprocessesthatgovernthephysicsofturbulentow overrippledbeds. Comparisonsofthehydrodynamicsandsedimentdynamicssimulatedbythe three-dimensionalparallelizedSedMix3Dwithlaboratoryobservationsareprovided inChapter 3.Velocityoweldswerecomparedtoparticleimagevelocimetry(PIV) datacollectedattheDelftUniversityofTechnologybyDr.DianeFosterandSylvia Rodriguez-AbudofromtheUniversityofNewHampshire.Thedatawerealsousedto qualitativelycompareconcentrationeldsandbedformmorphologypredictedbythe model.Themodelwasinexcellentagreementwiththeobservationsandprovidesan accuraterepresentationofturbulentowoverripplesfortheconditionsrepresentedby theexperiments.Wealsousedthemodeltoexaminethedependenceofsedimentand owparametersonmixturetheorysimulationsofturbulentbottomboundarylayerow. Inchapter 4,wetestedthemodelsensitivitytothreeeffectiveviscosityformulations andtheintrinsicviscosityparameterusedinSedMix3D.Wefoundahighermodel 15

PAGE 16

sensitivitytov ariationsintheeffectiveviscositywithintheripple-uidinterface(0.3 << 0.6)thanthesuspendedsedimentconcentrationregion(0.0 << 0.3).The existingviscosityformulationsrangeinvaluesandwereempiricallyttedtodatafrom experimentswithvaryingsedimentconcentrations,sizes,andtypes.Wefoundthat employingeffectiveviscosityformulationsthatwereempiricallyttedtoexperiments withsedimentpropertiesnearthesedimentrangepresentedheredoesnotsignicantly affectthemodeloutput.Wetestedthebulkhinderedsettlingvelocityandparticle pressureinchapter 5 .WhilethehinderedsettlingratespredictedbySedMix3Dagree wellwiththespeciedhinderedsettlingformulationdespitetheinclusionofadditional termsinthesedimentuxequation,theresultsarestronglydependentonthedenition oflocalsedimentconcentration.Themodelshowedalowsensitivitytochangesinthe particlepressurewithanglesofreposedifferingbylessthan5%fortherangeofvalues tested. SedMix3Dutilizesstate-of-the-artsupercomputingtechnologytoperformprototype scalehighresolutionsimulationsoftheseabedresponsewhensandripplesarepresent andprovidesthedetailedsmall-scaleuctuationsofboundarylayerprocesses.Chapter 6 presentsthreeprototypescalesimulationsofthreedifferentcomplexrippledbed geometries:alongatripple,abifurcatedripple,andripplesorientedobliquelytothe owdirection.Simulateddomainscoverupto32cm 12cmareasoftheseabed withanaverageof4milliongridpointseach.Atypicalsimulationofthissizerequires approximately150,000wallclockhourstosimulate30seconds.Eachsimulation generatesabout500GBofdataandcantakeupto3daystopost-processandplot. Currently,SedMix3Dpushesthelimitofavailablesupercomputinghardware.However, withincreasingtechnology,weexpectthewallclocktimetodecreaseandthesimulation storagespacetobecomemoreaccessibleandpractical.Despiteitscomputational resourcelimit,SedMix3Disapowerfulresearchtoolthatwewillusetostudythedetails ofsmall-scalesandrippledynamicsincluding(1)theeffectsofsuspendedsediment 16

PAGE 17

concentrationon turbulencemodulation,(2)thedynamicsofrippletransitionsfrom2Dto 3D(andbackto2D)underchangingforcingconditions,and(3)theroleofterminations andbifurcationsonripplemigrationandgrowthrates.Ultimately,allprocess-based modelsfornearshorebathymetricevolutionarelimitedbyshortcomingsinfundamental knowledgeofmultiphaseboundarylayerphysics.SedMix3Dprovidesanunprecedented levelofdetailforthestudyofuid-sedimentinteractionsthatisimpossibletoobtainwith availablemeasuringtechnologiesintheeldorlaboratory. 17

PAGE 18

CHAPTER2 MODELFOR MIXTURETHEORYSIMULATIONOFVORTEXSANDRIPPLE DYNAMICS Thischapterwasacceptedinaslightlydifferentformwithco-authorsJ.Calantoni, D.N.Slinn,andG.M.BurdicktotheJournalofWaterway,Ports,Coastal,andOcean Engineering. 2.1Introduction Sedimenttransport,waveattenuation,andtheacousticalpropertiesoftheseaoor ontheinnershelfarestronglyinuencedbythegeometricpropertiesanddynamic behaviorofsandripples.Assandripplesgrowfromnominallyplanarbedtopography, theroughnesslengthoftheseaoorchangesbyordersofmagnitude,producing quantiabledifferencesinnearbedturbulenceandbottomboundarylayerstructure. However,pastresearchhasignoredtheresponseofthewavebottomboundarylayer (WBBL)owtoresultingsedimenttransportandchangesinbedformmorphology( Barr etal. 2004 ; ChangandScotti 2006; Scanduraetal. 2000 ).Acompleteunderstanding ofthefeedbackbetweentheuidandsedimentisnecessaryforaccuratepredictionof bedformprolechange. Laboratoryandeldstudiesinvestigatingrippleevolutionhavefoundthatbedform typeisafunctionofthestrengthandnatureoftheowaswellassedimentcharacteristics. Asteadycurrent,tidalcurrent,waves,oracombinationofallthreewillinuencethe size,shape,andorientationofbedforms( Baas, 1999; Blondeaux 2001; Doucetteand O'Donoghue, 2006; Nielsen, 1981; vanderWerfetal. 2008, 2007).Usinglaboratory andelddata,empiricalformulaehavebeendevelopedtopredictrippleheight, wavelength,andsteepness( GrantandMadsen 1982; Mogridgeetal., 1994; Nielsen, 1981; Vongvisessomjai, 1984; WibergandHarris 1994 ).Foradetailedintercomparison ofempiricalripplepredictorssee Webb (2008).Inthisstudywecomparesimulation resultswiththerobustandpopularempiricalripplepredictorof Nielsen (1981). 18

PAGE 19

Wepresent anumericalmodel,SedMix3D,forsimulationofthree-dimensional sedimenttransportandbedformmorphologyintheWBBLbysolvingtheunltered Navier-Stokesequationsutilizingmixturetheory.Mixturetheoryallowsthesediment-laden watertobetreatedasasinglecontinuumwitheffectiveproperties(e.g.,density, viscosity,diffusion)thatarefunctionsofthetemporalandspatialvolumetricconcentration ofsediment.Numericalsimulationsusingmixturetheoryhavebeenappliedtomany particle-ladenows( BurdickandSlinn 2004; HoferandPerktold 1997; Miskinetal., 1996a,b; NirandAcrivos, 1990; NottandBrady, 1994; Sunetal. 2009 )yieldinggood comparisonswithlaboratoryexperiments;however,mixturetheoryhasnotbeen successfullyappliedtothepredictionofthree-dimensionalcoastalbedformmorphology. SolvingtheunlteredNavier-Stokesequationsusingmixturetheoryrequiresclosure relationshipsforthediffusionandviscosityoftheuid-sedimentmixture.Observations ofparticleresuspensionforcedbylaminarshearowhaveshownthatthediffusion fromtheshear-inducedmigrationofparticlesisafunctionofshearrate,particleradius, andlocalsedimentconcentration( LeightonandAcrivos 1987b).Adiffusiveux modelincorporatingthediffusionequationcoupledwithmassandmomentumbalance equationsalongwiththeeffectsofhinderedparticlesettling,particleresuspension, andbulkmotionhassuccessfullymodeledthesteadyowofasuspensionoveran inclinedsurface( NirandAcrivos, 1990).Thediffusionequationhasalsobeenextended toincludeparticleuxesduetobothspatialvariationsinconcentrationandviscosity (Phillipsetal., 1992).Thediffusionequationandgravitationaleffectincorporatedinto aNavier-Stokessolverrecentlysimulatedconcentratedsuspensionsofmono-disperse spheresinbatchsedimentation,wide-gapCouetteow,andincomplexgeometrieswith obstructionsyieldinggoodcomparisonswithexperiments( Raoetal., 2002, 2007). Theclosurefortheeffectiveviscosityofasediment-ladenmixtureistypically dependentonthesedimentconcentration,intrinsicviscosity,andthemaximumpacking concentration.Previouslyproposedeffectiveviscosityequationshavetwocommon 19

PAGE 20

features. Indilutesuspensions,concentrationandviscosityarelinearlyrelated( Einstein 1906),andatthemaximumpackingconcentration,theviscositybecomesinnite( Eilers 1941).Viscositiesmodeledbyconcentrationdependentequationscomparewellwith viscositymeasurementsofsmallparticles( O (0.001cm) )insuspension( deCindio etal. 1987 ; Ferrinietal. 1979; Huntetal., 2002; Krieger 1972; KriegerandDougherty 1959; LeightonandAcrivos 1987b; Mooney, 1951; Sudduth, 1993 )andlargeparticles (O (0.01cm) )indenseconcentrations(upto0.58volumefraction)( HuangandBonn 2007; Vand 1948). Mixturetheoryhasbeenusedtopredictrippleheightandlength(Charruand Mouilleron-Arnould 2002),buttheuid-sedimentcouplinghasonlybeenaccountedfor intermsofaparticletransportrate.SedMix3Distherstfullycoupleduid-sediment mixturemodelinathree-dimensionalripple-scaledomain. CharruandMouilleron-Arnould (2002)usedviscousresuspensiontheory,whichassumesthatthemovingbedthickness increaseslinearlywithshearstress( LeightonandAcrivos 1986)topredictthebed instabilityandsubsequentlytheripplegrowthrate.Whiletheirsimpleanalyticalmethod calculatestheshearinstabilityoftheparticlesataspeciclocationonthebed,it doesnotincludethecompletefeedbackofthesedimentontheturbulentow,nor doesithavetheabilitytopredictanequilibriumbedstate.Theresultsgenerallyagree withobservations,butabettercouplingbetweentheuidandsedimentisnecessary forfurtherinvestigationsofrippleevolution( CharruandMouilleron-Arnould, 2002 ). Numericalresultsofconcentrationprolescomparewellwithexperimentsusinga mixtureapproachtosimulateconcentratedsuspensions(upto0.68volumefraction) of0.02cmgrainsoveraxedbed( Mukhopadhyayetal. 2009 ).Thesimulation doesnotincludethefeedbackbetweenthesuspensionowandsedimentbed andthereforedoesnotallowforbedevolution.Ourresearchextendstheworkof Mukhopadhyayetal. (2009)toincludetheerosionanddepositionofsedimentto simulatethethree-dimensionalevolutionofthesedimentbedundervaryingow 20

PAGE 21

conditionsingood agreementwithexistingripplepredictorformulae.SedMix3Dexplicitly simulatesvortexdynamicsinathree-dimensionaldomainwhiletreatingtheuidand sedimentasaneffectivemixturewithpropertiesdependentonthelocalsediment concentration.Assuch,SedMix3Dsimulatesthethree-dimensionalhydrodynamics oftheow,suspendedandbedloadsedimenttransport,andtheresultingbedform morphology,includingthemergingandseparationofripplesandtheformationofripples fromaroughatbed.Inthispaper,weprovideadetaileddescriptionofthemodel,the modelsimulationresults,andadiscussionontheapplicabilityandlimitationsofthe model. 2.2Methodology Themixturemodel,SedMix3D,simulatestheuidowandsubsequentsediment transportoverevolvingbedgeometriesbytreatingtheuid-sedimentsystemasa mixtureconsistingoftwospecies.Themodelimplementsacontrol-volumeschemethat solvesthesedimentconcentrationfunctionandthemassandmomentumconservation equationsforthemixtureusingsecond-ordercentraldifferencinginspaceanda third-orderAdams-Bashforthschemeintime.Thegridisuniforminx,y,andz,withthe x-andy-gridspacingat0.09cmandthez-gridspacingat0.03cm.Themodeltime stepis7 10 )Tj /T1_4 7.97 Tf (6 s.Theimplementationofmixturetheoryrequiresaconstitutiveequation expressingthetotaluxofsedimentasafunctionofsedimentconcentration,mixture velocity,andmixturestresses.Bothuid-sedimentandsediment-sedimentinteractions aremodeledwithavariablemixtureviscosity( Eilers, 1941 ),abulkhinderedsettling velocity( RichardsonandZaki, 1954),andashear-induced,empiricallycalibrated, mixturediffusionterm( LeightonandAcrivos, 1987a,b). 21

PAGE 22

2.2.1Governing Equations ThegoverningequationsforSedMix3Dincludeamixturecontinuity,mixture momentum,andsedimentuxequation.Themixturecontinuityequationisderivedby combiningcontinuityequationsfortheuidandsediment, @ @ t + r ( u)=0, (2) where u isthethethree-componentvelocityofthemixture.Themixturedensity, ,isthe sumofthebulkdensitiesofeachspecies, = X n n n (2) where n and n arethevolumetricconcentrationsanddensitiesofspecies n ,respectively. Foratwo-species,sediment-watermixture, + f =1,where and f arethevolumetric concentrationsofsedimentandwater,respectively.Herewewritethemixturedensity as, = s +(1 )Tj /T1_2 11.955 Tf 11.95 0 Td () f (2) where s and f arethedensitiesofsediment(2.66gcm )Tj /T1_10 7.97 Tf (3 )andwater(1.0gcm )Tj /T1_10 7.97 Tf (3 ), respectively.Themixturestressescanbedenedbyassumingthemixturebehavesas aNewtonianuid( Bagnold, 1954)resultinginthemixturemomentumequation, @ u @ t + u ru = r P + r ( ru)+ F )Tj /T1_2 11.955 Tf 11.96 0 Td (g, (2) where P isthemixturepressure, F istheexternaldrivingforcevectorperunitvolume, and g isgravitationalacceleration(981cms )Tj /T1_10 7.97 Tf 6.59 0 Td (2 ^ k ).Theexternalforce, F,approximates thehorizontalpressuregradientduetothepassageofasurfacegravitywave.The forcingfunctionimplementedhereinducesaregularsinusoidalfree-streamvelocityin thex-directionwithmaximumvelocity, U o ,andperiod, T F = f U o 2 T cos 2 T t ^ i (2) 22

PAGE 23

Spatialvar iationsintheviscosityofuid-sedimentsuspensionscanbedenedas afunctionofsedimentvolumetricconcentration( Eilers, 1941 ; HuangandBonn, 2007; KriegerandDougherty 1959; LeightonandAcrivos 1987b; Mooney 1951).SedMix3D includesamodiedEilersequationtomodeltheeffectiveviscosity, ,herescaledbythe purewaterviscosity, f (0.0131gcm )Tj /T1_4 7.97 Tf 6.59 0 Td (1 s )Tj /T1_4 7.97 Tf 6.59 0 Td (1 ), f = 1+ 0.5[ ] 1 )Tj /T1_1 11.955 Tf 11.95 0 Td (= m 2 (2) where [] istheintr insicviscosity,and0.0 0.63,wherethelowerbound representspurewaterandtheupperboundroughlycorrespondstothemaximum concentrationofunconsolidatedsediment.Here,themaximumvalueofthemixture viscosityisxedbyspecifying m = 0.644.Theintrinsicviscosityhasbeenfoundtobe afunctionoftheparticleaxisratio, r (length:width)(NawabandMason 1958),withr=1 and [ ]= 2.5forsphericalparticles( Einstein, 1906).Mixtureswithlong,atparticles willhavelargerintrinsicviscositiesthanmixtureswithsphericalparticles.Although increasingtheintrinsicviscosityroughlyrepresentsthelengtheningandatteningofa particle, [] forirregularlyshapedparticlesisstilllargelyuncertain( Ferrinietal. 1979). When []= 3.0,(Equation 2)reducesto LeightonandAcrivos (1987b).Varyingthe intrinsicviscositybetween2.5and3.5causeslessthana10%differenceintheresulting totalsuspendedsedimentconcentrations( Penkoetal. 2009),thereforeweassume nearlysphericalsedimentparticlesanduseanintrinsicviscosity, []= 3.0.Varying theintrinsicviscosityinfutureinvestigationsmayallowfordifferentparticleshapes toberepresentedinthemodel.Thescaledeffectiveviscosity(Equation 2 )usedin SedMix3D,othercommonlyusedexpressions( Eilers, 1941; KriegerandDougherty, 1959; Mooney 1951 ),andseveralmodiedforms( HuangandBonn 2007; Huntetal., 2002; LeightonandAcrivos 1987b)areplottedasfunctionsofsedimentconcentration (Figure 2-1). 23

PAGE 24

Theconcentration ofsedimentismodeledwithasedimentuxequation(Nirand Acrivos, 1990 )thatdescribesthebalanceofsedimentuxbyadvection,shear-induced diffusion,andgravity.SincewesolvetheunlteredNavier-Stokesequations,andthe gridspacingandtimestepissmallerthantheKolmogorovscales,aturbulentdiffusion termisnotnecessaryinthesedimentuxequation. @ @ t + u r = D r 2 )Tj /T1_1 11.955 Tf 13.15 8.09 Td (@ W t @ z (2) where W t istheconcentr ationdependentbulkhinderedsettlingvelocity( Richardson andZaki 1954), W t = W t 0 (1 )Tj /T1_1 11.955 Tf 11.96 0 Td ( ) q (2) W t 0 isthesettlingvelocityofasingleparticleinaclearuid(5.3cm/s),and q isan empiricalconstant, q = 8 > > > > < > > > > : 4.35Re )Tj /T1_6 7.97 Tf 6.59 0 Td (0.03 p 0.2 < Re p 1, 4.45Re )Tj /T1_6 7.97 Tf 6.59 0 Td (0.10 p 1 < Re p 500, 2.39 500 < Re p (2) Re p isdenedastheparticleReynoldsnumber, Re p = d f jW t 0 j f (2) where d isthesediment grainsizediameter(0.04cm).Onlynon-cohesivesediments withthematerialpropertiesofquartzinwaterareconsideredinthemodel.The shear-induceddiffusionofsediment, D ,isrepresentedwithafunctionofparticlesize, sedimentconcentration,andmixturestresses( LeightonandAcrivos 1986).Assuming isotopicdiffusion(i.e. D xx = D yy = D zz ), D = 1 4 d 2 f ( ) jruj, (2) 24

PAGE 25

andwhere f ( ) is, f ()= 2 1+ 1 2 e 8.8 (2) where isanempir icalconstant.ForlargevaluesoftheShieldsparameter(0.5 << 30), isfoundtobeapproximately0.33bycombiningtheresultsfromthedilutelimit withtheresultsfrommeasurementsindenseconcentrationsuspensions.However,the diffusioncoefcientislikelyunderestimatedwiththisvalueof (LeightonandAcrivos 1986). Indilutemixtures,theratioofcontactareasofthesedimenttothetotalareais smallandthecontactstressescanbeneglected.Themixturestressisapproximately equaltothesurroundinguidstressintheseareas.However,inmixtureswithhigh volumetricconcentrationsofsediment(e.g.,inthepackedbedofasandripple),the contactstressesaresignicantandmustbeaccountedfor( Batchelor 1988; Drew, 1983).Therefore,aparticlepressureisnecessaryforamixturetheorymodelto buildandmaintainbedforms.TheparticlepressureisrepresentedinSedMix3Das aconcentrationdependentdampingfunction S b (),tostabilizethebed, S b ()= r 8 (2) where r is0.2.Themixturevelocity, u ,isdecreasedanamountdeterminedbythe bedstiffnessfunctionwhenthevolumetricconcentrationofsedimentisgreaterthan 0.30(Figure 2-2),whichroughlycorrespondstotheonsetoftheenduringcontact region,consideredtostartatapproximately0.35volumetricconcentrationofsediment (FredseandDeigaard, 1992).Theshapeofthebedstiffnessfunctionwasmodeled aftercalculationsofparticlepressurewithrespecttoboundarylayerheight( Jenkins andHanes 1998)andtheviscosity-concentrationrelationship(Figure 2-1).Wechose theeighthpowerexponentialfunctionduetoitsdivergencefromzeroaround0.30 volumetricconcentration(Figure 2-2).Thebedstiffnessfactor, r ,determinesthe amountofparticlepressureapplied. 25

