海岸动力学英文课件Coastal-Hydrodynam4

CoastalHydrodynamicsCoastalHydrodynamicsChapter4NEARSHORECURRENTS

StatingtypesofcurrentsStatingconceptofradiationstressStatingphenomenaofwaveset-upandwaveset-downStatingcharacteristicsoflongshorecurrents1/33Chapter4NEARSHORECURRENTSSDefinitionChapter4§4.2RadiationStress2.Expressions3.Applications2/33DefinitionChapter4§4.2RadChapter4Thereisastressfieldinwaterwaves,whichissimilartotheReynoldsstressinturbulence.Thisforceisusuallycalledmomentumflux,sinceitisresultedfromtheexchangeofmomentumamongthewaterparticles.1.Definition3/33Chapter4ThereisastressfiChapter4Radiationstressisdefinedastheexcessmomentumfluxinducedbytheexistenceofwavemotion.Itequalsthedifferencebetweenthetotalmomentumfluxesandthehydrostaticpressureintheabsenceofwaves.4/33Chapter4RadiationstressisChapter4Theradiationstressacrosstheplanex=constantinthedirectionofwaveadvanceisTheradiationstressofy-momentumacrosstheplaney=constantThetransverseradiationstressinthedirectionofwavesis5/33Chapter4TheradiationstressChapter4Ifthex-axisisplacedinthedirectionofwaveadvanceandthey-axisparalleltothewavecrests,thentherearetwononzerocomponentstotheradiationstress:thex-andy-fluxesof

x-momentumandy-momentum.2.Expressions6/33Chapter4Ifthex-axisisplaChapter4Inthemoregeneralcase,whenalinearwaveispropagatingatsomeangleα

tothex-axis,theradiationstresscanbeexpressedas7/33Chapter4InthemoregeneralChapter4Radiationstresshasbeenprovedtobeaverypowerfultoolinthestudyofavarietyofoceanographicphenomena.Inthecontextoflittoralprocesses,ithasbeenusedtopredictchangesinthemeanwaterlevel(set-upandset-down)inthenearshoreregionandtoanalyzethegenerationoflongshorecurrents.Otherapplicationshavebeentothegenerationofsurfbeat,theinteractionofwaveswithsteadycurrents.3.Applications8/33Chapter4RadiationstresshasWaveset-downChapter4§4.3WaveSet-downandWaveSet-up2.Waveset-up

9/33Waveset-downChapter4§4.3Chapter4Ifoneconsiderswavesarrivingatthebeachwiththeircrestsparalleltotheshoreline,therewillbeashorewardfluxofmomentum.Thismomentumfluxenteringthenearshorezonewiththeincomingwavescannotsimplydisappearbutrathermustbebalancedbyopposingforceswhichwilldissipatethemomentum.10/33Chapter4IfoneconsiderswavChapter4Consideratrainofwavesencounteringthecoastwithnormalincidence.Forashortdistancedx,aforcebalancecanbedeveloped.Thepressuregradientoftheslopingwatersurfacebalancesthechangeoftheincomingmomentum.Thereisthereforeachangeinmeanwatersurfaceslopewheneverthereisachangeintheradiationstress.11/33Chapter4ConsideratrainofChapter4Waveset-downisaphenomenonthatthemeansealevelfallsbelowthestillwaterlevelfromoffshoretothebreakingpoint.Basedontheradiationstressconcept,theamountofwaveset-downisfoundtobe1.Waveset-down12/33Chapter4Waveset-downisapChapter4Thisrelationshipdescribesagradualreductionofthemeanwaterlevelastheshorelineisapproached.Themeandisplacementinwaterlevelfromthestillwaterlevelisalwaysnegative,becomingmoresoasthewaveentersshallowwateruntilbreakingcommences.Thatistosay,themeansealevelfallsbelowthestillwaterlevel.13/33Chapter4ThisrelationshipdeChapter4Atthebreakingpoint,themaximumamountofwaveset-downisTheset-downislessthan5%ofthebreakingdepthbecausethebreakingcriterionequals0.78.14/33Chapter4AtthebreakingpoinChapter4Waveset-upisaphenomenonthatthemeansealevelrisesabovethestillwaterlevelinsidethesurfzone.Insidethesurfzone,basedonaspillingbreakermodel,theamountofwaveset-upcanbeexpressedas2.Waveset-up15/33Chapter4Waveset-upisapheChapter4Theaboveexpressionindicatesthatthemeanwatersurfacedisplacementincreaseslinearlywithdepthsastheshoreisapproached.Inthesurfzone,themeansealevelslopeisconstantandproportionaltothebeachslope.Thewatersurfaceslopeprovidesahydrostaticpressuregradientdirectedoffshoretocounterthechangeofwavemomentumbybreakingacrosstheshoreline.16/33Chapter4TheaboveexpressionChapter4Themaximumvalueofwaveset-upattheshorelineisForγ=0.8,themaximumamountofset-upisabout15%ofthebreakerdepthorabout25%ofthebreakerheight.17/33Chapter4ThemaximumvalueofChapter4Waveset-downandset-up18/33Chapter4Waveset-downandseMeanvelocityChapter4§4.4LongshoreCurrents2.Horizontalvelocitydistribution19/333.NumericalmodelingMeanvelocityChapter4§4.4Chapter419/33Longshorecurrent&longshoredriftChapter419/33LongshorecurreChapter4Bowen(1969)hassuggestedthatthelongshorecurrentduetoanobliquewaveapproachmaybegeneratedbythelongshorecomponentoftheradiationstress.1.Meanvelocity20/33Chapter4Bowen(1969)hassugChapter4FollowingBowen’ssuggestionanddevelopment,Longuet-Higgins(1970)derivedthefollowingrelationshipThisderivationisbasedontheassumptionthat

