A NEW MODEL FOR PREDICTING BED
EVOLUTION IN ESTUARINE AREA AND
ITS APPLICATION IN YELLOW RIVER
DELTA
AvaHabIoonlineat’_n{-旧n《I蒯Irc耄.corn
;一
;‘ScienceDirect
;JeumalofHydrodynamics
;201l,23(4):457-465
;DOI:10.1016/S1001—6058(10)60136—9
;457
;l|}1sciencedifeetcome
;sciencournal/lO016058
;ANEWMoDELFoRPREDICTINGBEDEVoLUTIoNINESTUAIUNE
;AREAANDITSAPPLICATIoNINYELLoWRIVERDELTA
;YANGChen,JIANGChun—bo
;StateKeyLaboratoryofHydroscienceandEngineering,TsinghuaUniversity,Beijing100084,China, ;E—mail:yangchen07@mails.tsinghua.edu.cn
;(ReceivedJanuary6,2011,RevisedFebruary26,2011)
;Abstract:Thisarticlediscussestheprocessofsedimenttransportandproposesamorphologica1modeltopredictthebedevolution
;inestuaries.Thehydrodynamicmoduleisbasedonanexistentmode1—DepthIntegratedVelocityAndS
oluteTransportrDIVAST)
;and也
ewettinganddryingmethodisadoptedtodealwiththemovingboundary.Bothcohesivesedimentandnon.cohesivesediment
;aretakenintoconsiderationinthesediment仃
ansportmodulewiththecapabilitvofsimulatingthetransportofgradedsediments ;undernon-equilibriumconditions.ThefaIlvelocityofthesuspendedsedimentismodifiedinthepresentmodelduetomehigh
;sedimentconcentration.A3-layerapproachisadoptedtosimulatethevariationsofsedimentgradationsofbedmaterials.
;Furthermore,themodelisusedtosimulatethebedevolutionintheYellowRiverDeltafYRD1from1992to1995.Fielddataare
;usedtocalibratetheparameters.ThenumericalresultsshowhowthemorphologywasdevelopedintheYellowRiverEstuarywitha
;goodagreementwiththefielddata.
;Keywords:bedevolution,gradedsediments,morphology,numericalmodel,sedimenttransport,Yello
wRiverDelta(YRD)
;Introduetion
;Thewaterbodiesinestuariesfeatureashallow ;waterdepth,acomplicatedgeometryandarather ;gradedsediment.Theinteractionamongthefluid ;flows,thesedimenttransportandthebedlevel ;changesisofgreatimportancetosomewaterenviro- ;nmentalissuesandrivermouthwetlandfunctions. ;Themotionofthesediment
;cularcharacteristics,suchas
;isrelatedwithitsparti—
;cohesiveandnon..cohe..
;siveproperties,whichplayimportantrolesinthe ;long—termbedevolution.Inthepastdecades,thebed ;evolutionprocessinestuarineandcoastalbasinswas ;extensivelyinvestigatedbothexperimentallyand ;numerically.Schramkowskieta1.【analyzedthe
;effectsofgeometryandbottomfrictiononlocalbed ;formsinatidalembayment.Intheirstudy.thewater ;motionwasmodeledbyusingthedepth—averaged
;ProjectsupportedbytheKeyProjectofNationalNatural ;ScienceFoundationofChina(GrantNo.51039002),theState ;KeyLaboratoryofHydroscienceandEngineering, ;Tsinghua
;Unive~ity(GrantNo.2009一TC.2,.
;Biography:YANGChen(1981.1,Male,Ph.D. ;C0rrespOnding:JIANGChun.bO.
;E-mail:job@mail.tsinghua.edu.cn
;shallowwaterequationsanddrivenbyanexternally ;prescribedM,tide.takingaccountofthe仃ansportof
;thesuspendedload.ZhangandLiudevelopeda ;numericalmodeltosimulatethesuspendedsediment ;transport,builtintheverticalo-coordinatefor ;fittingthefreesurfaceandbottom,andanalyzedvari—
;OUSparameters,inwhichtheeddydiffusion.thefa11 ;velocityandtheRousenumberarefoundtobethe ;predominantfactorsofthesedimenttransport.Chung ;andEppelinvestigatedthesensitivityofsediment ;transportandbedmorphologywithrespecttothebed ;slopeandgrainsize,andthenon—hvdrostaticpressure
;termwastreatedthroughnumericalsimulationsbased ;ona3一Dhydrodynamicandsedimenttransportmode1.
;Taneta1.【studiedtheerosionprocessofcohesive ;sedimentafterconsolidationexperimentallyina ;closedconduitsystemandderivedascourratefor. ;mulabasedontheexperimentalresults.Li【develo.