PAGE 26

2.2.2Initialand BoundaryConditions Weinitializethesimulationswithvaryingbedbathymetriesrangingfromaatbed tomultiplesinusoidalrippleswithdifferentheightsandlengths.Thebedconcentrationis initially0.63byvolumeandrapidlydecreasestozero(purewater)overthreegridpoints intheverticaldirection.Themixtureisinitiallyatrest( u =0).Weimplementperiodic boundaryconditionsinthex-andy-directions.Atthetopofthedomain,afree-slip boundaryconditionisusedforthe u and v velocities;thevolumetricconcentration, andthe w velocitiesarezero.Allthevelocitiesarezeroatthebottomofthedomain.A no-gradientconditionisimposedforthebottomboundaryconditionoftheconcentration, aswellasthetopandbottomboundaryconditionforthediffusioncoefcient, D 2.3Results Themodelisfullythree-dimensionalbutverycomputationallyexpensive(about 75daysofwall-clocktimefora10secondthree-dimensionalsimulationtorunin serialona2.6GHzprocessor).Two-dimensionalsimulationswereperformedinten casestoapproximatethemodel'sthree-dimensionalbehaviorinamorereasonable amountoftime(aboutoneweekofwall-clocktime).Weranthetwo-dimensional simulationswiththesamecodeasthethree-dimensionalsimulation,butreducedthe gridtocontainonlytwopointsinthecross-owdirection.Thereductionofgridpoints ultimatelydecreasedthecomputationaltimebyapproximatelyanorderofmagnitude. Wecomparedathree-dimensionalsimulationwith32gridpointsinthey-direction (3Dh02)toanequivalenttwo-dimensionalsimulationwithonlytwogridpointsinthe y-direction(2Dh02)toevaluatethedifferenceinmodeloutput.The v componentofthe velocityiszeroatallgridpointsinthetwo-dimensionalsimulation.Table 2-1 givesthe initialsimulationparametersforthetwo-andthree-dimensionalsimulations. Wecomparedtherippleheightandlengthoutputfromthemodelsimulationsto theempiricalripplepredictorof Nielsen (1981).Theempiricalformula( Nielsen, 1981) 26

PAGE 27

predictsequilibrium rippleheights( e ), e = a 0.275 )Tj /T1_3 11.955 Tf 11.95 0 Td (0.022 p (2) andlengths( e ), e = a )Tj /T1_3 11.955 Tf 5.48 -9.68 Td (2.2 )Tj /T1_3 11.955 Tf 11.96 0 Td (0.345 0.34 (2) where a is thewaveorbitalexcursion (U o T = (2 )) and isthemobilitynumber,aratioof thenon-stabilizingforcestothestabilizingforcesofthesediment, = U 2 o ( s = f )Tj /T1_3 11.955 Tf 11.95 0 Td (1) gd (2) Table 2-2 sho wstheequilibriumrippleheightsandlengthsandthesimulatedow parameters.TheReynoldsnumberandShieldsparameteraredenedby, Re = f U 2 o T f 2 (2) and 2.5 = 1 2 f 2.5 (2) respectively, where( Nielsen, 1992 ) f 2.5 =exp 5.213 2.5d a 0.194 )Tj /T1_3 11.955 Tf 11.95 0 Td (5.977 # (2) 2.3.1RippleHeight andLength Wecomparedtherippleheight, ,toNielsen's 1981 predictedequilibriumripple height( e )inallthesimulations(Table 2-3).First,therippleprolewasdeterminedat everytimeastheheightateachx-locationthatthevolumetricconcentrationofsediment becamelessthan0.58.Therippleheightisthendenedasthedistancebetweenthe minimumandthemaximumpointsoftherippleprole.Theripplelengthisdenedas thedistancebetweenthetwominimumpoints(rippletroughs)aroundthemaximum point(ripplecrest).Insixofthesimulations(2Dh01,2Dh02,2Dh03,2De01,2De02,and 27

PAGE 28

2De03),we initializedtheripplelengthatthepredictedequilibriumlength,butvariedthe initialrippleheightandtheowconditions.Intheremainderofthesimulations(2Dl01, 2Dl02a,2Dl02b,and2Df01),theowconditionswerekeptconstant,andtheripple lengthsandheightswereinitializeddifferentfromtheequilibriumheightandlength.A three-dimensionalsimulation(3Dh02)withadomainwidthof3cmwasalsocompared to Nielsen (1981 )andtoanequivalenttwo-dimesionalsimulation(2Dh02)withadomain widthof0.2cm. 2.3.1.1Varyinginitialrippleheights Therippleheightsinsimulations2Dh01,2Dh02,and2Dh03wereinitializedat onecmlessthanequilibriumheight,atequilibriumheight,andonecmgreaterthan equilibriumheight,respectively,withallotherparametersconstant.After10wave periods,theripplesequilibratedtothesameheight,approximately60%ofthepredicted equilibriumheight(Figure 2-3).Themodelmaintainedtheripplelengthsthroughout thesimulations.Wealsoranasimulation(3Dh02)initializedwiththesamerippleand forcedwiththesameowconditionsas2Dh02,butwitha3cmwidedomaininsteadof 0.2cm.Therippleinthisthree-dimensionalsimulationwasinitializedatitsequilibrium height.Unlikethesimulation,2Dh02,therippleheightdecayedonlyslightlyto95%of theequilibriumheight,thenremainedconstantthroughouttheremainderofthe12s simulation(Figure 2-3). 2.3.1.2Varyingowconditions Simulations2De01,2De02,and2De03wereforcedwithdifferentowconditions. Therippleswereinitializedatapproximatelytheequilibriumripplelengthforeachofthe givenconditionsandatarbitraryheights(Table 2-1).Therippleheightinthelowow simulation(2De01)decayedtoabout50%oftheequilibriumrippleheight,thenstayed fairlyconstant.After16waveperiods,therippleheightequilibratedtoabout50%ofthe equilibriumrippleheight(Figure 2-4).Therippleinthemidowsimulation(2De02)grew to95%ofthepredictedequilibriumheightafteronlythreewaveperiods(Figure 2-4). 28

PAGE 29

Theripple lengthsinbothsimulationsremainedconstantattheapproximateequilibrium ripplelength.Therewasnostablerippleformsoonafterthehighowsimulation (2De03)begins.Asexpected,theowistooenergeticforripplestoexist(Figure 2-5). 2.3.1.3Multipleripples Themultipleripplesimulations(2Dl01,2Dl02a,2Dl02b,and2Df01)illustratedthe model'sabilitytoallowripplestoformfromaatbed,merge,separate,andevolve towardsanequilibriumstate.Eachsimulationwasinitializedinadifferentripplestate thantheexpectedequilibriumstate(i.e.,initialripplelength,height,and/orshape weredifferentfromtheequilibriumlength,height,and/orshape).Twoslightlymerged sinusoidalripples,oradouble-crestedripple,wereinitializedwithapproximatelyhalf oftheequilibriumripplelengthinsimulation2Dl02a.Over32waveperiods,thepeaks ofthedouble-crestedripplemergedtoformoneripplewithalengthnearthepredicted equilibriumripplelength(Figure 2-6),andaheightthatroughlyequilibratedtoabout 55%oftheequilibriumheight(Figure 2-7).Simulation2Dl02bwasinitializedwithtwo rippleseachwithabouthalfthepredictedequilibriumripplelength.Onerippledecayed toabout0.2cmwhiletheotherripplegrewandtrendedtowardtheequilibriumheight over35waveperiods(Figure 2-8).Asingleripplewasinitializedatapproximatelytwice theequilibriumlengthinsimulation2Dl01(Figure 2-9).Over16waveperiods,foursmall ripples,abouthalfthelengthofanequilibriumripple,formedandbegantogrowonthe surfaceofthelongripple.Theripplesonthefarleftandrightweresmallerandless denedthanthetwomiddleripples.Insimulation2Df01,weinitializedaroughatbed withsmallperturbations O (0.1cm) .Thedomainlengthwasapproximatelythepredicted equilibriumlengthofoneripplefortheowconditions.Withinvewaveperiods,three smallripplesformedinthecenterofthedomain.Thethreeripplesthenevolvedintotwo after15waveperiodswithoneripplemoredominantthantheother(Figure 2-10).The dominantripplegrewsteadilytowardstheequilibriumrippleheight(Figure 2-7)andthe 29

PAGE 30

lessdominantr ippledecayedthroughoutthelastsevenwaveperiodsofthesimulation. Table 2-3 summarizestherippleheightandlengthresultsforthesimulations. 2.3.2RippleShape Weinitializedthemodelsimulationswithsinusoidalripples,ashapenottypically observedinlaboratoryandeldexperiments( HaqueandMahmood 1985 ).Throughout thesimulations,theinitialsinusoidalrippletransitionedintoasharpercrestedripple. Forexample,theripplein3Dh02initiallyhadsteepslopingsidesandroundedpeaks (Figure 2-11).Asthesimulationprogressed,therippletroughsbroadened,theripple crestsbecamemorepeaked,andthecrestsswayedbackandforthasseeninthe laboratoryandeld(e.g. WibergandHarris (1994)).Therippleprolewasdetermined astheheightatwhichthevolumetricconcentrationbecomeslessthan0.58. 2.4Discussion 2.4.1RippleHeightandLength Thesimulatedrippleheightsinsimulations2De02and3Dh02comparedwellto (Nielsen, 1981 ).Therippleheightsintheremainderofthesimulationseitherreached anequilibriumheightcomparabletoortrendedtowardtheequilibriumrippleheight. However,therippleheightsinsimulationswithequivalentowconditions(2Dh01, 2Dh02,2Dh03)equilibratedtoasingleheight,illustratingthemodel'sabilitytopredict anequilibriumstate.Althoughthemodelunderpredictedtheequilibriumrippleheight byabout40%inmostofthetwo-dimensionalsimulations,itpredicted95%ofthe equilibriumrippleheightinthethree-dimensionalsimulation(discussedbelow).The modelalsocorrectlysimulatedtheshearingoftherippleunderhighows.Witha mobilitynumberof222,simulation2De03wascorrectlyabsentofastableripple form.Thesimulatedripplelengthsinsimulations2Dh01,2Dh02,2Dh03,2De01, 2De02,2De03,and2Dl02acomparedwellwith( Nielsen, 1981 ).Theripplelengths insimulations2Dl01,2Dl02b,and2Df01trendedtowardtheequilibriumlength.In simulations2Dl02band2Df01,oneripplewasmoredominantthantheother,suggesting 30

PAGE 31

onewillcontin uetogrowandtheotherwillattenout,withthedominantrippletrending totheequilibriumripplelengthandheight.Simulation2Dl01hadtwodominantripples, againsuggestinggrowthinthetwodominantripplesandatteningintheothertwo decayingripples.Resultsfromtheroughatbed(2Df01)andthelongatripple(2Dl01) simulationagreedwithpreviousndings( FaraciandFoti, 2001 ; Forel 1883)that thelengthsofripplesthatbegintoformonaatbedinitiallyformatabouthalftheir equilibriumlengths.Atleastthree-hundredcyclesmaybenecessaryforaatbedto reachitsequilibriumstate( FaraciandFoti, 2001 )andpossiblymoreiftheripplesmust transitionfromanotherstate(asincases2Dl01,2Dl02a,2Dl02b,2Df01).Althoughitis currentlycomputationallyprohibitivetorunsimulationsforhundredsofwaveperiods, themodeldidpredictthetransitionofseaoorstatesindependentoftheinitialbed bathymetryandtheformationofripplesfromaroughatbed. 2.4.2RippleShape Wechoseamediangrainsizeof d = 0.04cmandthegivenowstosimulatean environmentconducivetotwo-dimensionalvortexrippleformation.Weusedacoarser sizesedimentsincetwo-dimensionalvortexripplesaredifculttogenerateinlaboratory experimentsusingnesands( Lofquist, 1978 ; O'DonoghueandClubb 2001).The ripplesinthesimulationsareinitializedwithasinusoidalshapenotcharacteristicof thoseseeninnature.Ripplesobservedunderpurelyoscillatoryowinthelaboratory aregenerallysymmetric,withnarrowcrestsandat,broadtroughs( WibergandHarris 1994),similartothoseseeninthesimulationspresentedhere.Theshapepredicted bythemodelprovidesstrongevidencethatthegoverningequationsusingthemixture theoryapproacharecapturingthephysicsofrippleformation. 2.4.3ComparisonsofTwo-andThree-DimensionalSimulations Thetwo-dimensionalripplesimulation(2Dh02)equilibratedtoapproximately60% oftheequilibriumrippleheightforthegivenowconditions.Therippleheightinthe three-dimensionalsimulation(3Dh02)withthesameinitialrippleandowconditions 31

PAGE 32

equilibratedto 95%oftheequilibriumheight(Figure 2-3).Thedifferencescanbe explainedbyexaminingthebedshearstress.Themaximumbedshearstress( b = f u 2 )isafunctionofthefrictionvelocity(u ).Thefrictionvelocitycanbeestimatedfrom theRMSverticalturbulentvelocity(e.g., Nielsen (1992))as u =2 w 0 rms .Themaximum bedshearstressabovetheripplecrestinthethree-dimensionalsimulation(3Dh02)is approximately50%lessthaninthetwo-dimensionalsimulation(2Dh02).Thereduced shearstressinthethree-dimensionalsimulationindicatesthattheripplewillgrowtoa largerheightuntiltheshearstressbalanceswiththegrowth,reachingequilibrium.Inthe two-dimensionalsimulation,theturbulencecannotdissipateinthecross-owdirection, increasingtheshearonthebed.Thedifferenceintherippleheightsbetweenthetwoandthree-dimensionalsimulationscanthereforebeattributedtoareductioninbed shearstressduetothedevelopmentofturbulenceinthecross-owdirection.Previous researchhasfoundthatthree-dimensionalvortexstructuresplayanimportantroleinthe transportofsediment,andhigherReynoldsnumberowsarestronglythree-dimensional (ZedlerandStreet, 2006).Three-dimensionalvortexstructuresalsosignicantlyaffect particletrajectoriesandcreaterelevantdispersioneffects( Blondeauxetal., 2004; Scanduraetal. 2000 );therefore,differencesbetweensimulationswithdifferentamounts ofgridpointsinthecross-owdirectionuptoacharacteristiclengthareexpected. Ananalysisofthree-dimensionalsimulationswithdomainwidthsofcharacteristic lengthswillbenecessarytoexaminesedimentconcentrationsandturbulencedueto thethree-dimensionalcomplexityofvortexformationanddissipation.Weexpectthatin ordertocapturethefullyresolvedow,thesimulationmusthaveadomainwidthofa characteristiclengthequaltoorgreaterthanthelengthscaleoftheturbulentvortices (approximatelytheheightoftheripple). 2.4.4BedStiffnessFunction Thebedstiffnessfunction(Figure 2-2)doesnotmakethebedcompletelyrigid, evenatavolumetricconcentrationof0.63(afullypackedbed).Porepressuredrives 32

PAGE 33

asmallmixture velocityinthepackedbed.Acompletelystationarybedwouldnot berepresentativeofthephysicsinthepackedbedregion.Thebedstiffnessfunction thereforeallowsthemodeltosimulateowthroughaporousmedium.Futureworkwill investigatehowtheowthroughrippledbedsisaffectedbyshapesandsizesofgrains, andbiologicalactivity. 2.5Conclusions Thethree-dimensionalmixturetheorymodel,SedMix3D,predictsripplegeometries underarangeofowconditionstypicallyfoundinthelaboratory(9000 < Re < 700,000).Themodelcanalsopredictthetransitionfromoneripplestatetoanother.We comparedthemodeloutputofripplegeometrytoexistingequilibriumripplegeometry formulae.Althoughuncertaintiesassociatedwithturbulenceclosureschemesare avoidedduetotheuseoftheunlteredNavier-Stokesequations,quantitativetests arenecessarytoexperimentallyverifytheempiricalsubmodelsforthesediment transportdynamics.Comparisonsbetweentwo-andthree-dimensionalsimulations revealedaninherentdifferenceinthebedshearstressthatresultedinconsiderable differencesinequilibriumrippleheight.Theseresultsindicatethatthree-dimensional simulationsareessentialforthedevelopmentofturbulenceinthecross-owdirection, thereforeresultingintheproductionofrealistichydrodynamics.Futureworkwillfocus onthree-dimensionalcomparisonsofsuspendedsedimentconcentrations,turbulence productionanddissipation,andvelocityprolestolaboratorydata.Thehighspatialand temporalresolutionmakesSedMix3Dapowerfulresearchtoolforsmall-scalesediment transportandbedformdynamics;however,currentlythemodelisimpracticalforuse inengineeringpracticeduetothehighcomputationalexpense.However,themodel hasthecapabilitytopredictnetsedimenttransportundervaryingwaveconditionsand scouraroundstationaryobjectssuchasburiedmunitionsandstructurepilings.Asthe modelandcomputertechnologyarefurtherdeveloped,SedMix3Dhasthepotentialto beutilizedinmanyaspectsofcoastalresearchandengineeringpractice. 33

PAGE 34

Table 2-1.Listedarethebed,domain,andowconditionsforallsimulations.Theinitial bedshapedescribesthetypeandnumberofripplesinitializedinthe simulation.Theinitiallengthoftherippleisthedomainlengthdividedbythe numberofripples.Allsimulationsaretwo-dimensional(domainwidth 0.2 cm)except3Dh02.Theripplelengthsinsimulations2De01and2De02were initializedattheequilibriumripplelengthfortheirowconditions.Theripple heightswereinitializedneartheequilibriumrippleheightfortheirow conditions. Sim.Initialbed shapeInit.Init.DomainDomainDomain U o T name ripplerippleheightlengthwidth heightlength (cm)(cm)(cm)(cm)(cm)(cm/s)(s) 2Dh01(1)sin usoidalripple1.012.016.012.00.240.02.0 2Dh02(1)sinusoidalripple2.012.016.012.00.240.02.0 2Dh03(1)sinusoidalripple3.012.032.012.00.240.02.0 2De01(1)sinusoidalripple2.28.016.08.00.120.02.0 2De02(1)sinusoidalripple1.616.016.016.00.160.02.0 2De03(1)sinusoidalripple1.68.016.08.00.1120.04.0 2Dl01(1)sinusoidalripple0.824.016.024.00.240.02.0 2Dl02a(2)sinusoidalripples1.46.016.012.00.240.02.0 2Dl02b(2)sinusoidalripples1.66.016.012.00.240.02.0 2Df01roughatbed 0.10.08.012.00.240.02.0 3Dh02(1)sinusoidalripple2.012.016.012.03.040.02.0 Table 2-2.Rangeofparametersforthepresentedsimulationsandresultsfromexisting ripplepredictorformulae.Theequilibriumrippleheightsandlengthsare calculatedfrom Nielsen (1981).The120cm/smaximumfreestreamvelocity istooenergeticforripplestopersistandnostablerippleexistedthroughout thesimulation. U o T Re 2.5 e e (cm/s)(s) (cm)(cm) 20.02.0 9719 60.08 9.9 1.4 40.02.0 38878 250.2415.0 2.0 60.02.0 87474 560.4616.2 2.1 120.04.06997962221.18N/AN/A 34

PAGE 35

Table 2-3.Thepercentageofequilibriumrippleheightreachedforthepresented simulations.Theequilibriumrippleheightsarecalculatedfrom Nielsen (1981).Thelastcolumnisthetotalnumberofperiodsinthesimulation. Sim. Description Final Per iods name f = e 2Dh01 o < e 60% 16 2Dh02 o = e 60% 16 2Dh03 o > e 60% 16 2De01 Lo wow 50% 16 2De02 Midow 95% 6 2De03 Highow N/A N/A 2Dl01 One-ripple 50% 16 2Dl02a Double-crested 55% 33 2Dl02b Two-ripple 30% 35 2Df01 Flatbed 30% 33 3Dh02 Three-dimensional 95% 6 Figure2-1.V ariouspublishedeffectiveviscosityequations(lines)andexperimentaldata (symbols)scaledwiththeviscosityofwater( f ).Thetwosetsofdata ( HuangandBonn 2007 ; Huntetal. 2002)areplottedwiththeauthors'ts totheKrieger-Doughertyequation(solidblacklinesthatgothrough respectivedatapoints).SedMix3DemploysanEilersequationwithan intrinsicviscosityof3.0,alsoequivalentto LeightonandAcrivos (1987b). 35

PAGE 36

Figure2-2.Bed stiffnesscoefcient, S b ,plottedversusconcentration.Thefunction determinesthepercentamounttodampthevelocityintheenduringcontact regionofthedomain(i.e., > 0.30).Notethebedstiffnessfunctiononly dampsthevelocityabout0.5%inthepackedbedregion.Thesmall correctionmakesasignicantdifferenceinthebedstiffness. Figure2-3.Time seriesofthenormalizedrippleheight(= e )for2Dh01,2Dh02,2Dh03, and3Dh02. e istheequilibriumheightcalculatedfrom Nielsen (1981) equilibriumformulaforthesimulationconditions( e =2 cm).Theripplesin thethreetwo-dimensionalsimulations(2Dh01,2Dh02,2Dh03)were initializedat50%,100%,and150%oftheequilibriumheight,respectively. Allthreeripplesequilibratedtoapproximately60%oftheequilibriumheight after8waveperiods.Thesimulationwithawidthof0.2cm(2Dh02)isalso comparedtoanequivalentsimulationwithawidthof3cm(3Dh02)( e =2 cm).Theripplein3Dh02decaysonlyslightlytoabout95%ofthe equilibriumheight. 36

PAGE 37

Figure2-4.Time seriesofthenormalizedrippleheight(= e )for2De01( e =1.4 cm) and2De02( e =2.1 cm). e istheequilibriumheightcalculatedfrom Nielsen (1981)forthesimulationconditions. Figure2-5.Time seriesoftherippleheight( )for2De03.Theowin2De03istoo energetictosustainripples.Weplotthedimensionalbedheightherefor 2De03becausetheequilibriumheightcalculatedfrom Nielsen ( 1981 )is e =0.0 cm.Thereisnostablerippleformthroughoutthesimulation. 37

PAGE 38

Figure2-6.Time seriesoftherippleprolefor2Dl02a.Thetwoinitialripplesbeginto mergetoformoneripplewithalengthof12cm.Thepeaksoftheripples swaybackandforthwiththeoscillatoryow. Figure2-7.Time seriesofthenormalizedrippleheight(= e )for2Dl01,2Dl02a,2Dl02b, and2Df01. e istheequilibriumheightcalculatedfrom Nielsen (1981)forthe simulationconditions( e =2 cm). 38

PAGE 39

Figure2-8.Time seriesoftherippleprolefor2Dl02b.Oneofthetwoinitialripples becomeslessprominentandstartstomergewiththeotherrippleafterabout 30waveperiods.Thepeaksoftheripplesswaybackandforthwiththe oscillatoryow. Figure2-9.Time seriesoftherippleprolefor2Dl01.Foursmallripplesbegintoform onthesingleinitialrippleafterabout5waveperiods.Thepeaksofthe ripplesswaybackandforthwiththeoscillatoryow. 39

PAGE 40

Figure2-10.Time seriesoftherippleprolefor2Df01.Threeripplesbegintoformon the0.1cmperturbedbed.Twooftheripplesthenstarttomergeafterabout 10waveperiods.Thepeaksoftheripplesswaybackandforthwiththe oscillatoryow. 40

PAGE 41

Figure2-11.Ripple proletimeseriesfor3Dh02.Timeincreasesontheverticalaxis. Theslopearoundthecrestincreases,whiletheslopearoundthetrough decreasesthroughoutthesimulation.Notethepeakswayingbackandforth withtheoscillatoryow. 41

PAGE 42

CHAPTER3 MODEL-DA TACOMPARISONOFATHREE-DIMENSIONALMIXTUREMODEL 3.1Introduction Presentedherearecomparisonsofafullythree-dimensionalmixturetheory model(SedMix3D)thatcansimulateowvelocitiesandsedimentconcentrations inprototypescaledomains.WhileSedMix3Disinherentlythree-dimensional,in situmeasurementsofvectorandscalarquantitiesofathree-dimensionaldomain aresparse,asthetechnologytotakesuchmeasurementshasonlyrecentlybeen developedandisstillbeingrened(e.g.,Tomo-PIV).Whilethecomparisonshereare oftwo-dimensionalverticalslices,itisimportanttonotethatitwasnecessarytorun SedMix3Dinthree-dimensionstocapturethesignicant,real-world,three-dimensional turbulence,thencompareaverticalslicefromthe3Ddomaintothe2Dobservations. Oncevalidated,thefullthree-dimensionaldomaincanbeanalyzedforfurtherresearch. Thediscussionwillfocusheavilyonthedifferencesbetweentwo-andthree-dimensional simulationsaswellasananalysisofthemodel'ssedimentclosures. 3.2Methodology 3.2.1SedMix3D Thethree-dimensionalmixturemodelof Penkoetal. (2010b)solvestheunltered Navier-Stokesequationsandasedimentuxequationforauid-sedimentmixture resultinginthetime-dependentsedimentconcentrationandthree-componentvelocity vectoreldinathree-dimensionaldomain.Themodeltreatstheuid-sediment mixtureasacontinuumwitheffectivepropertiesthatparameterizetheuid-sediment andsediment-sedimentinteractionsincludingabulkhinderedsettlingvelocity,a shear-induceddiffusion,aneffectiveviscosity,andaparticlepressure,withgrid spacingontheorderofaparticlediameterandtimestep O (10 )Tj /T1_4 7.97 Tf (5 s).Themodelonly simulatesowintheboundarylayer(i.e.,nofreesurface).Thenumericalscheme isnitedifferencewithsecond-ordercentraldifferencesemployedonastaggered 42

PAGE 43

grid. Theboundaryconditionsforthevelocitiesandconcentrationareperiodicinthe horizontal.Thevelocityisassumedtofollowthefree-streamatthetopoftheboundary, andthe v and w velocitiesaresettozeroatthetopofthedomain.Ano-slipcondition existsforthevelocitiesatthebottomboundary.Theconcentrationisequaltothe concentrationofconsolidatedsedimentatthebottomboundary( = 0.63)andzeroat thetopboundary. 3.2.2ExperimentalFacilityandConditions TheexperimentswereperformedinawaveumeattheFluidMechanicsLaboratory atDelftUniversityofTechnology,Netherlands( Rodriguez-AbudoandFoster 2010).The freesurfaceumewas40minlength,0.8minwidth,with0.36mwaterdepthanda 1:20slopedbottomcoveredwithalayerofsediment.Thesamplingwindow(11cm 11 cm)waslocatedapproximately20mfromthewavegenerator.Forthisexperiment,the wavegeneratorproducedregularsinusoidalwaves5cminheightwith2speriods.The sedimentintheumehadameangraindiameterof0.054cmandaspecicgravityof 1.2. ADantecparticleimagevelocimeter(PIV)systemobtainedtwo-dimensional vertical(x-z)planeopticalimagesofthesamplingwindowusinga120mJNd-Yag pulsedlasersynchronizedwitha1MegaPixelcamera.Thelaserwaslocatedina watertighthousingapproximately27cmabovethebedandthecamerawasoutside theume,perpendiculartotheoscillatoryow.AnAcousticDopplerVelocimeter(ADV) time-synchronizedwiththePIVsystemmeasuredthefreestreamvelocityapproximately 17cmabovethebed.Thecameracapturedimagepairs(10mstimelagbetweenpair members)ofthesamplingwindowfor60sburstsatapproximately12Hz.Suspended sediment,organicmatter,andmicro-bubblesactedasseedingagentsinthewater column.Thevelocityvectorswerecalculatedbycorrelatingtheimagepairsusing64 32pixelinterrogationwindowswith50%overlap.Theresultingspatialresolutionof 43

PAGE 44

thevector eldwas3.48mm 1.74mm.Outlierswereremovedwithathreestandard deviationlterandreplacedwiththelocalensembleaverage. 3.3Model-DataComparisonResults ThemodelwasdrivenbythefreestreamvelocityacquiredfromtheADVoveran observationtimeseriesof18waveperiods.Threeregularsinusoidalwaveswereadded tothebeginningoftheobservationtimeseriesasspin-upperiodsforthemodel.The freestreamvelocitytimeseriesfromtheADVisplottedinFigure 3-1.Weinitializedthe modelbedprolewiththeobservedbedproleaveragedovertherstwaveperiodin theobservationtimeseries.Theprolerepeatedeveryx-zplaneexceptforaonez-grid pointoffseteveryotherx-zplaneforaslightlyroughbed.Aperturbationinthecenter ofthedomainwithawidthofthreegridpointsandaheightoftwogridpointsbrokethe symmetryofthesimulationinitialization(Figure 3-2).Thedomainwas10.6cm 2.6 cm 10.8cmwith128 32 256gridpoints.Theuidproperties( =0.998 gcm )Tj /T1_6 7.97 Tf 6.59 0 Td (3 =1 10 )Tj /T1_6 7.97 Tf (2 gcm )Tj /T1_6 7.97 Tf (1 s )Tj /T1_6 7.97 Tf 6.59 0 Td (1 )andsedimentparameters(d = 0.054cmand s = 1.198g cm )Tj /T1_6 7.97 Tf (3 )approximatelymatchedthoseoftheobservations. Wedeterminedthemodelx-zplanetobeusedinthecomparisonsbyrst time-averagingboththemodelandobservationhorizontalvelocityeldsoverthe18 waveperiods,thencalculatingtheRMSdeviationbetweentheobservationsandeach x-zplanefromthemodel(32y-planesinthiscase).Themodelx-zplanewiththe spatiallyaveragedminimumRMSdeviationwascomparedheretotheobservedx-z planefromthePIVdata.Bothensemble-averagedandinstantaneoustimeseriesx-z planevelocityeldsarecomparedinthefollowingsections. 3.3.1Hydrodynamics Figure 3-3 showsthemodeledandobservedensemble-averaged v vorticity eldsatdifferentphaseangles.Thetoppanelisaplotoftheensemble-averagedfree streamvelocitytoindicatephaselocationofpanels(a-f).Flowisinitiallydirectedto theleft(onshore)andpositive(red)contoursindicateacounter-clockwiserotation. 44

PAGE 45

Themodelv orticityplotsshowtheboundarylayershearonthefaceoftheripplesat andnearmaximumfreestreamvelocity(Figure 3-3b,d,e,f).Atowreversal,vortices aregeneratedontheleesideoftheripple,andastheowincreases,areejectedand advectedwiththeow.Thevorticesthendissipateaftermaximumowandbecome lesscoherentbythenextowreversal.Theobservationsalsoshowvortexformation andejection,andtheboundarylayershear;notethevorticitymagnitudeonlydiffersby approximately7%.Theobservedcoherentvortexstructuresarelessclearlydened thaninthemodel.Themodelpredictsthelocation,size,androtationaldirectionof thevorticesforallphasesfairlywell.Theshapeofthevortexstructure,includingthe vortextails(theareaofvorticityconnectingtheejectedvortextothegenerationpoint (asinFigure 3-3a,f)isalsopredictedwellbythemodel.Thesmallermagnitudeofthe observedvorticityincomparisontothemodel,specicallynearthebed,couldbethe resultofdecreasedcondenceinthemeasurementofthenearbedvelocitiestobe discussedinlatersections. Incomplex,three-dimensionalandoscillatoryows,thevortexstructuresare oftendifculttodistinguishfromthevorticityduetotheboundary-generatedshear. Usingthemethodof Zhouetal. (1999),wecalculatedtheswirlingstrength, ci ,to identifythecoherentclosedrotationalvortexstructuresexcludingtheinterferencefrom boundary-generatedshear(Figure 3-4).Themethodiseffectiveindeterminingthe locationofvortexcoresinboundarylayershearow,butdoesnotidentifytherotational direction.Thehorizontalandverticalpositionsofthevorticesandthetimingrelativeto thewavephasepredictedbythemodelareingoodagreementwiththeobservations. Thestrengthofthevorticespredictedbythemodelisonlyslightlygreaterthanthe observations.Theobservationsshowmorecoherentvorticesformingastheow reversesfromoff-toonshoredirectedow(Figure 3-4l-g-h)thanon-tooffshoredirected ow(Figure 3-4h-i-j),whichischaracteristicofonshoreripplemigration.However,the modelpredictsrelativelysymmetricalvortexsize,shape,andgenerationfrequency 45

PAGE 46

duringboth owreversals.Thedifferenceheremaybeaninherentproductofthe periodicboundaryconditionsusedinthemodel. Thesymmetryofthemodeloutputisalsoillustratedbytakingthetime-average ofthehorizontalvelocities(Figure 3-5).Themeanvelocities, u ,inbothrippletroughs aredirectedtowardstherippleanksinthemodel;however,theobservationsexhibit lesssymmetrywithmeanvelocitiesdirectedtowardstheanksoftheleftripple,but nottherightripple.Themodelisinbetteragreementwiththeobservedtime-averaged horizontalvelocityintheleftportionofthedomain.Theobservationsexhibitmuchmore symmetryintheplotoftime-averagedverticalvelocity(Figure 3-6).Themodelagrees wellwiththeobservationsthroughouttheentiredomain. Verticalprolesofstandarddeviationofthehorizontalvelocity, u ,inthemodel (blackarrows)andtheobservations(redarrows)atvariouslocationsalongthebed proleareplottedinFigure 3-7.Themodelisinremarkableagreementwiththe observationsforallbutnearthebedabovetheleftripplecrest.Thereisexcellent agreementinthetroughandontheanksoftheripples.Themodeloverestimatesthe standarddeviationofthehorizontalvelocitybyapproximately2cm/snearthecrestsof theripple.Modelestimationsof w arealsoingoodagreementwiththeobservationsin thetroughoftheripples,butdeviatefromtheobservationsontheripplecrests(Figure 3-8). Furtherexaminationofthehorizontalvelocities(averagedovertheentiredomain length)revealsthatthemodelpredictsthehorizontalvelocityovershoottypically observedinoscillatoryowsnearaboundaryatvariousphasesofthewave(Figure 3-9).Theovershootislessdenedintheobservationsprobablyduetothelimitations inresolvingthenear-bedvelocitieswithPIV.Inthenear-bedregion(1.5cmabovethe ripplecrest),themodelandobservationsdonotcomparewellatmaximumfreestream velocity(yellowprole).Abovetheovershootarea,themodelandobservationsdiffer byapproximately10%to20%.Sincetheprolesareaveragedovertheentirebed,we 46

PAGE 47

woulde xpectincreasedvariabilityinthevelocitiesnearthebedduetothebedforms. Thetime-averaged u velocityprolesatdifferentxlocationsalongthebedcompare considerablybetter(Figure 3-10).Thexlocationsherearecollocatedwiththelocations inFigure 3-7.Themodeliscapturingthegeneralshapeandmagnitudeoftheobserved velocityproles;however,itdoespredictsaslightlylarger(0.5cm/s)maximumvelocity overshootthanobservedatsomexlocations. Acrossspectralanalysisofthemodeledandobservedhorizontalvelocitieswiththe velocitymeasuredbytheADVillustratesthatthemodelalsocorrectlypredictsthetiming oftheow(Figure 3-11).Positivecontoursindicatethemodeledorobservedvelocity leadstheADVvelocity.Thephaseleadinthemodelisapproximatelyzerofromz=5cm tothetopofthedomain.Intheobservations,thereisaphaselagovertheleftrippleand aleadovertherightripple.Within2cmofthebed,themodelshowsgoodagreement withtheobservations,specicallyovertheleftripple.Themodelandobservations bothshowavelocityphaseleadontheanksoftheripplesandaphaselagabove thetrough.Themagnitudeofthemodeledphasesareinexceptionalagreementwith observations.However,themodelpredictsaphaseleadnearthebedinthetroughof theripplesthatisnotobserved. 3.3.2SedimentDynamics ExtractingmeasurementsofconcentrationwithPIVsystemsisfairlyunreliable duetotheexistenceofnon-sedimentparticlesinthewatercolumn(e.g.,microbubbles, organicmatter)thatscatterthelaserlight,therefore,quantitativeestimatesofsediment concentrationwerenotmadewiththisdataset.Herewepresentaqualitativecomparison oftheconcentrationandbedmorphologybasedontheobservedPIVimageintensity (Figure 3-12,rightpanels).Thecontoursaretheensemble-averagedintensityofthePIV rawimages,lteredbysubtractingtheensemble-averagedminimumintensityateach gridpoint.Theleftpanelsarethemodeledconcentrationeldforthex-zplaneusedin thepreviouscomparisons.Onlythelocationofthesedimentplumecanbecompared 47

PAGE 48

here.W ecannotprovideanumericalrelationshipbetweenthemagnitudeoftheimage intensityandtheconcentration,therefore,thecolorbarshavebeenexcludedfromthe plots.Wecaninferasuspendedsedimentplumeinregionsofhighintensity.Usingthis assumption,themodelpredictsthelocationofthesedimentplumesforthefourphases ofthewaveshown.Alsoplottedarethepredictedandobservedvelocityvectors(down sampledtoeaseviewing).Ingeneral,themodelvelocityvectorsareingoodagreement withtheobservations.Theensemble-averagedbedprolesarealsoshowninFigure 3-12.Wecalculatedthebedproleinthemodelbyensemble-averagingthebedlocation whentheconcentrationis10%byvolumetoincludethebedloadandmovementofthe crests.Thebedlocationoftheobservationswascalculatedbydeterminingthelowest pointofthewavemaximumpixelintensityimageplusanoffsetcalculatedfromthewave averagedpixelintensityimage.Thebedlocationswerethenensembleaveragedover theentiretimeseries.Theripplecrestshiftswiththeowphaseinboththemodeled andobservedripples.TheshiftingoftherippleshapecanalsobeseeninFigure 3-13. Theplotshowstherippleprolesensemble-averagedoverthersteightwaveperiods plottedat15 phaseintervalsstackedwith0.8cmoffsets.Theripplesinthemodel migratedslightlythroughoutthetimeseries.Weensembleaveragedtheprolesoverthe rstofthesimulationtoreducethedistortionoftherippleshapefromthemigration.The modeledripplespeakandattenatapproximatelythesamephaseofthewaveasthe observations(owaccelerationtomaximumow,andowreversal,respectively). 3.4Discussion 3.4.1Hydrodynamics Vortexstructureshavebeenshowntobehighlythree-dimensional( Blondeaux etal. 2004 ; Scanduraetal. 2000 ; ZedlerandStreet, 2006)andsignicantlyaffect thehydrodynamicsoftheow.Therefore,athree-dimensionalmodelisnecessary toanalyzetheturbulentoweldsoverbedforms.Sincethevortexstructuresplaya signicantroleinsedimenttransport,itisimportanttocorrectlypredictthevorticityeld. 48