;pednumericalmodelsoftidalcurrentandsediment ;movementunderthecombinedactionofwaveand ;currentwithanirregulartriangulargrid,carriedout ;numericalsimulations,andtheeffectofreclamationin ;0ujiangEstuarywasanalyzedbythemodels. ;TheYellowRiverDeltafYRD)islocatedina ;jointzoneofYellowRiverandBohaiSea.andisthe ;baseofenergysources,petroleumandagricultureof ;蠹一
;458
;ShandongProvinceofChina.TheYellowRiverhas ;thehighestsedimentconcentrationintheworld. ;whichtakesnearly10tofsedimenttotheYRDand ;BohaiSeaeveryyear_【)J.Becauseoftheweaktidein
;BohaiBaythetidecurrentcanonlytake1/3ofthe ;sedimentintotheoutersea.somostofthesedimentis ;heldupattherivermouthandmakethetopographyof ;theYRDgreatlychangableallthetime.
;Withrespecttothenumericalinvestigationsof ;theYellowRiver.Zhangeta1.【developeda1.D
;modelforunsteadysedimenttransportintheNingxia ;reachoftheYellowRiver.thecOncentrationdistri—
;butionsandthemeandiameterdistributionsofSHS—
;pendedsedimentinthetransversa1directionwerealso ;estimatedbyusingthismodel,andaftervalidation ;themodelwasusedtopredicttheriverbeddefor—
;marionduringtheperiodofl999—2019intheNingxia
;reachoftheYellowRiver.Caoeta1.Lestablisheda ;2一Dnumericalmodelbasedon”slotmethod”forun—
;steadyflowandsedimenttransportandeffectively ;simulatedthesedimenttransport,scouringandsilting ;ofseabedandthevariationofcoastline.Lieta1.【
;builta2.DmodelbasedontheVplumeOfFluid ;(VOF1techniqueandapplieditinPaniiataiShoal,one ;oftheimportantreachesintheYellowRiver.Zhaoet ;a1.【…derivedaset0fnew2.Dequationsforinter—
;changesbetweensuspendedsedimentandbedmate—
;rialsbasedonrelatedstudiesfortheLowerYellow ;River.Kongeta1.【appliedtheEnvironmentalFluid
;DynamicsCode(EFDC,codetosimulatethebed
;evolutionprocessintheYRDfrom1992to2000and ;obtainedsomereasonableresults.
;Inthepresentstudy.a2一Ddepth.integrated
;numericalmodelisdevelopedtopredictthehydro—
;dynamic,sedimenttransportandmorphologicalpro—
;cessesintheYRD.Themodelhastheabilityto ;simulatethetransportofgradedsedimentsundernon—
;equilibriumconditions.Thebedmixtureisdivided ;intofractions.withconsideratiOnofboththecohesive ;sedimentandthenon—cohesivesediment,andeach
;fractionofsedimentissimulatedseparatelybyassu—
;mingthatthefractionsdonotinteractwitheachother ;inthewaterbody.Theevolutionofthebedisthe ;resultoferosionorsedimentation.Inordertoaccount ;f0rtheinfluenceofbedsedimentcompositiononthe ;overalltransportprocessamethodofmultiplebed ;layersisusedtorepresentthespatialandtemporal ;variationsofsedimentgradationsofthelposebed ;layers.Inviewofthehighsedimentconcentrationof ;YellowRiver.thefallvelocityofthesuspendedsedi—
;mentiSmodifiedinthepresentmodelaccordingtothe ;practicalsedimentconcentration.Thepresentmodelis ;usedtosimulatethebedevolutionintheYRDfrom ;1992tol995.andthenumericalpredictionsbythe ;presentmodelarecomparedwithexperimentalmea—
;surementsandthepredictionsbasedonnon—fractional
;mode1s.
;1.Numericalmodeldetails
;1.1Governingequationsforhydrodynamicprocess ;Thehydrodynamicmodelforpredictingthe ;waterelevationandvelocityfieldsincoasta1.estua—
;rineandriverinewatersinvolvesthesolutionofthe ;governingequationsoffluidflow.The2一Dhydro—
;dynamicequationsaregenerallybasedonthedepth—
;integrated3一DReynoldsequationsforincompressible ;andunsteadyturbulentflows.withcOnsiderationsof ;theeffectsoftheearth’srotation,bottomfrictionand
;windshear.Thehydrodynamicmoduleinthepresent ;modelisbasedonanexistentmodel—DepthIntegrated
;VelocityAndSoluteTransportrDIVAST).withits ;capacityindealingwiththefloodinganddryingpro—
;cessesasausefulfeature.Moredetailsofthehydro ;dynamicgoverningequationsandsolutionmethods ;canbefoundinFalconer’sarticlellz1.