PAGE 49

Themodelag reesremarkablywellwiththecomparisonsoflocationsofcoherentvortex structures(Figure 3-4).Discrepanciesinthevorticitycomparisonscouldresultfrom severalcontributingfactors.Thedifferencesinthestrengthofthevorticescouldbedue torandomnessassociatedwithinsituvelocitymeasurements.Themagnitudeofthe swirlingstrengthisbasedonthedegreeofclosedstreamlines.Velocitymeasurements usingPIVareextractedfromseededparticlesandsuspendedsediment;however, dependingonthesedimentStokesnumber,theparticleswillnotalwaysfollowthe streamlineoftheow,therefore,capturingclosedstreamlineswithPIVmeasurements islesslikelyifseededuidisnotused.Typicallyonlyverystrongcirculationevents arerecordedinsitu( NicholsandFoster, 2007).Thelargelightreectionsatthe uid-sedimentinterfaceresultinveryhighlightintensityinthenearbedregionregion (uptoabout0.3cmabovethebed).Theresultisadecreaseinthethepeakcorrelations andlowercondenceinthevelocityestimatesinthisregion.Theinherentabilityof themodeltocalculatevelocitieswithequalresolutioneverywhere,eveninthehighly concentratedlayerofmovingsedimentwithin0.1-0.3cmofthebedmayaccountforthe discrepanciesinthevorticitybetweenthemodelandobservationsinthenearbedregion (Figure 3-3). Ingeneral,thecomparisonsofthemodeledandobservedowstatisticsareinvery goodagreement.Theverticalvelocitycomparisonsillustratethelargestdiscrepancies. However,thedifferencesbetweenthemodelandtheexperimentalsetupmayprovidean explanationformanyofthediscrepancies.Themodelismorerepresentativeofaclosed lidu-tubeexperimentalsetup,whereastheobservationsweretakeninafree-surface ume.Thesurfacegravitywavescreateellipticalparticlepathsintheobservationsand thevelocitieshighinthewatercolumnwillhaveanon-negligibleverticalcomponent. Themodel'sclosedlidforcesstraightlineparticlepathswithzeroverticalvelocities outsidetheboundarylayer.Aphaselagovertheleftrippleandaleadovertheright rippleintheobservations(Figure 3-11)couldalsobetheresultoftheellipticalvelocity 49

PAGE 50

particlepath inducedbythepassingofasurfacegravitywaveortheplacementofthe ADVdirectlyoverthecenteroftheobserveddomain.Thephaseleadinthemodelis approximatelyzerointheupperpartofthedomainduetotheconstantspatialforcingat everytimestep.Thedifferenceinthetopboundarymayalsoaccountforthedisparityin the w standarddeviation(Figure 3-8). 3.4.2SedimentDynamics Qualitatively,themodelshowsgoodagreementwiththelocationsoftheobserved sedimentplumesandbedproles.Thedifferenceintherippleheightsispartiallydueto theslightmigrationinthemodeloftheripplesoverthecompletetimeseries.Bytaking thephaseaveragesoverthersteightperiodswhentherewasnegligiblemigration,the comparisonsareconsiderablybetter(Figure 3-13).Theplotclearlyshowstheshiftingof themodeledripplesthatareingoodagreementwiththeobservations,especiallynear owreversal.Previouslyshown,themodelislessabletocapturethemaximumow, whichcouldexplainthedifferencesinbedprolesatmaximumow.Themodelpredicts aslightlyhighermaximumowthantheobservations,resultinginahigherbedstress andatterbed. 3.4.3ComparisonsofTwo-andThree-DimensionalSimulations Previousresearchhasshownthatdirectnumericalsimulationsmustbethree-dimensional tocapturethecompletephysicsofturbulentbottomboundarylayerow( Barretal. 2004; Blondeauxetal., 2004; Scanduraetal. 2000; ZedlerandStreet 2006).While thecomparisonsaboveareoftwo-dimensionalplanes,theyaredepictionsfroma three-dimensionalow,therefore,areappropriatetocompare.Recently,wecompared theequilibriumrippleheightsofequivalenttwo-andthree-dimensionalsimulations (Penkoetal., 2010b).Anestimateoftheresultingbedstressonthecrestoftheripplein thetwo-dimensionalsimulationwastwicethatofthethree-dimensionalsimulationdueto theinabilityoftheturbulentkineticenergytodissipateinthecross-owdirection.Even thoughthetwo-dimensionalsimulationsdonotincludeany3Dvorticity,wecanusethe 50

PAGE 51

information providedfromthecomparisonsoftwo-andthree-dimensionalsimulationsto gaininsightintotheeffectsofthree-dimensionalturbulence. Byanalyzingthesamethree-dimensionalsimulationcomparedhere,butin two-dimensions,wecanseefromthevelocityprolesthattheboundarylayerappears toextendtothetopofthedomain(Figure 3-14).Theowabovearippledbedwill bedominatedbycoherentvortexstructuresupto1.5timestherippleheightabove theripplecrests( vanderWerfetal., 2006),inthiscaselessthan 1.5cmabovethe tallestripplepeak.Abovethisheight,thecoherentvorticesdissipateandonlyrandom turbulenceexistsinthewatercolumn.Theincreasedenergyinthewatercolumninthe two-dimensionalcasecausesothersignicantdifferencesbetweenthetwosimulations. Oneeffectisthemigrationofthebedformsthroughoutthetimeseries(Figure 3-15). Thebedheightfromthethree-dimensionalsimulationistakenfromthex-zplane analyzedpreviously.Thethree-andtwo-dimensionalsimulatedripplesmigrateatslightly differentspeedsof1.8and1.2cm/min,respectively.Thethree-dimensionalsimulation isalsomoreuniformwitheachwave.Thepeaksandtroughsofthetwo-dimensional beductuateconsiderablyfromonewavetothenext.Perhapscounter-intuitively,the three-dimensionalturbulenceseemstoprovidestabilityandordertothebedprole evolution.Althoughsomestatisticsofthetwo-dimensionalsimulationcomparewellwith theobservations,othersshownon-physicaltendencies(e.g.,vorticitynearthetopofthe domainandsignicant w velocitiesthroughoutthewatercolumn). 3.4.4ModelDependenceonSedimentPhaseClosures SeveralclosuresareappliedinSedMix3Dtoparameterizetheuid-sediment andsediment-sedimentinteractionsincludingashearinduceddiffusionterm,abulk hinderedsettlingfunction,aneffectiveviscosityformulation,andaparticlepressure. Allarewellconstrainedbyexistingexperimentsandtheoryandwehavetestedthe sensitivityoftheseparameterizationstothemodeloutput.Chapters 4 and 5 describe theeffectiveviscosityandthebulkhinderedsettlingfunction,respectively.Wetested 51

PAGE 52

thesensitivityof themodeltothreedifferenteffectiveviscosityformulationsandthe intrinsicviscositywithintheequations.Increasingtheeffectiveviscosityspecicallyin thehigherconcentrationregion(0.3 << 0.63)willdecreasetheamountofsediment suspendedintothewatercolumn( Penkoetal., 2009).Theconcentrationdependent bulkhinderedsettlingvelocityfunctioninuencestheamountofsuspendedsediment inthewatercolumnandsedimentphaselageffects.Itisparameterizedusingawell knownempiricalfunctionformulatedbytakingmeasurementsofthesettlingspeedof concentratedparticlesinapipewithanitediameter( RichardsonandZaki, 1954 ). Modeloutputofthebulksettlingofconcentratedsedimentagreeswellwiththespecied hinderedsettlingformulation( Penkoetal., 2010a);however,theresultsaredependent onthedenitionoflocalsedimentconcentrationusedintheformulation.Recentdirect numericalsimulationsofsedimentsettlinginaninnitedomainshowadivergence fromthe RichardsonandZaki (1954 )empiricalformulation( Simeonovetal. 2010). Furtherresearchandexperimentswilllikelybenecessarybeforewecanimproveon thebulksettlingparameterization.Aparticlepressureisinducedduetotheenduring contactsofsedimentparticlesintheconcentratedbedregionandistypicallyassumed tobeapowerorexponentialfunctionofsedimentconcentration( Buyevich, 1999 ; Chen etal. 2003 ).TheparticlepressureterminSedMix3Dparameterizestheforcesdue totheenduringcontactofsedimentwhentheconcentrationexceeds30%byvolume byapplyinganexponentialdampingfunctiontothevelocitythatisdependentonthe concentration.Therigidityofthebedishighlydependentontheparticlepressureterm. Withouttheinclusionofaparticlepressure,thebediscompletelyuidizedandwill notsupportanysandripplegeometry.Thedampingfunctionshapeisdependenton acoefcientandtheconcentrationraisedtoapower.Thepowerisdeterminedfroma thresholdconcentrationabovewhichthepressureisapplied.Increasingthethreshold concentrationresultsinamorerelaxedbedanddecreasingthethresholdconcentration willcauseamorerigidbed.Increasingthecoefcientwillresultinastifferbed.The 52

PAGE 53

coefcientwas determinedbycomparingthesizeandshapesoftheripplespredictedby themodeltoobservations.Thediffusiontermactsasthepickupfunctioninthemodel andhasaneffectontheamountandspreadingofsedimentsuspendedinthewater column.Theempiricalequationfordiffusionhasbeenwelldocumented( Leightonand Acrivos, 1986 ),butwillbemorecloselytestedwhendirectobservationsofconcentration becomeavailable. 3.5Conclusions Overall,themodelshowsexcellentagreementwiththeobservations.Discrepancies maybeduetothefollowingreasons:1)theexperimentwasperformedinafree-surface ume;however,themodelhasarigidlidboundarycondition;2)lowercondence invelocityestimatesfromPIVmeasurementsnearthebedduetohighlaserlight reection;and3)thestatisticsoftheowpropertiescomparedherearedependent onthelocationoftheripplecrestsandtroughs;however,themigrationoftheripples differinthemodelcomparedtotheobservations.Despitetheslightdifferencesfromthe observations,themodelprovidesafairlyaccuraterepresentationofturbulentowover ripplesfortheconditionspresentedhere. Weusedthemodeltoexaminethedependenceofsedimentandowparameters inmixturetheorysimulationsofturbulentbottomboundarylayerow.Increasing theeffectiveviscosity,especiallyintheconcentratedregimes(0.3 << 0.63), decreasesthesuspendedsedimentconcentrationinthewatercolumn.Decreasing thebulkhinderedsettlingvelocityincreasesthesuspendedsedimentandsediment phaselageffects.Aparticlepressureisrequiredfortheapplicationofmixturetheory totheuid-sedimentsimulationspresentedhereduetothehighconcentrationsof theparticulatephase.Therigidityofthebedisdependentonthemagnitudeand concentrationthresholdoftheparticlepressure;however,itneedstobeonlyafunction oflocalsedimentconcentrationandsedimentpropertiestobeapplicabletomost sedimentandowregimessimulatingrippledynamics. 53

PAGE 54

Whiletwo-dimensional modelsaretypicallylesscomputationallyexpensive andgenerallyrequirelessstorageandprocessing,theymustcompensatefortheir decienciesinthephysicsbyintroducingnon-physicalterms.Ourthree-dimensional simulationsprovideanunprecedentedlevelofdetailaboutsandrippledynamicsthat exceedseldandlaboratorytechnologiesandcanbeusedtoexaminethecomplex, three-dimensionalityoftheturbulentbottomboundarylayerowoverrippledbeds. 54

PAGE 55

Figure3-1.V elocitytimeseriesusedtodrivethemodel.Threespin-upperiods(red) wereaddedtothebeginningofthefreestreamvelocitytimeseries measuredbytheADV(black).Positivevelocitiesareoffshore. 55

PAGE 56

Figure3-2.Initial modelbedprole.Thedomainis128 32 256gridpointsand10.6 cm 2.6cm 10.8cm.Theperturbationextendsthelengthofthedomain inthex-directionandoverthreegridpointsinthey-direction. 56

PAGE 57

Figure3-3.Ensemb le-averagedmodelandobservedvorticityelds, n (s )Tj /T1_3 7.97 Tf (1 ),atsix phaselocationsofawave.Flowisinitiallydirectedtotheleft(onshore). Positive(red)contoursindicatecounter-clockwiserotation.Atime-averageof themodeledandobservedbedproleisplottedforreference. 57

PAGE 58

Figure3-4.Ensemb le-averagedmodelandobservedswirlingstrength, ci (s )Tj /T1_4 7.97 Tf 6.59 0 Td (1 ),atsix phaselocationsofawave.Flowisinitiallydirectedtotheleft(onshore). Darkerareasindicatecoherentvortexstructures.Atime-averageofthe modeledandobservedbedproleisplottedforreference. 58

PAGE 59

Figure3-5.Modeled andobservedtime-averagedhorizontalvelocity( u ).Atime-average ofthemodeledandobservedbedproleisplottedforreference. Figure3-6.Modeled andobservedtime-averagedverticalvelocity( w ).Atime-average ofthemodeledandobservedbedproleisplottedforreference. 59

PAGE 60

Figure3-7.Standard deviation( u )ofthehorizontalvelocityfromthemodel(black)and theobservations(red)atsevenlocationsalongthebedprole.Ascale vectorislocatedinthelowerleftcorneroftheplot.Atime-averageofthe observedbedproleisplottedforreference. 60

PAGE 61

Figure3-8.Standard deviation( w )oftheverticalvelocityfromthemodel(black)and theobservations(red)atvelocationsalongthebedprole.Ascalevector islocatedinthelowerleftcorneroftheplot.Atime-averageoftheobserved bedproleisplottedforreference. 61

PAGE 62

Figure3-9.Hor izontalvelocityprolesaveragedoverthedomainlength(x)fromthe model(lines)andobservations(dots)atsevendifferentphaseangles.Top panelisaplotoftheensemble-averagedfreestreamvelocityanddenotes thephaselocationsofthevelocityprolesbycolor.Minimumandmaximum bedheightisapproximatelyz=2.5andz=3.5cm,respectively. 62

PAGE 63

Figure3-10.V erticalprolesofthetime-averagedhorizontalvelocity( u )atvaryingxlocationsfromthemodel(lines)and observations(dots).ThexlocationsarethesameasthoseplottedinFigures 3-7 and 3-8.Thetime-averaged bedattheplottedxlocationislledinbrown.63

PAGE 64

Figure3-11.A crossspectralanalysisshowsthehorizontalphasedifferencebetween theADV u andthemodeledandobserved u .Positivecontoursindicate wherethemodeledorobservedvelocitiesleadtheADVvelocity.A time-averageofthemodeledandobservedbedproleisplottedfor reference. 64

PAGE 65

Figure3-12.Ensemb le-averagedvelocityvectorsplottedwithcomparisonsofmodel concentrationandimageintensityatfourphaseangles.An ensemble-averageofthebedproleateachoftheanglesfromthemodel andobservationsisplottedforreference. 65

PAGE 66

Figure3-13.Modeled bedproles(black)andobservedbedproles(red) ensemble-averagedoverthefulltimeseriesat15 intervalsofphase. Phaseincreasesontheverticalaxisandprolesareoffsetby0.8cm.A verticalscalebarislocatedinthelowerrightcorneroftheplots. 66

PAGE 67

Figure3-14.Hor izontalvelocityprolesaveragedoverthedomainlengthfromthe three-dimensionalsimulation(solidlines)andthetwo-dimensional simulation(dashedlines)ateightdifferentphasesofawave.Maximumbed heightisatapproximately z = 3.5cm. 67

PAGE 68

Figure3-15.Contours ofbedheight(cm)fortheentiretimeseriesofthetwo-and three-dimensionalsimulations.Thebedheightinthethree-dimensional simulationistakenfromthex-zplanecomparedpreviously.Colorbar denotesbedelevation(cm). 68

PAGE 69

CHAPTER4 MIXTURETHEOR YMODELSENSITIVITYTOEFFECTIVEVISCOSITYIN SIMULATIONSOFSANDYBEDFORMDYNAMICS Thischapterwaspublishedinaslightlydifferentformwithco-authorsJ.Calantoni andD.N.SlinnintheProceedingsoftheMTS/IEEEOCEANS09Conference,Biloxi, MS. 4.1Introduction Thelocalpropertiesoftheseaoorsuchasbedformsizeandshape,grainsize distribution,andsedimenttypeallinuencebottomboundarylayerow,waveenergy dissipation,andsedimenterosionanddepositioninthecoastalregion.Pastresearch hasfocusedonpredictingtheturbulentowoverxedbedforms,ignoringtheresponse oftheowtoresultingsedimenttransportandchangesinbedmorphology( Barretal. 2004; ChangandScotti, 2006; Scanduraetal., 2000).Acompleteunderstandingof thefeedbackbetweentheuidandsedimentinaturbulentbottomboundarylayeris necessaryforaccuratepredictionofbedformprolechangesandmigrationrates. Weimplementathree-dimensionalbottomboundarylayermodel(SedMix3D)using mixturetheorytosimulatethecoupledinteractionbetweentheuidandsediment. SedMix3Dtreatstheuid-sedimentmixtureasasinglecontinuumwitheffective propertiesthatparameterizetheuid-sedimentandsediment-sedimentinteractions usingavariablemixtureviscosity,aconcentrationspecicsettlingvelocity,anda shear-induced,empiricallycalibrated,mixturediffusionterm.Whilemixturetheoryhas beenwellstudiedformanytypesofparticleladenows( HoferandPerktold 1997; Miskinetal. 1996a,b; NirandAcrivos, 1990; NottandBrady, 1994; Sunetal. 2009), andyieldsreasonablecomparisonswithlaboratoryexperiments,ithasnotyetbeen appliedtocoastalsedimenttransport. Theclosurefortheeffectiveviscosityofthemixtureisafunctiondependent onthelocalsedimentconcentration,thesedimentshape,themaximumviscosity, andthemaximumpackingconcentration.Thedocumentedrelationshipsforthe 69

PAGE 70

effective viscosityhavetwocommonfeatures.Indilutesuspensions,concentration andviscosityarelinearlyrelated( Einstein, 1906),andatacertainmaximumpacking concentration,theviscositybecomesinnite( Eilers, 1941).Studieshavefoundthat viscositiesmodeledbyconcentrationdependentequationscomparewellwithviscosity measurementsofsmallparticles( O (0.001cm))insuspension( deCindioetal., 1987; Ferrinietal. 1979; Huntetal., 2002; Krieger 1972; KriegerandDougherty 1959; LeightonandAcrivos, 1987b; Mooney, 1951; Sudduth, 1993)andlargeparticles (O (0.01cm))indenseconcentrations(upto0.70volumefraction)( HuangandBonn 2007; Vand 1948).WeuseaneffectiveviscosityformulationintheformofanEilers' equation( Eilers, 1941)andchoosethemaximumpackingconcentrationtobe0.63, roughlyequivalenttorandomclosepackingforidenticalspheres.Theintrinsicviscosity parameter, [],accountsfortheparticleshape(NawabandMason 1958)andhasbeen welldocumentedforsphericalparticlesas2.5( Einstein 1906).Forirregularlyshaped particles, [ ] isstilllargelyuncertain(Ferrinietal. 1979).Here,wetestedthesensitivity ofthesedimentphaseclosureforeffectiveviscositybyvaryingtheintrinsicviscosity andexaminingchangesinsuspendedsedimentconcentration.Additionally,wechose asingleintrinsicviscosityandcomparedsuspendedsedimentconcentrationsforthree differenteffectiveviscosityformulations. 4.2Methodology ThegoverningequationsforSedMix3Dincludeasedimentcontinuity,mixture continuity,andmixturemomentumequations.Thesedimentphaseclosuresincludea mixtureviscosityformulation,ashearinduceddiffusionterm,andahinderedsettling function.Themixturecontinuityequationisderivedbycombiningtheuidandsediment phasecontinuityequations, @ @ t + r ( u)=0, (4) 70

PAGE 71

where u isthemixture velocityand isthemixturedensity, = s +(1 )Tj /T1_2 11.955 Tf 11.95 0 Td () f (4) where isthesedimentvolumefraction,and s and f arethesedimentanduid densities,respectively. Themixturemomentumequationisalsoderivedfromthesumoftheindividual phasemomentumequations.Themixturestressescanbedenedbyassumingthe mixturebehavesasaNewtonianuid( Bagnold, 1954 )resultingin, @ u @ t + u ru = r P + r ( ru)+ F )Tj /T1_2 11.955 Tf 11.96 0 Td (g, (4) where P isthemixturepressure, isthemixtureviscosity, F istheexternaldrivingforce vectorperunitvolume,and g isgravitationalacceleration(981cms )Tj /T1_8 7.97 Tf 6.59 0 Td (2 ^ k ).SedMix3D employsamodiedEilersequation( Eilers, 1941 )torepresentmixtureviscosity, ,here scaledbythepurewaterviscosity, f f = 1+ 0.5[ ] 1 )Tj /T1_2 11.955 Tf 11.95 0 Td (= m 2 (4) where [] istheintr insicviscosity,adimensionlessparameterrepresentingthesediment grainshape,and0.0 0.63,wherethelowerboundrepresentspurewaterand upperboundroughlycorrespondstothemaximumconcentrationofunconsolidated sediment.Here,wexthemaximumvalueofthemixtureviscositybyspecifying m = 0.644.Theexternaldrivingforce, F,approximatesthehorizontalpressuregradient producedbythepassageofasurfacegravitywave.Hereweuseasimplesinusoidal forcinginthex-directionwithamplitude, U o andperiod, T (Figure 4-1), F = f U o 2 T cos 2 T t ^ i (4) 71

PAGE 72

Theconcentration ofsedimentismodeledwithasedimentcontinuityequation(Nir andAcrivos, 1990)thatdescribesthebalanceofsedimentuxbyadvection,gravity,and shear-induceddiffusion, @ @ t + u r = D r 2 )Tj /T1_1 11.955 Tf 13.15 8.09 Td (@ W t @ z (4) where W t istheconcentr ationspecicsettlingvelocity( RichardsonandZaki 1954), W t = W t 0 (1 )Tj /T1_1 11.955 Tf 11.96 0 Td ( ) q (4) where W t 0 isthesettlingvelocityofasingleparticleinaclearuidand q isanempirical constant, q = 8 > > > > < > > > > : 4.35Re )Tj /T1_6 7.97 Tf 6.59 0 Td (0.03 p 0.2 < Re p 1, 4.45Re )Tj /T1_6 7.97 Tf 6.59 0 Td (0.10 p 1 < Re p 500, 2.39 500 < Re p (4) Re p isdenedastheparticleReynoldsnumber, Re p = d f jW t 0 j f (4) where d isthesediment grainsizediameter(0.04cm).Weconsideronlynon-cohesive grainswiththematerialpropertiesofquartzinwater( s = 2.66g/cm 3 ).Theclosurefor theshear-induceddiffusionofsediment, D ,isafunctionofparticlesize,concentration, andmixturestresses( LeightonandAcrivos, 1986).Assumingisotropicdiffusion(i.e., D xx = D yy = D zz ), D = 1 4 d 2 f ( ) jruj, (4) 72

PAGE 73

where jruj q 1 2 (u : u T ) and f () isanempir icallydeterminedcoefcient, f ()= 2 1+ 1 2 e 8.8 (4) where isanempir icalconstantfoundtobeapproximately0.33forlargevalues oftheShieldsparameter(0.5 << 30)bycombiningresultsfromthedilutelimit withmeasurementsindenseconcentrationsuspensions.Itisnotedthattheabove formulationmayresultinanunderestimationofthediffusioncoefcient( Leightonand Acrivos, 1986 ). Themodelusesanitevolumemethodwithastaggeredgridtosolvethe time-dependentsedimentconcentrationfunctionandthemassandmomentum conservationequationsfortheuid-sedimentmixturetosecond-orderaccuracyin spaceandthird-orderaccuracyintime.Withgridspacingtypicallyaboutanorderof magnitudelessthanthesmallest(Kolmogorov)turbulentlengthscaleandtimesteps nearlyfourordersofmagnitudelessthanthesmallestturbulenttemporalscale,we considerSedMix3Dtobeadirectnumericalsimulation. 4.3Results 4.3.1IntrinsicViscosity Wetestedthemodelsensitivitytothechoiceofintrinsicviscosityin(Equation 4) byexaminingthesuspendedsedimentconcentrationoutputfromvesimulationswith identicalforcingbutwithvaryingintrinsicviscositiesrangingfrom2.5 [ ] 5.0, whichrepresentawiderangeofpossiblegrainshapes.Figure 4-2 isaplotofthescaled effectiveviscosityofthemixture(Equation 4 )versusvolumetricconcentration, ,for thevaryingintrinsicviscosities.Theintrinsicviscosityisafunctionoftheparticle'saxis ratio, r (particlelength:particlewidth)( NawabandMason 1958 ).Mixtureswithlong,at particleswillhavelargerintrinsicviscositiesthanmixtureswithsphere-likeparticles.The intrinsicviscosityofauid-sedimentmixturewithsphericalsandparticles( r =1)has beendocumentedas2.5( Einstein 1906).Weuse2.5asabasevalueandcompare 73

PAGE 74

simulationswith intrinsicviscositiesof3.0,3.5,4.0,and5.0.Anintrinsicviscosityof5.0 correspondstoaparticleaxisratioofapproximately5:1. Thesimulatedowhasamaximumfreestreamvelocityof40cm/sanda2speriod (Figure 4-1).Thesedimentsizewasxedat0.04cm.Weinitializedthesimulations withasinusoidalrippleofheight1cmandlength12cm.Thesimulationsranfor5 waveperiods(10s).Althoughthemodelisfullythree-dimensional,thesimulationsran herecontainedonlytwogridpointsinthey-directiontoreducethecomputationaltime necessarytoobtain10sofreal-timeoutput.SeetheDiscussionforanexplanation ofmodelgridresolution.Wesummedtheconcentrationeldsinthey-directionand ensembleaveragedoverthelastthreewaveperiods,allowing2waveperiodsofmodel spin-up,toobtainconcentrationeldsinthex-andz-domainthroughoutafullow phase.Here,wequalitativelycomparedtheensembleaveragedconcentrationelds atowreversal( =0 ),maximumowacceleration( = 45 ),andmaximumow deceleration( =135 )forallvesimulations(Figures 4-3, 4-4,and 4-5).Forthethree phasesoftheowshown,thesuspendedsedimentplumeswereinsimilarlocations alongtherippleproleandatsimilarheightsinthewatercolumninallthesimulations. InFigure 4-3,thefreestreamvelocityiszeroandtheowisreversingfromlefttoright. Astheowchangeddirection,sedimentwaspickedupfromtheleftsideoftheripple andadvectedintothewatercolumn.Forthesimulationswithintrinsicviscositiesof4.0 and5.0(hereinreferredtoashigherintrinsicviscositysimulations),muchlesssediment wassuspendedcomparedtothesimulationswithintrinsicviscosityvaluesof2.5to3.5 (hereinreferredtoaslowerintrinsicviscositysimulations),butwasinsimilarlocations alongtherippleproleandatsimilarheightsinthewatercolumn.Atmaximumow acceleration(Figure 4-4),thesuspendedsedimentspreadthroughoutthedomainbut concentratedoverthepeakoftheripple.Again,thelowerintrinsicviscositysimulations hadgreateramountsofsuspendedsedimentinthewatercolumnthanthehigher intrinsicviscositysimulations.Theturbulentvorticesgeneratedinthebeginningofthe 74

PAGE 75

phaseadvected totherightsideoftherippleandbegantosettleoutatmaximumow deceleration(Figure 4-5)forthelowerintrinsicviscositysimulations.Astheintrinsic viscosityincreasedfrom2.5to3.5,theturbulentvorticesstretchedhorizontallyandone canobserveaslightphaselagbetweenthevortexcenters.Almostallthesuspended sedimenthadsettledinthehigherviscositysimulations. Aquantitativeanalysisoftheamountofsuspendedsedimentinthewatercolumn conrmedthequalitativecomparisoninFigures 4-3, 4-4,and 4-5.Atimeseriesofthe sumofthetotalsuspendedsedimentinthewatercolumnshowsapproximatelya16% differencebetweenthelowerintrinsicviscosityandhigherintrinsicviscositysimulations (Figure 4-6).Theamountofsuspendedsedimentinthewatercolumnalsovaried morewiththephaseinthelowerintrinsicviscositythanthehigherintrinsicviscosity simulations.Wealsoexaminedthetimeseriesofsuspendedsedimentconcentration overthecrestoftheripple(x=6cm)ensembleaveragedoverthelast3periodsfor allvesimulations(Figure 4-7).Sedimentplumesovertheripplecrestoccurredat approximatelythesamephaseoftheowandheightinthewatercolumnforthelower intrinsicviscosityvalues.However,thelargedifferenceintheamountofsuspended sedimentovertheripplecrestbetweenthelowerintrinsicviscosityandthehigher viscositysimulationsremainedevident. 4.3.2EffectiveViscosityFormulations Numerouseffectiveviscosityequationsareavailableforthesedimentphase viscosityclosureinmixturetheory.WeuseamodiedversionofEilers'equation (Eilers, 1941 )inSedMix3Dbecauseitiswelldocumentedassuccessfullynumerically modelingtheviscosityofsuspensionows.Theequationisadvantageousforcoastal sedimenttransportbyallowingtheparticleshapetovarywiththeintrinsicviscosity parameter.Here,weexaminedthesensitivityofsuspendedsedimentconcentrations predictedbythemodelbyreplacingEquation 4 withtwoadditionalcommoneffective 75

PAGE 76

viscosityequations. Thersteffectiveviscosityequationwillbereferredtohereasthe Krieger-Doughertyequationandisgivenas, f = 1 )Tj /T1_1 11.955 Tf 16.92 8.09 Td ( m )Tj /T1_7 7.97 Tf ( m [ ] (4) Thesecondeff ectiveviscosityequationwillbereferredtohereastheMooneyequation andisgivenas, f =exp [ ] 1 )Tj /T1_1 11.955 Tf 11.96 0 Td (= m (4) Notethatboth Equation 4 and 4 containthesameintrinsicviscosity,maximum packingconcentration,andapproximatelyequalmaximumviscositiesasouroriginal effectiveviscosityformulation(Equation 4).The m parameterfortheMooney equationwastakentobe0.82tokeepthemaximumviscosityconsistentbetween thesimulations.Ourbaselinesimulationhereisthesimulationdescribedabove using(Equation 4)withtheintrinsicviscosity, []= 3.0.BothEquation 4 and 4 wereinsertedintothemodelwithanintrinsicviscosity, [ ]= 3.0,andallother parametersincludingwaveforcingconditionsconstrainedasdescribedaboveandinthe Methodology.Wecomparedthemodeloutputforthethreedifferenteffectiveviscosity formulations.Figure 4-8 isaplotofthescaledeffectiveviscosityversusvolumefraction ofsediment, ,forthethreeeffectiveviscosityformulations.Allthreeequationsresult insimilareffectiveviscositiesfor0 << 0.4.TheMooneyequation(Equation 4) producesthehighestviscosityofthethreeequationsfor > 0.4(Figure 4-8). Theconcentrationeldsatowreversal( = 0 ),andatmaximumowacceleration ( = 45 and = 225 )forthethreeeffectiveviscosityequationsimulationsensemble averagedoverthreewaveperiodsareplottedinFigures 4-9, 4-10 ,and 4-11.A qualitativecomparisonofthesimulationsshowedmuchlesssuspendedsediment abovetherippleintheMooneysimulationthantheEilersandKrieger-Dougherty simulations.Atowreversal(Figure 4-9),theturbulentvorticieswereclearlydened 76

PAGE 77

andwere atsimilarlocationsalongtherippleandheightsinthewatercolumninthe EilersandKrieger-Doughertysimulations.TherewerenodenedvorticesintheMooney simulation.Atmaximumowacceleration(Figures 4-10 and 4-11),therewasagain muchmoresuspendedsedimentintheEilersandKrieger-Doughertysimulations thantheMooneysimulation.Thesuspendedsedimentplumelocationsalongthe rippleproleandheightsinthewatercolumnwerealmostidenticalintheEilersand Krieger-Doughertysimulations. Figure 4-12 isaplotofthequantitativeanalysisofthesuspendedsedimentabove therippleforthethreesimulations.Thereexistsabouta14%differencebetweenthe averageamountoftotalsuspendedsedimentintheKrieger-DoughertyandMooney simulations,butonlyabouta5%differencebetweentheKrieger-DoughertyandEilers simulations.Thephaseofmaximumsuspendedsedimentisnotconsistentbetweenthe simulations;however,thesuspendedsedimentfromtheEilersandKrieger-Dougherty simulationsvarieswithinagreaterrangethroughouttheowphasethanintheMooney simulation. Theamountofsuspendedsedimentabovetheripplecrest(x=6cm)throughouta waveperiodisplottedinFigure 4-13.Theamountandheightofthesedimentwasfairly consistentbetweentheEilersandKrieger-Doughertysimulations.Theonlyphaseat whichtherewasasignicantamountofsuspendedsedimentabovetheripplecrestin theMooneysimulationwaswhentheowwasacceleratingfrom0to40cm/s. 4.4Discussion 4.4.1IntrinsicViscosity Atowreversal,turbulenteddiesshedofftheleftsideoftheripple,pickingup sedimentintothewatercolumn.InallveofthesimulationsemployingtheEilers Equation 4 at0 phase,thesedimentispickedupontheleftsideoftherippleand advectedbytheturbulenteddies(Figure 4-3).However,forthethreelowerintrinsic viscositysimulations,thesuspendedsedimentconcentrationsaremuchgreaterthan 77

PAGE 78

thehigherintr insicviscositysimulations.Increasingtheeffectiveviscosityofthemixture causesadampeningofturbulenteddiesandtherefore,lesssuspendedsediment.The decreasedamountofturbulenteddiesinthehigherviscositysimulationsisevidentatall threephasesshown(Figures 4-3 and 4-5).Atmaximumowacceleration(Figure 4-4), turbulenteddieshavebrokenupandspreadthesuspendedsedimentacrosstheripple prole.Thesuspendedsedimentisagaininsimilarlocations(overtheentirecrestof theripple)andatsimilarheightsinallthesimulations.Increasingtheintrinsicviscosity alsoaffectsthehorizontalstretchingoftheturbulenteddies.Atmaximumdeceleration, (Figure 4-5),thewidthoftheeddiesincreaseas [ ] increasesfrom2.5to3.5;however, theheightoftheeddiesstaysfairlyconstant. Aquantitativeanalysisofthetotalsuspendedsedimentinthewatercolumnreveals thatthelowerintrinsicviscositysimulationshaveonaverageabout16%moresediment suspendedthanthehigherintrinsicviscositysimulations.Theviscosityofthemixture increasesastheintrinsicviscosityvalueincreases,andthesedimentwilladvectless forlargerintrinsicviscosities.Onlyan11%differenceinaveragesuspendedsediment existsbetweenthelowerintrinsicviscositysimulations.Themostsignicantdifference intheeffectiveviscosityoccursatconcentrationsgreaterthan0.4volumefraction (Figure 4-2).Inarippledbedenvironment,concentrationsrangefrom0.4to0.6atthe ripple-uidinterface,wherethedifferencesbetweentheeffectiveviscositiesarelarge. However,mostofthesuspendedsedimentoccursbetween0.0 << 0.3,wherethe differenceineffectiveviscosityisnotasprominent.Therefore,oncethesedimentgets pickedupintothewatercolumn,thedifferenceintheeffectiveviscosityhaslessofan impactontheoutput.However,itisunknownwhythereisa16%differencebetween lowerintrinsicviscosityandthehigherintrinsicviscositysimulations,butonlyabouta 10%differencebetweenthetotalsuspendedsedimentconcentrationwithinthetwo groups.Intrinsicviscosityvaluesinthehigherrange(4 < [ ] < 5)correspondto asedimentaxisratioofabout5,whichissignicantlylargerthanthetypicalvalues 78

PAGE 79

ofquartz sand(1-3).Therangebetweenthemaximumandminimumamountof suspendedsedimentisalsogreaterinthelowerviscositysimulationsthanthehigher viscositysimulations.Theamountofsedimentinsuspensionvarieswiththeowphase inthelowerintrinsicviscositysimulations,whichisconsistentwithlaboratoryandeld observations.Weuseanintrinsicviscosityvalueof3.0forthenumericalsimulations ofsedimenttransportbecauseitproducedthemedianamountofsuspendedsediment withinthevesimulations.Simulationsusingthe3.0valuepredictedsmall-scale bedformheightsandlengthsthatareingoodagreementwithcommonripplepredictor methodsandshapessimilartothosefoundinthelaboratoryandeld( Penkoetal., 2010b).Simulatedconcentrationelds,specicallythelocationandphasingofsediment plumes,werefoundqualitativelyconsistentwithlaboratorymeasurements. 4.4.2EffectiveViscosityFormulations Bychoosingthreedifferentcommoneffectiveviscosityformulations,wetested thesensitivityofSedMix3Dtothesedimentphaseeffectiveviscosityclosure.Of thethreeeffectiveviscosityformulationswetested,thewidelyacceptedEilers andKrieger-Doughertyequationshadverysimilaroutput.However,theMooney equationgeneratedmuchlesssuspendedsedimentinthewatercolumnthantheother twoformulations.TheKrieger-Doughertyequationproducedthemostsuspended sedimentonaverage,about14%morethantheMooneyequationandabout5%more thantheEilersequation(Figure 4-12).Thesuspendedsedimentpredictedinthe Krieger-DoughertyandEilerssimulationsalsovariesmorewiththeowphasethan thesuspendedsedimentintheMooneysimulation,whichsuggeststhatdecreasingthe effectiveviscositywillincreasetheresponseofthesedimenttotheow. Theeffectiveviscositiesproducedfromtheformulationsincreasinglydifferas > 0.4(Figure 4-8),whichisapproximatelytheconcentrationoftheregionattheinterface betweentherippleanduid.Inthisregion,thesedimentgrainsarerollingandsliding overthepackedbed,arepickedup,andareadvectedintothewatercolumn.Asthe 79

PAGE 80

effective viscosityincreasesinthisregion,lessgrainswillbepickedupbytheow, decreasingtheamountofsuspendedsediment.Themodelseemstobesensitiveto differencesineffectiveviscosityatconcentrationsbetweenabout0.4and0.6volume fraction.Astheintrinsicviscositysimulationsshowed,oncethesedimentisadvected intothewatercolumn,thedifferenceintheeffectiveviscositydoesnotsignicantlyaffect theconcentrationeldoutputfromthesimulations. 4.4.3ModelLimitations Mixturetheorysubsumesthephysicsofuid-sedimentinteractionsinthebottom boundarylayertonumericallymodelcoastalsedimenttransport.However,dueto thehighresolutionofthegrid,themodelisverycomputationallyexpensive(about 75daysofCPUtimefora10sthree-dimensionalsimulation).Here,thesimulations arequasi-three-dimensionaltoapproximatethemodel'sthree-dimensionalbehaviorina morereasonableamountoftime(aboutoneweekpersimulation).Aquasi-three-dimensional simulationhasfulldimensionsinthex-andz-directions,buthasonlytwogridpointsin they-direction.Theconcentrationisthensummedoverthetwogridpointsinthe y-directiontoobtainaconcentrationeldinthex-andz-domain.Thereductionofgrid pointsultimatelyreducesthecomputationaltimebyafactorofabout10;however,we foundasignicantdifferencebetweentheeffectsofthree-dimensionalvortexstructures andtwo-dimensionalstructuresontheturbulentowandsedimenttransport.Parallel algorithmsarebeingdevelopedtoallowforthree-dimensionalsimulationdomainsto approachlaboratoryscales. 4.5Conclusions Althoughmixturetheoryhasbeenwelldocumentedasaneffectiveapproachto numericallymodelsuspensionows,ithasnotyetbeenappliedtostudysediment transportoverrippledsandbeds.Here,wetestedthemodelsensitivitytotheeffective viscositybyvaryinganadjustableparameterwithintheeffectiveviscosityformulation inSedMix3D.Byvaryingtheintrinsicviscosityvaluebetween2.5and5.0,wefound 80