;1.2Governimzequationsforsealimenttianspot, ;Proeess
;Inestuarineandcoastalwaters.thesedimentsare ;usuallyhighlygraded,rangingfromveryfinetorather ;coarseparticles.Thetransportpropertiesofsuchsedi—
;mentsmayvarysignificantly.Thusinsomesituations ;itwouldnotbereasonabletouseasinglediameterto ;represental1sediments.Inthepresentstudy,the ;gradedsedimentisdividedintoNfractionsacco—
;rdingtotheparticlesizedistribution. ;Itiswidelyacceptedthatthesuspendedsediment ;concentrationcanbedescribedbytheadvective—
;diffusionequation.Forhorizontalorquasi—horizontal
;flows.the3.Dsolutemassbalanceequationcanbe ;integratedoverthewaterdepthtoobtainthe2一D
;depth.integratedadvective—diffusionequation,as
;+—
;OHU
;—
;@+:旦fD盟+
;Ot3x(f
;H
;]+Dyx望Ox+.-’望av)]+,
;(1)
;where谚isthedepthaveragedsuspendedsediment ;concentrationfortheith(i=1,2…?)fraction,D,
;D,Darethedepthaverageddiffusion
;coefficientsinthexanddirections.S,isasource ;termforthethfractionwhichrepresentstheerosion ;anddepositionfluxes.
;Incoastalandestuarinewaters,thewaterdepthH ;mayvarygreatly,thusthemonotonicityofthedepth ;integratedconcentration(0,H)maybedifferentfrom ;thatofthesoluteconcentration().Inordertoachi ;eveahighaccuracyandthemassconservation,Eq.(1) ;couldberecastwithanadditionalsourcetermbeing ;introducedintothe2一Ddepthintegratedadvective—
;diffusionequation.Inthecurrentstudy,thismodifica_ ;tionisincludedinthesedimenttransportequation, ;i.e.,
;3t+O
;x
;+=
;H(盟Ox+ay\
;D.H
;)+吉专-gx+考]+
;S+Sdi(2)
;whereSmistheadditionalsourcetermfortheith ;fraction,whichcanbeformulatedintheformas ;+
;](3)
;Theadditionalsourcetermisshowntobevital ;forthemassconservationinmodellingmassand ;solutetransport.
;Forcohesivesediment<0.063mm),where ;disthesedimentparticlediameter,finEq.(2) ;canbeobtainedas
;i-百Ei-D~(4)
;whereDiisthedepositionalfluxand巨istheero
;sionflux,whosemostwidelyusedexpressionsare[]: ;D/=wsirbi<Z’cd
;0,>
;E.=
;(/l
;巨0,?Le
;i>
;(5a)
;(5b)
;(6a)
;459
;abouttheparameterscouldbefoundinWinterwerp ;andVanKesteren.
;Fornon.cohesivesediment,Sscanbeobtained ;as
;[14]
;(0a一)
;H
;(7)
;whereisthesedimentconcentrationforthefth ;fractionatareferencelevel”a”nearthebed.and
;…
;istheequilibriumsedimentconcentrationforsize ;fractionatthereferenceleve1.Thefallvelocity ;wwillbegreatlyreducedwhenthesedimentcon- ;centrationislargerthan10000mg/1.whichiscalled ;thehinderedsettling.Theseeffectsareincorporatedin ;thefollowingrelationshipforthesettlingvelocityJ ;一
;(8)
;wherePsisthesedimentdensity,isacoefficient ;forthenormalflowcondition,whichtakesavalueof ;about4【15].
;Forequilibriumsuspendedsedimentfluxes, ;f=and0.Thereferencelevel”a”is
;equaltotheequivalentroughnessheightwitha ;minimumvalueofa=0.01.
;Theexpressionusedinthisstudytodefne ;followsfromVanRijn[anditiswrittenas ;~aei=0.0i5D
;n
;S~i
;T
;U
;/
;I’5
;(9)
;where0fisthemediangrainsizeforthefIhfra—
;ction,putisthepercentageoftheithfractioninthe ;looselayerofbed,isthedimensionlessparticle ;sizeandisthetransportstageparameterforthefth ;fraction.