PAGE 81

thelow ervalues( [ ]= 2.5,3.0,and3.5)generateonaverageabout16%more suspendedsedimentinthewatercolumnthanthehigherintrinsicviscosityvalues ([]= 4.0and5.0).However,withinthetwogroups,thetotalsuspendedsedimentinthe watercolumnvariedbyapproximately10%.Thelocationsofthesedimentplumeswere similarwithinthetwogroupsofsimulations;however,thesuspendedsedimentplume concentrationsinthehigherintrinsicviscositysimulationswerelessthanthelower intrinsicviscositysimulations.Therefore,choosinganintrinsicviscosityvaluewithinthe rangeof2.5.5whenemployingEilers'equationwillnotsignicantlyaffectthemodel outputforthepresentedsimulationconditions. Additionally,wetestedthemodelsensitivitytotwoothereffectiveviscosity formulationswhilekeepingtheintrinsicviscosityandforcingconditionsconstant.There isaslightdifferenceinthemodeloutputbetweentheEilersandKrieger-Dougherty effectiveviscosityformulations;however,alargedifferenceexistsbetweenthe outputfromtheMooneyeffectiveviscosityequationandtheothertwoequations. Thedifferencesuggestsahighermodelsensitivitytovariationsintheeffective viscositywithintheripple-uidinterface(0.3 << 0.6)thanthesuspendedsediment concentrationrange(0.0 << 0.3).Thevariationsinthetotalsuspendedsedimentwith theowphaseineachsimulationsuggeststhatthesuspendedsediment'sresponse totheowincreaseswithdecreasingeffectiveviscosity.Comparisonsofconcentration eldstolaboratorydatashouldprovideinsighttothemostaccurateeffectiveviscosity equationandintrinsicviscosityvalueforspecicsedimentsizesanddistributions; however,usingeitherEilers'orKrieger-Dougherty'sequationwithanintrinsicviscosity, []= 3.0,didnotsignicantlyaffectthesimulationpredictionsofsuspendedsediment concentrationfortherangeofconditionstestedhere. 81

PAGE 82

Figure4-1.The freestreamvelocitytimeseriesforawaveperiod. Figure4-2.The scaledeffectiveviscosity(Equation 4)resultingfromvaryingintrinsic viscosities, [],versusvolumefractionofsediment, 82

PAGE 83

Figure4-3.Suspended sedimentconcentrationeldsensembleaveragedoverthree waveperiodsatowreversal( = 0 )forvaryingintrinsicviscosities. 83

PAGE 84

Figure4-4.Suspended sedimentconcentrationeldsensembleaveragedoverthree waveperiodsatmaximumowacceleration( = 45 )forvaryingintrinsic viscosities. 84

PAGE 85

Figure4-5.Suspended sedimentconcentrationeldsensembleaveragedoverthree waveperiodsatmaximumowdeceleration( = 135 )forvaryingintrinsic viscosities. 85

PAGE 86

Figure4-6.Time seriesoftotalsuspendedsedimentabovetherippleprole(< 0.58) ensembleaveragedoverthreewaveperiods.Solidgraylinesrepresentthe phaseaveragedtotalsuspendedsedimentamountforthelowerintrinsic viscosityandhigherintrinsicviscositysimulations,respectively. 86

PAGE 87

Figure4-7.Time seriesofthesuspendedsedimentconcentrationsoverthecrestofthe rippleensembleaveragedoverthreewaveperiods. 87

PAGE 88

Figure4-8.Three scaledeffectiveviscosityformulations, = f versusvolumefractionof sediment, 88

PAGE 89

Figure4-9.Suspended sedimentconcentrationeldsensembleaveragedoverthree waveperiodsatowreversal( = 0 )forvaryingeffectiveviscosity equations. 89

PAGE 90

Figure4-10.Suspended sedimentconcentrationeldsensembleaveragedoverthree waveperiodsatmaximumowacceleration( = 45 )forvaryingeffective viscosityequations. 90

PAGE 91

Figure4-11.Suspended sedimentconcentrationeldsensembleaveragedoverthree waveperiodsatmaximumowdeceleration( = 225 )forvaryingintrinsic viscosities. 91

PAGE 92

Figure4-12.Time seriesoftotalsuspendedsedimentabovetherippleprole(< 0.58) ensembleaveragedoverthreewaveperiods.Solidgraylinesrepresentthe phaseaveragedtotalsuspendedsedimentamountforthe Krieger-Dougherty,Eilers,andMooneyformulationsimulations, respectively. 92

PAGE 93

Figure4-13.Time seriesofthesuspendedsedimentovertheripplecrestensemble averagedoverthreewaveperiods. 93

PAGE 94

CHAPTER5 CONTROLLED SIMULATIONSCOMPARINGEMPIRICALSUBMODELSINSEDMIX3D Thischapterwaspublishedinaslightlydifferentformwithco-authorsJ.Calantoni andD.N.SlinnintheProceedingsofthe7thInternationalConferenceonMultiphase Flow,Tampa,FL. 5.1Introduction Sedimentationratesdirectlyaffectsuspendedloadtransportandconsequentlyhave astronginuenceonerosion,deposition,andbedmorphologyinthecoastalregion. Netsedimenttransportratesaredependentonthesedimentsettlingvelocity,especially negrainsands,whenphaselagsbetweensedimentconcentrationsandnear-bed oscillatoryvelocitiesarecommon( Dohmen-Janssenetal. 2002).Therefore,arobust andaccuratespecicationofthesedimentationrateinnumericalmodelsofsediment transportisnecessarytosimulatebedformprolechangesandmigrationrates. Weimplementathree-dimensionalbottomboundarylayermodel(SedMix3D)using mixturetheorytosimulatethecoupledinteractionbetweentheuidandsediment. SedMix3Dtreatstheuid-sedimentmixtureasasinglecontinuumwitheffective propertiesthatparameterizetheuid-sedimentandsediment-sedimentinteractions usingavariablemixtureviscosity,ahinderedsettlingvelocity,aparticlepressure,and ashear-induced,empiricallycalibrated,mixturediffusionterm.Whilemixturetheory hasbeenwellstudiedformanytypesofparticleladenows( HoferandPerktold, 1997; Miskinetal. 1996a,b; NirandAcrivos, 1990; NottandBrady, 1994; Sunetal., 2009),andyieldsreasonablecomparisonswithlaboratoryexperiments,ithasnot yetbeenappliedtocoastalsedimenttransport.Themodelframeworkdescribing thesedimentuxincludestheeffectsofadvection,diffusion,andsettling.SedMix3D parameterizesthehinderedsettlingofsedimentsinthesedimentuxequationwith aclassicbulksettlingformulation( RichardsonandZaki, 1954 ). RichardsonandZaki (1954)performedlaboratoryexperimentsinapipetomeasurethebulksettlingrate 94

PAGE 95

asafunction oflocalsedimentconcentration.Weinvestigatethedelityofthemodel tothespeciedhinderedsettlingformulationthroughasetofcontrolledsimulations withidealizedsettlingconditionsthatalsoincludeaffectsfromadvectionanddiffusion. Wecomparedthebulksettlingratesofplanesofsedimentsettlingthroughastillwater columnsimulatedbySedMix3Dtotheempiricalresultsof RichardsonandZaki (1954). Ingeneral,themodelreproducesthehinderedsettlingformula;however,thedegreeto whichthesettlingratepredictedbythemodelagreedwiththehinderedsettlingformula wasstronglydependentonthedenitionofthelocalsedimentconcentration. Wealsotestthesensitivityofthemodeltotheparticlepressureparameterization.A particlepressureisincludedtomodeltheenduringcontactsofsedimentparticlesinthe concentratedbedregion.Themodelwastestedusingsimulationstoestimatetheangle ofreposeundernoowconditions.Theangleofrepose, r ,istheslopeangleatwhich thesedimentrelaxesafteravalanching.Simulationsestimatingtheangleofrepose exhibitedalowsensitivitytochangesintheparticlepressurefunctionwithresulting relaxationanglesdifferingbylessthan5%. 5.2Methodology ThemodelingframeworkofSedMix3Dincludesgoverningequationsforsediment ux,mixturecontinuity,andmixturemomentum.Themixturecontinuityequationwas derivedbycombiningtheuidandsedimentphasecontinuityequations, @ @ t + r ( u)=0, (5) where u isthemixturevelocityand isthemixturedensity, = s +(1 )Tj /T1_1 11.955 Tf 11.95 0 Td () f (5) where isthesedimentvolumetricconcentration,and s and f arethesedimentand uiddensities,respectively. 95

PAGE 96

Themixturemomentum equationwasderivedfromthesumoftheindividualphase momentumequations.Themixturestressescanbedenedbyassumingthemixture behavesasaNewtonianuid( Bagnold 1954)resultingin, @ u @ t + u ru = r P + r ( ru)+ F )Tj /T1_1 11.955 Tf 11.96 0 Td (g, (5) where P isthemixturepressure, istheeffectiveviscosity, F istheexternaldriving forcevectorperunitvolume,and g isgravitationalacceleration( 981cms )Tj /T1_7 7.97 Tf 6.59 0 Td (2 ^ k ). SedMix3DemploysamodiedEilersequation( Eilers, 1941 )torepresenteffective viscosity, ,herescaledbythepurewaterviscosity, f f = 1+ 0.5[ ] 1 )Tj /T1_1 11.955 Tf 11.95 0 Td (= m 2 (5) where [] istheintr insicviscosity,adimensionlessparameterrepresentingthesediment grainshape,and0.0 0.63,wherethelowerboundrepresentspurewaterand upperboundroughlycorrespondstothemaximumconcentrationofunconsolidated sediment.Here,wexthemaximumvalueoftheeffectiveviscositybyspecifying m = 0.644.Wechosethemaximumpackingconcentrationtobe = 0.63,roughly equivalenttorandomclosepackingforidenticalspheres.Theintrinsicviscosity parameter, [],accountsfortheparticleshape(NawabandMason 1958)andhas beenwelldocumentedforsphericalparticlesas2.5( Einstein, 1906 ).Forirregularly shapedparticles, [] isstilllargelyuncertain(Ferrinietal., 1979).Hereweusean intrinsicviscosityvalueof3.0inthemodiedEilersequation.Previousworkhasshown thatanintrinsicviscosityvaluewithintherangeof2.5.5whenemployingEilers' equationwillnotsignicantlyaffecttheSedMix3Doutput( Penkoetal., 2009).Studies havefoundthatviscositiesmodeledbyconcentrationdependentequationscomparewell withviscositymeasurementsofsmallparticles( O (0.001cm))insuspension(deCindio etal. 1987 ; Ferrinietal. 1979; Huntetal., 2002; Krieger 1972; KriegerandDougherty 1959; LeightonandAcrivos 1987b; Mooney, 1951; Sudduth, 1993 )andlargeparticles 96

PAGE 97

(O (0.01cm))in denseconcentrations(upto0.70volumetricconcentration)(Huangand Bonn, 2007; Vand 1948).Figure 5-1 comparescommoneffectiveviscosityequations. Theconcentrationofsedimentismodeledwithasedimentuxequation(Nirand Acrivos, 1990 )thatbalancesthetemporalgradientsinsedimentconcentrationwith advection,gravity,andshear-induceddiffusion, @ @ t + u r = D r 2 )Tj /T1_2 11.955 Tf 13.15 8.09 Td (@ W t @ z (5) where W t istheconcentr ationspecicsettlingvelocity( RichardsonandZaki 1954), W t = W t 0 (1 )Tj /T1_2 11.955 Tf 11.96 0 Td ( ) q (5) where W t 0 isthesettlingvelocityofasingleparticleinaclearuidand q isanempirical constant, q = 8 > > > > < > > > > : 4.35Re )Tj /T1_6 7.97 Tf 6.59 0 Td (0.03 p 0.2 < Re p 1, 4.45Re )Tj /T1_6 7.97 Tf 6.59 0 Td (0.10 p 1 < Re p 500, 2.39 500 < Re p (5) Re p isdenedastheparticleReynoldsnumber, Re p = d f jW t 0 j f (5) where d isthesediment grainsizediameter.Weconsideronlynon-cohesivegrains withthematerialpropertiesofquartzinwater( s = 2.66g/cm 3 ).Theshear-induced diffusionofsediment, D ,isafunctionofgrainsize,volumetricconcentration,and mixturestresses( LeightonandAcrivos 1986).Assumingisotropicdiffusion(i.e., D xx = D yy = D zz ), D = 1 4 d 2 f ( ) jruj, (5) 97

PAGE 98

where jruj q 1 2 (u : u T ) and f () is, f ( )= 2 1+ 1 2 e 8.8 (5) where isanempir icalconstantfoundtobeapproximately0.33forlargevaluesof theShieldsparameter(0.5 << 30)bycombiningresultsfromthedilutelimitwith measurementsindenseconcentrationsuspensions. Indilutemixtures,theratioofcontactareasofthesedimenttothetotalareais smallandthecontactstressesmaybeneglected.Themixturestressisapproximately equaltothesurroundinguidstressintheseareas.However,inmixtureswithhigh volumetricconcentrationsofsediment(e.g.,inthepackedbedofasandripple),the contactstressesaresignicantandmustbeincluded( Batchelor, 1988 ; Drew, 1983). Therefore,aparticlepressureisnecessaryforamixturetheorymodeltobuildand maintainbedforms.Followingtheworks Chenetal. (2003 )and Buyevich (1999),we assumetheparameterizationofparticlepressuretobeanexponentialfunctionof sedimentconcentration.Theparticlepressureisappliedinthemodelasavelocity dampingfunction, S b (),tostabilizethebed, S b ()= r 8 (5) where r is0.2.Themixturevelocity, u ,isdecreasedanamountdeterminedbythe bedstiffnessfunction, S b ( ) .Theeighthpowerfunctionwaschosenbecauseof itsdivergencefromzerowhenthevolumetricconcentrationofsedimentis 0.30 (Figure 5-2),whichroughlycorrespondstotheonsetoftheenduringcontactregion (FredseandDeigaard, 1992).Thebedstiffnessfactor, r ,determinestheamountof particlepressureapplied.Here,wetestedthesensitivityofthemodeltochangesin r (Figure 5-2).Weranvetwo-dimensionalsimulationswithvaryingvaluesof r inthebed stiffnessfunction(Figure 5-2).Eachsimulationwasinitializedwithatriangularripple withsidesata40 angletothehorizontal.Thesimulationsthenranwithnoexternal 98

PAGE 99

forcing(i.e .,gravityonly)andtheripplessettledtoarelaxationangle(i.e.,angleof repose). 5.3Results Weexaminedthesettlingrateofaplaneofhighlyconcentratedsedimentina stillwatercolumnusingthree-dimensionalsimulationsfortwograinsizes( d = 0.2 cmand d = 0.04cm).Theonlyexternalforcinginthesimulationswasgravity.Figure 5-3 plotstheconcentration( )contours(averagedinthey-direction)forthe d = 0.2cmsimulation.Thefullthree-dimensionaldomainwas5cmx5cmx60cm. Initiallytheplaneofsedimentwasablockwithauniformconcentrationof0.567,but quicklydiffusedoutasitsettledthroughthewatercolumn.Figure 5-4 plotsthexandy-averagedconcentrationthoughthewatercolumnasafunctionoftime.The dashedblacklinesdenotetheboundariesoftheconcentrationplane(thepointatwhich theconcentrationgoestozero)andthesolidblacklinedenotesthelocationofthe centroidoftheconcentrationplane.Wecalculatedthesettlingrateofthesediment planebytakingthetimederivativeofthepositionofthecentroid.Thetimeseriesofthe concentrationofthesedimentplane(Figure 5-5a)wascalculatedusingtwodifferent methods.Firstbyhorizontallyaveragingtheconcentrationatthelocationofthecentroid, andalsobyhorizontallyandverticallyaveragingtheconcentrationbetweenthedashed linesinFigure 5-4.Figure 5-5aplotstheconcentrationcalculatedusingthetwomethods asafunctionoftime.Thebluelinerepresentstheconcentrationhorizontallyaveraged atthelocationofthecentroidoftheplane(thesolidblacklineinFigure 5-4).Thegreen linerepresentstheconcentrationhorizontallyandverticallyaveragedovertheentire planeofsediment(betweenthedashedlinesinFigure 5-4).Figure 5-5bcomparesof thesettlingrateofthecentroidoftheplanetotheempiricalformulaforhinderedsettling usedinthemodel( RichardsonandZaki, 1954).ThebluelineisEquation 5 calculated withtheconcentrationhorizontallyaveragedatthecentroid.ThegreenlineisEquation 5 calculatedwiththeconcentrationhorizontallyandverticallyaveragedovertheentire 99

PAGE 100

planeofsediment. Theplotillustratesthedependenceoftheempiricalformulationon thedenitionoflocalsedimentconcentration.Figures 5-6, 5-7,and 5-8 areanalogousto Figures 5-3, 5-4,and 5-5,respectively,with d = 0.04cm.Thedomainforthe d = 0.04 cmsimulationwas6cmx6cmx12cm.Theresultsalsoshowadependenceonthe denitionoflocalsedimentconcentration. Wealsoanalyzedtheangleofreposeresultingfromvaryingtheamountof particlepressureappliedinthemodel.Theanglesofreposeachievedineachof thevesimulationsareplottedinFigure 5-9.Theresultinganglesofreposeinthe two-dimensionalsimulationsdifferbylessthan5%. 5.4Discussion 5.4.1BulkHinderedSettling 5.4.1.1Dependenceonlocalsedimentconcentration Ourresultsdemonstratetheinherentambiguityoftheclassicbulksettling formulation( RichardsonandZaki, 1954)inthatthepredictionofthebulksettlingrateis stronglydependentonthedenitionoflocalsedimentconcentration(Figures 5-5band 5-8b).Therewasapproximatelya22%differenceinthesettlingratescalculatedfrom theempiricalformula( RichardsonandZaki, 1954)usingthetwodifferentdenitions ofconcentrationchoseninthesimulationresults.Calculatingthelocalsediment concentrationusingaplaneaverageratherthanacentroidaveragedecreasedthe valueofthelocalconcentration,therefore,increasingtheempiricallycalculatedsettling rate(Equation 5).ThesettlingrateofthecentroidfromSedMix3D(blacklinein Figures 5-5band 5-8b)isinbetteragreementwiththequantitativevalueofthehindered settlingrate(Equation 5)calculatedfromtheplaneaveragedconcentration(green lineinFigures 5-5band 5-8b)forbothsimulations;however,theslopeofthesettlingrate fromSedMix3Dmatchesbetterwiththeslopeofthehinderedsettlingratecalculated fromtheconcentrationatthecentroidinbothsimulations. 100

PAGE 101

5.4.1.2Dependenceon grainsize Theconcentrationsasfunctionsoftimeinthetwosimulationsdifferminimally, however,thetime-averageddifferencebetweenthetwosettlingratesisapproximately threetimeslargerinthe d = 0.2cmsimulationthaninthe d = 0.04simulation.This resultcouldbebecausetheaveragesettlingrateisalsothreetimeslargerinthe d = 0.2 cmsimulationthaninthe d = 0.04cmsimulation.Thesedimentplanealsodiffusesout slightlydifferentlyinthetwosimulations.Theheightofthesedimentplaneinthe d = 0.2 simulationisinitiallyabout15graindiametersanddiffusestoapproximately100grain diametersover1.4s(cyanlineFigure 5-10).The d = 0.04cmsimulationisinitialized withaplaneheightofabout8graindiametersanddiffusestoabout115graindiameters overthesametime(magentalineFigure 5-10).Theplaneinbothsimulationsdiffuses outataboutthesamerateinitially,butthenthe d = 0.04cmsimulationbeginstodiffuse faster.Theincreaseddiffusioninthe d = 0.04cmsimulationwasexpectedduetothe decreasedsizeofthegrains. 5.4.2ParticlePressure Themodelshowsalowsensitivitytochangesinthemagnitudeoftheparticle pressureappliedwithinthetestedrangeofthebedstiffnessfactor, r .Althoughthe resultinganglesofreposeareslightlylessthanthetypicalangleofreposeforbeach sand( 31 ),theangleofreposeresultingfromthecurrentbedstiffnessfactorused inthemodel( r = 0.2, r 18 )issimilartothetheoreticalangleofreposeforsmooth spheres( 22 )(Albertetal. 1997).Othershavemeasuredtheangleofreposefor sphericalparticlestobe23 < r < 32 dependingontheparticlesizeandshape (Doppleretal., 2007; duPontetal. 2003; PhilippeandRichard, 2008).However,the modelisnothighlysensitivetothetestedrangeofvaluesofthebedstiffnessfactor.No guidancecurrentlyexistsonhowtoincludeaparticlepressureparameterizationina mixturetheorymodelappliedtosandrippledynamics.Realisticanglesofreposeanda 101

PAGE 102

lowmodel sensitivitytovariationsintheamountofdampingappliedillustratesthatthe velocitydampingfunctionisanappropriateapplicationforthismodel. 5.5Conclusions Thehinderedsettlingratespredictedbythemixturetheorymodel(SedMix3D) agreewellwiththespeciedhinderedsettlingformulation( RichardsonandZaki, 1954) despitetheinclusionofdiffusionandadvectiontermsinthesedimentuxequation. The RichardsonandZaki (1954)empiricalformulationisdependentonlyonthelocal sedimentconcentrationandtheparticleReynoldsnumber.WhiletheparticleReynolds numberisreadilycalculated,thedenitionoflocalsedimentconcentrationissomewhat ambiguousandstronglyinuencesthepredictedbulkhinderedsettlingrates.Themodel sensitivitytotheparticlepressureparameterizationwasalsotested.Anglesofrepose resultingfrommodelsimulationswitharangeofvelocitydampingfunctionsdifferedless than5%illustratingalowmodelsensitivitytotheparticlepressureparameterization functionstested. Figure5-1.Eff ectiveviscosityformulations. 102

PAGE 103

Figure5-2.Bed stiffnesscoefcient, S b ,withvaryingvaluesof r plottedversus concentration.Thefunctiondeterminesthepercentamounttodampthe velocityintheenduringcontactregionofthedomain.Thecurrentmodel usesavalueof r = 0.2.Notethebedstiffnessfunctiononlydampsthe velocityby 0.1%0.85%inthepackedbedregion.Thesmallcorrection makesasignicantdifferenceinthebedrigidity. 103

PAGE 104

Figure5-3.Snapshots ofconcentration()contoursduringgravitationalsettlingofa sedimentplane(averagedinthey-direction)initializedwithaconcentration of0.567andsedimentgrainsizeof0.2cm. 104

PAGE 105

Figure5-4.Contoured timeseriesofthehorizontallyaveragedconcentrationfor d = 0.2 cm.Thesolidblacklinedenotesthelocationofthecentroidofthesediment plane.Theblackdashedlinesdenotetheboundariesoftheconcentration plane(thepointatwhichtheconcentrationgoestozero). 105

PAGE 106

Figure5-5.a) Timeseriesofthehorizontallyaveragedconcentrationatthelocationof thecentroidoftheplane(blueline)andthehorizontallyandvertically averagedconcentrationovertheentireplane(greenline)forthe d = 0.2cm simulation.b)Timeseriesofthesettlingrateofthecentroidoftheplane (blackline)plottedwiththebulksettlingrate(RichardsonandZaki, 1954) calculatedusingthetwoconcentrations:horizontallyaveragingatthe centroid(blueline)andhorizontallyandverticallyaveragingovertheentire plane(greenline). 106

PAGE 107

Figure5-6.Snapshots ofconcentration()contoursduringgravitationalsettlingofa sedimentplane(averagedinthey-direction)initializedwithaconcentration of0.567andsedimentgrainsizeof0.04cm. 107

PAGE 108

Figure5-7.Contoured timeseriesofthehorizontallyaveragedconcentrationfor d = 0.04cm.Thesolidblacklinedenotesthelocationofthecentroidofthe sedimentplane.Theblackdashedlinesdenotetheboundariesofthe concentrationplane(thepointatwhichtheconcentrationgoestozero). 108

PAGE 109

Figure5-8.a) Timeseriesofthehorizontallyaveragedconcentrationatthelocationof thecentroidoftheplane(blueline)andthehorizontallyandvertically averagedconcentrationovertheentireplane(greenline)forthe d = 0.04cm simulation.b)Timeseriesofthesettlingrateofthecentroidoftheplane (blackline)plottedwiththebulksettlingrate(RichardsonandZaki, 1954) calculatedusingthetwoconcentrations:horizontallyaveragingatthe centroid(blueline)andhorizontallyandverticallyaveragingovertheentire plane(greenline). 109

PAGE 110

Figure5-9.Angle ofreposeforvaryingvaluesof r intheparticlepressure parameterization. Figure5-10.Height ofthesedimentplane(h )normalizedwiththegrainsize(d )plotted withtimeforthetwosimulations. 110

PAGE 111

CHAPTER6 MORPHODYNAMICS OFTHREE-DIMENSIONALRIPPLEGEOMETRIES 6.1Introduction Seabedmorphologyisamajorsourceofenergydissipationandcanstrongly modulateowresistanceincoastalanduvialenvironments.Rippledbedshave recentlybeenfoundtocausesignicantwaveenergydissipationoutsidethesurfzone, affectingwaveandcirculationforecasting( Ardhuinetal. 2002 ; SherwoodandGanju 2010; Warneretal. 2008).Vortexsheddinginducedbythepresenceofsandripplesis aneffectivemechanismofsedimenttransportandultimatelycausesbedformmigration andlarge-scalemovementofsediment.Sanddunemigrationinuvialenvironmentscan affectriverbedandbankstability,sedimentation,andowresistance( Ashworthetal. 2000; Best 2005).Recentresearchexaminingtheturbulentdissipationovertwo-and three-dimensionalrippleshasemphasizedthedependanceoftheowstructureonthe bedmorphology.Asingleroughnesslengthisaninadequateparameterizationofthe energydissipationoverspatiallyandtemporallyevolvingtwo-andthree-dimensional rippledbeds( Venditti, 2007). Ourlackofdetailedknowledgeofvorticitydynamicsandthetransportofsediment overrippledbedshindersourabilitytofullyunderstandthemechanicsandeffectsof bedformmorphology.Therefore,itisnecessarytodeterminethecorrelationbetween three-dimensionalbedformmorphology,turbulence,andboundarylayershearstressto understandthecomplexbottomboundarylayerprocessesoccurringoverrippledsea beds.Understandingtheseprocesseswillultimatelyprovideinsightintotheeffectsof terminationsandbifurcationsofnaturalripples,transitiontimescales,andrippleand sedimenttransportmigrationrates. Considerableresearchhasfocusedonnumericallysimulatingsteadyandoscillatory owsoversandyrippledbeds.Two-dimensionaltheoreticalmodelshavebeenused tocalculatethevorticityandvelocityeldsoverrippledbeds( BlondeauxandVittori 111

PAGE 112

1991; ChangandScotti 2003; HaraandMei, 1990; ZedlerandStreet 2001);however, two-dimensionalmodelsmustuseempiricalapproximationstodescribethedissipation oftwo-dimensionalvorticestosmallerthree-dimensionalvortices.Theexamination ofsmall-scalevorticityandsedimentdynamicsinthree-dimensionsismuchmore difcultforseveralreasons.Increasedcomputingpowerinthelastdecadehasonly madethree-dimensionalsimulationsofprototypescalespossible,butnotpractical. However,recentadvancesincomputationalresourceshaveallowedformassively scalable,high-resolution,three-dimensionalsimulationsatprototypetimescales( Penko etal. 2010b).Additionally,veryfewlaboratoryandeldstudieshavemeasuredthe small-scaleuctuationsofboundarylayerprocessesinthree-dimensionstocompareto therecentlydevelopedthree-dimensionalmodels( OurmieresandChaplin, 2004 ). Theexistingthree-dimensionalresearchcomparesthedifferencesinthree-dimensional owsovertwo-andthree-dimensionalripples.Studieshavefoundanincreaseinenergy dissipation,butadecreaseinturbulencewhencomparingtheowover2Dto3Ddunes (Madduxetal., 2003a,b; SchindlerandRobert 2005).Theenhancedturbulenceover the2Dripplesisduetoaverticaldivergenceofmeanowandanupwarddirected secondaryowthatisabsentover3Dripples( Venditti, 2007).Thethree-dimensional oweldischaracterizedbysmall-scalevortexstructuresthathaveasignicant impactonsedimentdynamics.Thesesmallthree-dimensionalstructuresenhance mixingandthesuspensionofsediment( Scanduraetal. 2000 ).Recently, Bhaganagar andHsu ( 2009 )performedhighlyresolveddirectnumericalsimulationsofowover rippledbedsandfoundthattheowstructures,thereforeuctuatingvelocitiesand higherorderstatistics,arehighlydependentonwhethertherippleswere2Dor3D. Inthisnewlydevelopedareaofresearch,moreanalysisandmeasurementsmustbe performedtoincreaseourunderstandingofthesmall-scaleboundarylayerprocesses thatgovernsandrippledynamics.Here,wepresenthighlyresolvedsimulationsof owoverthree-dimensionalrippledbedsthatmaybeutilizedtoreneourpresent 112

PAGE 113

understandingofuid-sediment boundarylayerdynamics.Inthisstudywedemonstrate thecapabilityofSedMix3Dtosimulateprototypescaleowsanddomainsthatwill beusedtoexaminethesmall-scaleuctuationsinthree-dimensionalowsoversand ripples.Themodelpushesthelimitofhardwaretechnology,providinganunprecedented levelofdetailofbottomboundarylayerdynamics. 6.2Methodology Weexaminethesedimentandvorticitydynamicsoverthree-dimensionalripple geometriesusingthemixturemodelof Penkoetal. (2010b)(SedMix3D).SedMix3D solvestheunlteredNavier-Stokesequationsandasedimentuxequationthat considersthebalancebetweengravitationalsettling,advection,anddiffusionina uid-sedimentmixtureresultinginthetime-dependentsedimentconcentrationand three-componentvelocityvectoreldinathree-dimensionaldomain.SeeChapter 2 forafulldescriptionofthemodel.Flowsimulationsofprototypescaledomainswith threedifferentthree-dimensionalripplegeometries(longatripple,bifurcatedripples, andripplesorientedobliquelytotheow)arepresentedtodemonstratetheutilityof SedMix3D. 6.3Results 6.3.1LongFlatRippleSimulation Thelongatripplesimulationdomainis32cm 4cm 12cmwith256 32 384gridpoints.Thebedgeometryisasinglelongrippleofheight2cm(Figure 6-1). Themodelisforcedwitharegularsinusoidalwavewithmaximumfreestreamvelocity of50cm/sanda2secondperiodforatotalsimulationtimeof24seconds.Fluidand sedimentpropertiesofthesimulationare = 1.0gcm )Tj /T1_6 7.97 Tf (3 = 1.3110 )Tj /T1_6 7.97 Tf 6.59 0 Td (2 gcm )Tj /T1_6 7.97 Tf (1 s )Tj /T1_6 7.97 Tf (1 d = 0.04cm,and s = 2.66gcm )Tj /T1_6 7.97 Tf (3 .Thetimestepis t =1 10 )Tj /T1_6 7.97 Tf 6.59 0 Td (5 sandoutputles arewrittenat32Hz.Eachsecondofrealtimesimulationrequiresabout16hoursof wallclocktimeon192processorsofaCRAYXT5attheERDCDSRCforatotalof about73,000CPUhoursforthefull24secondsimulation.Thetotalstoragerequired 113

PAGE 114

forthis simulationisapproximately450GB,whichincludesoutputbinarylesand post-processedresults. SnapshotsfromthesimulationareshowninFigure 6-2.Contoursofthexand yvorticityareplottedonthey-zandx-zplanewallsofthedomain,respectively, andthethree-dimensionalvelocityvectorsarealsoplottedonthex-zdomainwall. Concentrationisosurfacesarecontouredat10%concentrationbyvolume.Theforcingis appliedinthex-direction.Within5waveperiods,eightripplesbegintoformontheat bedthatmergetofourripplesafter10waveperiods.Thesimulationclearlyillustrates thecomplexthree-dimensionalvortexdynamicsgoverningtheowoverripples,even whentherippleitselfisrelativelytwo-dimensional. 6.3.2BifurcatedRipples Thebifurcatedripplesimulationdomainis12cm 24cm 10cmwith128 256 256gridpoints.Thegeometryconsistsoftwoparallelripplesconnectedwitha 45 angledripple(Figure 6-3).Themodelisforcedwitharegularsinusoidalwavewith maximumfreestreamvelocityof26cm/sanda2secondperiodalongthex-direction. Fluidandsedimentpropertiesofthesimulationare = 1.0gcm )Tj /T1_6 7.97 Tf (3 = 1.010 )Tj /T1_6 7.97 Tf 6.59 0 Td (2 g cm )Tj /T1_6 7.97 Tf (1 s )Tj /T1_6 7.97 Tf (1 d = 0.04cm,and s = 2.65gcm )Tj /T1_6 7.97 Tf 6.59 0 Td (3 .Thetimestepisslightlylargerthanthe atbedsimulationat t = 410 )Tj /T1_6 7.97 Tf 6.59 0 Td (5 sandlesareoutputat32Hz.Withover8million gridpoints,thissimulationisthemostcomputationallyexpensiveofthethreepresented simulations.Eachsecondofrealtimetakes64wallclockhourson128processorsof aCRAYXT3attheERDCDSRC.The32processedlesper1ofsimulationrealtime areabout1GBeach,withthesimulationrequiringatotalofaround550Gbofstorage currently. Figure 6-4 showssixsnapshotsfromthebifurcatedripplesimulation.Theow directionisperpendiculartotheripples(inthex-direction).Contoursofyvorticityare plottedintheplanesbisectingtheripples.Duringtheinitialspin-up,theowcirculates overthebifurcation,transportingsedimentintotheterminationareas.Thebifurcation 114

PAGE 115

isalmostcompletely erodedafter3waveperiods.Thissimulationwillallowustobetter understandtheprocessesgoverningtwo-tothree-dimensionalrippletransitionsandthe roleoftheterminationsandbifurcationsinthree-dimensionalrippledbeds. 6.3.3RipplesOrientedObliquelytoFlowDirection Thelastsimulationdomainis12cm 12cm 12cmwith128 128 256grid points.Theinitialbedgeometryincludesripplesthatareorientedata45 angletothe freestreamowdirection(Figure 6-5).Themodelisforcedwitharegularsinusoidal wavewithmaximumfreestreamvelocityof26cm/sanda2secondperiodalong thex-direction.Fluidandsedimentpropertiesofthesimulationare = 1.0gcm )Tj /T1_6 7.97 Tf 6.59 0 Td (3 = 1.010 )Tj /T1_6 7.97 Tf 6.59 0 Td (2 gcm )Tj /T1_6 7.97 Tf 6.59 0 Td (1 s )Tj /T1_6 7.97 Tf 6.59 0 Td (1 d = 0.04cm,and s = 2.65gcm )Tj /T1_6 7.97 Tf 6.59 0 Td (3 .Thetimestepis t = 1.510 )Tj /T1_6 7.97 Tf 6.59 0 Td (5 s.Thesimulationrequiresabout32wallclockhoursper1secondof simulationrealtimeon128processorsofaCRAYXT3attheERDCDSRC.Filesare outputat32Hzandabout8secondsofthe30secondsimulationnishedcurrently. Thetotalstoragerequiredforthissimulationisapproximately500GB,includingoutput binarylesandpost-processedresults. SixsnapshotsfromtheobliqueripplesimulationareplottedinFigure 6-6.Vorticity contoursandthree-dimensionalvelocityvectorsareplottedonthebackwallsofthe domain.Concentrationisosurfacesarecontouredat10%concentrationbyvolume. Again,thehighlythree-dimensionalvorticesareclearlypresentastheowoscillates overtheripples.Thedissipationofthesmall-scalevorticesisalsoevidentasthe structuresareadvectedupintothewatercolumn.Thecomplexowandsediment transportpatternscanbestudiedfromthissimulation. 6.4Conclusions Ourthree-dimensionalmodel(SedMix3D)simulatesuid-sedimentinteractions withinthewavebottomboundarylayerandcanbeusedtoinvestigatethesmall-scale uctuationsinowsoverripplesincoastalanduvialenvironments.SedMix3Dutilizes state-of-the-artsupercomputingtechnologytoperformprototypescalehighresolution 115

PAGE 116

simulationsof theseabedresponsewhensandripplesarepresentandprovides insighttothedetailedsmall-scaleuctuationsofboundarylayerprocesses.Here,we presentedthreeprototypescalesimulationstodemonstratethecapabilityofSedMix3D toprovidedetailedinformationaboutcurrentlyunknownprocessesthatgovernripple morphodynamicsincludingtheroleofrippleterminationsandbifurcationsonripple growthratesandmigrationtimescales,theeffectofsuspendedsedimentonturbulence modulation,andthebasisfortransitionsbetweentwo-andthree-dimensionalripples. 116

PAGE 117

Figure6-1.Initial bedinthelongatripplesimulation.Simulationforcingisapplied alongthex-axis. 117

PAGE 118

Figure6-2.Snapshots fromthelongatripplesimulation.Contoursofxandyvorticity areplottedonthey-zandx-zbackplanes,respectively.Three-dimensional vectorsplottedonthebackwallofthedomainindicateinstantaneousow direction.Onlyeverytenthvectorinthex-andz-directionisplottedforease ofviewing. 118

PAGE 119

Figure6-3.Initial bedinthebifurcatedripplesimulation.Thebifurcatedrippleisat45 angletotheparallelripples.Simulationforcingisappliedalongthex-axis. 119

PAGE 120

Figure6-4.Snapshots fromthebifurcatedripplesimulation.Contoursofxandyvorticity areplottedonthey-zandx-zbackplanes,respectively.Three-dimensional vectorsplottedonthebackwallofthedomainindicateinstantaneousow direction.Onlyeveryfthvectorinthex-directionandtenthvectorinthe z-directionisplottedforeaseofviewing. 120

PAGE 121

Figure6-5.Initial bedintheobliqueripplesimulation.Ripplesareorientedata45 angletotheow.Simulationforcingisappliedalongthex-axis. 121

PAGE 122

Figure6-6.Snapshots fromtheobliqueripplesimulation.Contoursofxandyvorticity areplottedonthey-zandx-zbackplanes,respectively.Three-dimensional vectorsplottedonthebackwallofthedomainindicateinstantaneousow direction.Onlyeveryfthvectorinthex-directionandtenthvectorinthe z-directionisplottedforeaseofviewing. 122