;Inadepth—integrated2一Dmode1.onlythemean
;sedimentconcentration谚isconsidered.Hencethe
;(6b)valueofthereference
;wherewisthefa11velocityofsedimentparticle, ;fbistheflowinducedbedshearstress,cdandce ;arethecriticalshearstressesfordepositionandero. ;sion,respectively,isthenearsedimentconcentra—
;tion,Mistheerosionparameterwhichshouldvary ;withtimeanddepthbutisgenerallyassumedasa ;constant.Theexponent/70isgenerallyunity.Details ;foreberelatedtothe
;whichisassumedtobe
;一
;谚0e
;concentrationmustthere-
;depthmeanconcentration0/,
;inthefollowingform[]
;(10)
;wherefisthedepthmeanequilibriumconcentra- ;tion.CombiningEqs.(7)and(10),oneobtainsthe ;460
;followingneterosionordepositionrate ;where
;W
;s(一妒
;H
;Thedepthmeanequilibriumconcentration ;cannowbecalculatedfromtheratioofthedepthinte—
;gratedequilibriumsuspendedsedimentfluxqto ;thedepthintegratedfluidfluxq,as ;=
;g
;inwhicht2”isaprofilefactor,beingassumedtobe
;1.131钔.
;SuspensionDepositionFlow
;Il…
;L
;PTHT
;Toplayer
;r
;P?HM
;Middlelayer1r
;Pfl//L
;Bottomlayer1
;Fig.1Bedsedimentlayers
;?
;1.3Bedlevelchange
;Foreachfractionofthecohesivesediment,the ;correspondingbedelevationchangeduringAtcan ;bedeterminedby
;l~kZBi
;一
;1(—Ei)0(13)
;Foreachfractionofthenon—cohesivesediment,the ;correspondingbedelevationchangeduringAtcan ;beobtainedfromtheequation
;aZBi
;一
;1(一).(14)
;whereP0istheporosityofthebedlayersediment. ;Withinatimestep,thetotalvariationofthebedlevel
;B
;isobtainedas
;AZ日
;1.4Bedsedimentsizevariation
;Thedeformationofthebed.especiallyduringthe ;degradingprocess.iSdominantlycontrolledbythe ;compositionofthebedmateria1.Thescouredbed ;tendstobearmouredtopreventfurthererosionorto ;becomerefinedinthecaseofdeposition.Toaccount ;fortheinfluenceofthebedsedimentcomposition, ;numericalmodelsweredevelopedtosolvethespatial ;andtemporalvariationsofthesedimentgradationof ;theloosebedlayers.Thiscanbedonebydividingthe ;loosesedimentbedintosevera1vertica1layers.AS ;showninFig.1.theloosebediSdividedintothetop ;middleandbottomlayerswiththethicknessand ;volumetricfractionsofthese1ayersbeingdefinedas ;HT,HM,HLandPTl,PMl,Pl_Irespectively. ;Thesuperscript0indicatesthevaluesoflasttimestep. ;x/kn
;Fig.2LocationofYellowRiverEstuary
;Table1Averagefractionaldiametersandcorresponding ;Duetoerosionordeposition,thefractionper—
;centageofthetoplayerHr+AZ口duringasmall
;timeinterva1canbeobtainedas
;HTl
;七AZB
;HT+AZB
;whereAZ口isthescouredordepositedthicknessoi ;?
;?
;一
;anindividualsedimentfraction
;4000
;3000
;2000
;l000
;0
;0500l500
;t/d
;Fig.3InflowfluxatLijinStationfrom1992to2000 ;120000
;80000
;4OooO
;0
;050010001500
;t/d
;Fig.4SedimentconcentrationinLijinStationfrom1992to
;2000
;Inthecaseofdeposition,i.e.,AZB>0,the ;fractionpercentageofthetoplayeriscalculatedby ;Eq.(16).Thefractionpercentageofthemiddlelayer ;canbecalculatedas
;,AZB?Hr(17a)
;:—
;AZ.PT,+(/-/—
;T-AZ.)P~i
;,?Z<(17b)LH
;M
;，B…T
;Thefractionpercentageofthebottomlayercan ;becalculatedas
;,?Z
;Hl+uj
;—
;AZ
;—
;B
;P
;—
;Mi
;_
;+
;一
;HLPL~
;i
;,?<
;HL+AZB
;(18a)
;(18b)
;Ontheotherhand,inthecaseoferosion,i.e., ;AZ口<0,thepositionofthetoplayershouldbe ;adjusted.Theadjustedfractionpercentageofthetop ;layercanbecalculatedas
;=盟f19)
;Thefractionpercentageofthemiddlelayercanbe ;calculatedas
;=
;46l
;(2O)
;Thefractionpercentageofthebottomlayerkeeps ;unchanged,butthethicknessofthelowerlayeris