PAGE 123

APPENDIX MESSAGE-PASSING INTERFACE(MPI)IMPLEMENTATION TheparallelizationofthemodelwasimplementedusingtheMessage-Passing Interface(MPI).MPIisalibraryofroutinescalledfromwithinprogramminglanguages toallowseparatecentralprocessingunits(CPUs)tocommunicateandsharedata witheachother.ForanumberofCPUs, n ,thesimulateddomainisdecomposedinto n xedsizeblocks.EachCPUisassignedarank( 0 to n )Tj /T1_2 11.955 Tf 12.8 0 Td (1)andisresponsiblefor processingtheprogramalgorithmforitsuniquepartofthesimulationdomain.The CPUsthencommunicatewitheachotherbysendingandreceivinganydatanecessary forcalculations(i.e.,message-passing).Itisimportanttonotethateachprocessingunit runsthesamesourcecode;theportionofthedomainbeingprocessedisbasedonthe CPU'sranknumber.TheresultofMPIisdecreasedwallclocktimenecessaryforeach simulationduetothedecreasedcomputationaldomainsizeonaCPU. MPIwaschosentomaximizeportabilityandscalabilityoftheparallelversion ofSedMIx3D.Parallelizationoftheserialcodewasnecessarytosimulateprototype scaledomainsformultiplewaveperiods.Developmentanddebuggingoftheparallel codetookapproximatelyoneyearoffocusedeffortandresultedina15timesspeedup fromtheoriginalserialcode(Figure A-1).UsingAmdahl'slaw(Equation A), P ,the percentageofthesourcecodethatisparallelized,is94%forparallelSedMix3Dusing 128processors. lim n !1 = 1 1 )Tj /T1_1 11.955 Tf 11.95 0 Td (P (A) EachSedMix3Dsim ulationdomain(withnx ny nzgridpoints)isruninparallel on nz =2 CPUs;therefore,eachCPUperformscalculationsontwoadjacentx-ygrid planes.Themodelisnitedifferenceinthez-directionusingsecondordercentral differences.Equation A isasecond-orderderivativeof f withrespectto z .Derivative calculationsof f atz-gridpoint, k ,require f at k +1 and k )Tj /T1_2 11.955 Tf 11.95 0 Td (1, @ f k @ z = f k +1 )Tj /T1_1 11.955 Tf 11.95 0 Td (f k )Tj /T1_7 7.97 Tf (1 2z (A) 123

PAGE 124

EachCPUsends andreceivesghostcellstoandfromtheirneighboringprocessors (i.e.,x-yplanesat z = k )Tj /T1_2 11.955 Tf 12.83 0 Td (1 and z = k +1 ).TheCPUsperformthecalculations, thensendandreceivethenewlycalculateddata.Thespeeddoesnotincrease linearlywiththenumberofCPUs.AsthenumberofCPUsincreases,theamountof message-passingalsoincreases(Figure A-1). FigureA-1.Sim ulationwallclocktimespeedupresultingfromrunningSedMix3Din parallelonvaryingnumbersofprocessors. 124

PAGE 125

REFERENCES Albert,R., Albert,I.,Hornbaker,D.,Schiffer,P.,Barabasi,A.L.,1997.Maximum angleofstabilityinwetanddrysphericalgranularmedia.PhysicalReviewE56(6), R6271R6274. Ardhuin,F.,Drake,T.G.,Herbers,T.H.C.,2002.Observationsofwave-generated vortexripplesonthenorthcarolinacontinentalshelf.JournalofGeophysicalResearch 107(C10),3143. Ashworth,P.J.,Best,J.L.,Roden,J.E.,Bristow,C.S.,Klaassen,G.J.,2000. Morphologicalevolutionanddynamicsofalarge,sandbraid-bar,JamunaRiver, Bangladesh.Sedimentology47(3),533. Baas,J.H.,1999.Anempiricalmodelforthedevelopmentandequilibriummorphology ofcurrentripplesinnesand.Sedimentology46(1),123. Bagnold,R.A.,1954.Experimentsonagravity-freedispersionoflargesolidspheresin aNewtonianuidundershear.ProceedingsoftheRoyalSocietyofLondon,SeriesA 225(1160),49. Barr,B.C.,Slinn,D.N.,Pierro,T.,Winters,K.B.,2004.Numericalsimulationof turbulent,oscillatoryowoversandripples.JournalofGeophysicalResearch 109(C9),1. Batchelor,G.K.,1988.Anewtheoryoftheinstabilityofauniformuidized-bed.Journal ofFluidMechanics193,75. Best,J.,2005.Theuiddynamicsofriverdunes:Areviewandsomefutureresearch directions.JournalOfGeophysicalResearch-EarthSurface110(F4). Bhaganagar,K.,Hsu,T.J.,2009.Directnumericalsimulationsofowover two-dimensionalandthree-dimensionalripplesandimplicationtosedimenttransport: Steadyow.CoastalEngineering56(3),320. Blondeaux,P.,2001.Mechanicsofcoastalforms.AnnualReviewofFluidMechanics33, 339. Blondeaux,P.,Scandura,P.,Vittori,G.,2004.Coherentstructuresinanoscillatory separatedow:numericalexperiments.JournalofFluidMechanics518,215. Blondeaux,P.,Vittori,G.,1991.Vorticitydynamicsinanoscillatoryowoverarippled bed.JournalofFluidMechanics226,257. Burdick,G.M.,Slinn,D.N.,2004.Modelingsheetowinoscillatoryowsusinga mixtureapproach.EosTrans.AGU85(47),FallMeet.Suppl.,AbstractOS21B. Buyevich,Y.A.,1999.Particulatestressesindensedisperseow.Industrial& EngineeringChemistryResearch38(3),731. 125

PAGE 126

Chang,Y. S.,Scotti,A.,2003.Entrainmentandsuspensionofsedimentsintoaturbulent owoverripples.JournalofTurbulence4,019. Chang,Y.S.,Scotti,A.,2006.Turbulentconvectionofsuspendedsedimentsduetoow reversal.JournalofGeophysicalResearch111(C7),C07001. Charru,F.,Mouilleron-Arnould,H.,Feb.2002.Instabilityofabedofparticlesshearedby aviscousow.JournalofFluidMechanics452,303. Chen,Z.,Gibilaro,L.G.,Jand,N.,2003.Particlepackingconstraintsinuid-particle systemsimulation.Computers&ChemicalEngineering27(5),681. deCindio,B.,Nicodemo,L.,Masi,P.,1987.Onthenon-Newtonianbehaviorof suspensions.RheologicaActa26(1),100. Dohmen-Janssen,C.M.,Kroekenstoel,D.F.,Hassan,W.N.,Ribberink,J.S.,2002. Phaselagsinoscillatorysheetow:experimentsandbedloadmodelling.Coastal Engineering46(1),6187. Doppler,D.,Gondret,P.,Loiseleux,T.,Meyer,S.,Rabaudi,M.,2007.Relaxation dynamicsofwater-immersedgranularavalanches.JournalofFluidMechanics577, 161. Doucette,J.,O'Donoghue,T.,2006.Responseofsandripplestochangeinoscillatory ow.Sedimentology53(3),581. Drew,D.A.,1983.Mathematical-modelingoftwo-phaseow.AnnualReviewofFluid Mechanics15,261. duPont,S.C.,Gondret,P.,Perrin,B.,Rabaud,M.,2003.Granularavalanchesinuids. PhysicalReviewLetters90(4). Eilers,H.,1941.Theviscosityoftheemulsionofhighlyviscoussubstancesasfunction ofconcentration.Kolloid-Zeitschrift97(3),313. Einstein,A.,1906.EineneueBestimmungderMolek uldimensionen(German)[Anew determinationofmoleculardimensions].AnnalenderPhysik19,289. Faraci,C.,Foti,E.,2001.Evolutionofsmallscaleregularpatternsgeneratedbywaves propagatingoverasandybottom.PhysicsofFluids13(6),1624. Ferrini,F.,Ercolani,D.,Cindio,B.D.,Nicodemo,L.,Nicolais,L.,Ranaudo,S.,1979. Shearviscosityofsettlingsuspensions.RheologicaActa18(2),289. Forel,M.,1883.Lesridesdefond.ArchivesdesSciencesPhysiquesetNaturelles. Fredse,J.,Deigaard,R.,1992.MechanicsofCoastalSedimentTransport.World Scientic,Singapore. 126

PAGE 127

Grant,W .D.,Madsen,O.S.,1982.Movablebedroughnessinunsteadyoscillatoryow. JournalofGeophysicalResearch87(C1),469. Haque,M.I.,Mahmood,K.,1985.Geometryofripplesanddunes.JournalofHydraulic Engineering111(1),48. Hara,T.,Mei,C.C.,1990.Oscillatingowsoverperiodicripples.JournalofFluid Mechanics211,183. Hofer,M.,Perktold,K.,1997.Computersimulationofconcentrateduid-particle suspensionowsinaxisymmetricgeometries.Biorheology34(4-5),261. Huang,N.,Bonn,D.,2007.Viscosityofadensesuspensionincouetteow.Journalof FluidMechanics590,497. Hunt,M.,Zenit,R.,Campbell,C.,Brennen,C.,2002.Revisitingthe1954suspension experimentsofR.A.Bagnold.JournalofFluidMechanics452,1. Jenkins,J.T.,Hanes,D.M.,1998.Collisionalsheetowsofsedimentdrivenbya turbulentuid.JournalofFluidMechanics370,29. Krieger,I.M.,1972.Rheologyofmonodisperselatices.AdvancesinColloidand InterfaceScience3(2),111. Krieger,I.M.,Dougherty,T.J.,1959.Amechanismfornon-Newtonianowin suspensionsofrigidspheres.JournalofRheology3(1),137. Leighton,D.,Acrivos,A.,1986.Viscousresuspension.ChemicalEngineeringScience 41(6),1377. Leighton,D.,Acrivos,A.,1987a.Measurementofshear-inducedself-diffusionin concentratedsuspensionsofspheres.JournalofFluidMechanics177,109. Leighton,D.,Acrivos,A.,1987b.Theshear-inducedmigrationofparticlesin concentratedsuspensions.JournalofFluidMechanics181,415. Lofquist,K.,1978.Sandripplegrowthinanoscillatory-owwatertunnel.Technical Memo78-5,CoastalEngineeringResearchCenter. Maddux,T.B.,McLean,S.R.,Nelson,J.M.,2003a.Turbulentowover three-dimensionaldunes:2.Fluidandbedstresses.JournalofGeophysicalResearch -EarthSurface108(F1). Maddux,T.B.,Nelson,J.M.,McLean,S.R.,2003b.Turbulentowover three-dimensionaldunes:1.Freesurfaceandowresponse.JournalofGeophysical Research-EarthSurface108(F1). Miskin,I.,Elliott,L.,Ingham,D.B.,Hammond,P.S.,1996a.Steadysuspensionows intotwo-dimensionalhorizontalandinclinedchannels.InternationalJournalof MultiphaseFlow22(6),1223. 127

PAGE 128

Miskin,I.,Elliott, L.,Ingham,D.B.,Hammond,P.S.,1996b.Theviscousresuspension ofparticlesinaninclinedrectangularfracture.InternationalJournalofMultiphase Flow22(2),403. Mogridge,G.,Davies,M.,Willis,D.,1994.Geometrypredictionforwave-generated bedforms.CoastalEngineering22,255. Mooney,M.,1951.Theviscosityofaconcentratedsuspensionofsphericalparticles. JournalofColloidScience6(2),162. Mukhopadhyay,S.,Usha,R.,Tulapurkara,E.G.,2009.Numericalstudyofconcentrated uid-particlesuspensionowinawavychannel.InternationalJournalforNumerical MethodsinFluids59(10),1125. Nawab,M.A.,Mason,S.G.,1958.Theviscosityofdilutesuspensionsofthread-like particles.JournalOfPhysicalChemistry62(10),1248. Nichols,C.S.,Foster,D.L.,2007.Full-scaleobservationsofwave-inducedvortex generationoverarippledbed.JournalofGeophysicalResearch-Oceans112. Nielsen,P.,1981.Dynamicsandgeometryofwavegeneratedripples.Journalof GeophysicalResearch86(C7),6467. Nielsen,P.,1992.CoastalBottomBoundaryLayersandSedimentTransport.World Scientic,Singapore. Nir,A.,Acrivos,A.,1990.Sedimentationandsedimentowoninclinedsurfaces.Journal ofFluidMechanics212,139. Nott,P.,Brady,J.,1994.Pressure-drivenowofsuspensions-simulationandtheory. JournalofFluidMechanics275,157. O'Donoghue,T.,Clubb,G.S.,2001.Sandripplesgeneratedbyregularoscillatoryow. CoastalEngineering44,101. Ourmieres,Y.,Chaplin,J.R.,2004.Visualizationsofthedisturbed-laminar wave-inducedowabovearippledbed.ExperimentsInFluids36(6),908. Penko,A.M.,Calantoni,J.,Slinn,D.N.,2009.Mixturetheorymodelsensitivityto effectiveviscosityinsimulationsofsandybedformdynamics.Proceedingsofthe Oceans2009MTS/IEEEBiloxiConference&ExhibitionBiloxi,MS,CDROM. Penko,A.M.,Calantoni,J.,Slinn,D.N.,2010a.Directnumericalsimulationofsediment transportandseabedmorphologyatlaboratoryscales.Proceedingsofthe7th InternationalConferenceonMultiphaseFlowTampa,FL. Penko,A.M.,Slinn,D.N.,Calantoni,J.,Burdick,G.M.,2010b.Modelformixturetheory simulationofvortexsandrippledynamics.JournalofWaterway,Ports,Coastal,and OceanEngineering. 128

PAGE 129

Philippe,P .,Richard,T.,2008.Startandstopofanavalancheinagranularmedium subjectedtoaninnerwaterow.PhysicalReviewE77(4). Phillips,R.,Armstrong,R.,Brown,R.,Graham,A.,Abbott,J.,1992.Aconstitutive equationforconcentratedsuspensionsthataccountsforshear-inducedparticle migration.PhysicsofFluidsA-FluidDynamics4(1),30. Rao,R.,Mondy,L.,Sun,A.,Altobelli,S.,2002.Anumericalandexperimentalstudyof batchsedimentationandviscousresuspension.InternationalJournalforNumerical MethodsinFluids39(6),465. Rao,R.R.,Mondy,L.A.,Altobelli,S.A.,2007.Instabilitiesduringbatchsedimentation ingeometriescontainingobstacles:Anumericalandexperimentalstudy.International JournalforNumericalMethodsinFluids55(8),723. Richardson,J.F.,Zaki,W.N.,1954.Sedimentationanduidisation:part1.Transactions oftheInstitutionofChemicalEngineers32,35. Rodriguez-Abudo,S.,Foster,D.,2010.Characterizationofthewavebottomboundary layerovermovablerippledbeds.EosTrans.AGU,OceanSci.Meet.Suppl.,Abstract PO21B. Scandura,P.,Vittori,G.,Blondeaux,P.,2000.Three-dimensionaloscillatoryowover steepripples.JournalofFluidMechanics412,355. Schindler,R.J.,Robert,A.,2005.Flowandturbulencestructureacrosstheripple-dune transition:anexperimentundermobilebedconditions.Sedimentology52(3), 627. Sherwood,C.R.,Ganju,N.K.,2010.Inuenceofsmall-scaletopographyandbottom roughnessonmodeledwavesandcirculation.EosTrans.AGU91(26),OceanSci. Meet.Suppl.,AbstractGO35A. Simeonov,J.,Penko,A.M.,Calantoni,J.,2010.Directnumericalsimulationsofthe gravitationalsettlingandtheshear-stressrheologyofsuspensionsofnite-size particles.EosTrans.AGU91(26),OceanSci.Meet.Suppl.,AbstractGO31A. Sudduth,R.D.,1993.Ageneralized-modeltopredicttheviscosityofsolutionswith suspendedparticles.JournalofAppliedPolymerScience48(1),25. Sun,D.W.,Annapragada,S.R.,Garimella,S.V.,2009.Experimentalandnumerical studyofmeltingofparticle-ladenmaterialsinacylinder.InternationalJournalofHeat andMassTransfer52(13-14),2966. vanderWerf,J.,Magar,V.,Malarkey,J.,Guizien,K.,O'Donoghue,T.,2008.2DV modellingofsedimenttransportprocessesoverfull-scaleripplesinregular asymmetricoscillatoryow.ContinentalShelfResearch28(8),1040. 129

PAGE 130

vander Werf,J.J.,Doucette,J.S.,O'Donoghue,T.,Ribberink,J.S.,2007.Detailed measurementsofvelocitiesandsuspendedsandconcentrationsoverfull-scaleripples inregularoscillatoryow.JournalofGeophysicalResearch-PartF-EarthSurfaces, F02012. vanderWerf,J.J.,Ribberink,J.S.,O'Donoghue,T.,Doucette,J.S.,2006.Modelling andmeasurementofsandtransportprocessesoverfull-scaleripplesinoscillatory ow.CoastalEngineering53(8),657. Vand,V.,1948.Viscosityofsolutionsandsuspensions:1.Theory.JournalofPhysical andColloidChemistry52(2),277. Venditti,J.G.,2007.Turbulentowanddragoverxedtwo-andthree-dimensional dunes.JournalofGeophysicalResearch-EarthSurface112(F4),F04008. Vongvisessomjai,S.,1984.Oscillatoryripplegeometry.JournalofHydraulicEngineering 110(3),247. Warner,J.C.,Sherwood,C.R.,Signell,R.P.,Harris,C.K.,Arango,H.G.,2008. Developmentofathree-dimensional,regional,coupledwave,current,and sediment-transportmodel.Computers&Geosciences34(10),1284. Webb,B.M.,2008.Small-scalesedimenttransportprocessesandbedformdynamics. PhDThesis,UniversityofFlorida. Wiberg,P.L.,Harris,C.K.,1994.Ripplegeometryinwave-dominatedenvironments. JournalofGeophysicalResearch99,775. Zedler,E.A.,Street,R.L.,2001.Large-eddysimulationofsedimettransport:currents overripples.JournalofHydraulicEngineering127(6),444. Zedler,E.A.,Street,R.L.,2006.Sedimenttransportoverripplesinoscillatoryow. JournalofHydraulicEngineering132(2),180. Zhou,J.,Adrian,R.J.,Balachandar,S.,Kendall,T.M.,1999.Mechanismsfor generatingcoherentpacketsofhairpinvorticesinchannelow.JournalofFluid Mechanics387,353. 130

PAGE 131

BIOGRAPHICALSKETCH AllisonP enkogrewupontheshoresofLakeErieinEuclid,Ohio,asuburbof Cleveland,Ohio.AfterearningaBachelorofScienceinCivilEngineeringfromtheOhio StateUniversityin2004,shewasofferedaGraduateResearchpositionatUniversityof Floridatoworkonasmall-scalesedimenttransportnumericalmodelingprojectwithDr. DonaldSlinn.InSeptember2006,shewasawardedthethreeyearNationalDefense ScienceandEngineeringGraduateFellowshipfromtheDepartmentofDefense. SheearnedherMasterofScienceinCoastalandOceanographicEngineeringin Mayof2007andcontinuedontoherPh.D.researchatUniversityofFloridauntil 2009.InOctoberof2008,shewasofferedaprestigiousresearchpositiontoperform herPh.D.researchattheNavalResearchLaboratoryatStennisSpaceCenteron theMississippiGulfCoast.SheearnedherPh.D.inCoastalandOceanographic EngineeringinDecemberof2010andplanstocontinueattheNavalResearch Laboratoryinapost-doctoralpositionresearchingwavebottomboundarylayer dynamicsofsediment-uidandmud-uidinterfaces. 131