Sxy

isdissipatedinthenearshorezonebytheproductionofthelongshorecurrentanditsassociatedbottomdrag.

21/33Chapter4FollowingBowen’ssuChapter4ThesandtransportstudiesofKomarandInman(1970)hadearliersuggestedthatThiswaspromptedbytheagreementbetweentwoseeminglyindependentestimatesofthelittoralsandtransport,theagreementonlybeingpossibleifthelongshorecurrentduetoanobliquewaveapproachisgivenbytherelationshipoftheaboveequation.22/33Chapter4ThesandtransportsChapter4Itwasfoundthattheremaininglaboratorymeasurementsaswellasallthefielddataareinagreementwiththeaboveequation.Sincetheagreementismuchbetterthanwiththeotherexistingtheories,andsinceithasthebesttheoreticalbasis,beingderivablefromradiationstressconcepts,thisequationoffersthebestavailablepredictionofthelongshorecurrentvelocityatmid-surfgeneratedbywavesbreakingatanangletotheshoreline.23/33Chapter4ItwasfoundthatthChapter4Inordertoestablisharelationshipbetweenthelongshorecurrentandcoastalsedimentphenomena,itisnecessarytoknowthehorizontalandverticallongshorecurrentvelocitydistributionsinthenearshorearea.Extensiveanalyseshavebeencarriedoutonthehorizontaldistribution.However,theverticaldistributionisstillaproblemtobesolvedinthefuture.2.Velocitydistribution24/33Chapter4InordertoestablisChapter4ConsiderthelocalspatialchangeofSxyasthedrivingthrust,andincludeahorizontaleddyviscosity,ahorizontalmixingeffectwhichproducesanonshore-offshoretransferofthemomentum.Againusingtheradiationstressapproachleadstothesolution25/33Chapter4ConsiderthelocalsChapter4whereXandVarenon-dimensionalvariables,representingtherelativedistanceandrelativevelocity,26/33Chapter4whereXandVarenoChapter4Afamilyoflongshorecurrentprofilesacrossthesurfzone27/33Chapter4AfamilyoflongshorChapter4ThedimensionlessparameterPreflectsthesignificanceofthehorizontaleddytransfer:thelargerthevalueofPthemoreimportantthiseffect.isanon-dimensionalparameterrepresentingtherelativeimportanceofthehorizontalmixingandbottomfriction.28/33Chapter4ThedimensionlesspaChapter4ComparisonofthesolutionswiththelaboratorymeasurementsofthevariationsinvelocityacrossthenearshoresuggestsarangeofPfrom0.1upto0.4.ItisseenthatforthesevaluesofPthecurrentshouldbelargelyconfinedtothesurfzone,decreasingrapidlyoutsidethebreakerzone.Thisconformswithwhatisobservedinnature.29/33Chapter4ComparisonofthesoChapter4Theinclusionofhorizontalmixingeffectivelycouplestogethertheadjacentelementalwatercolumns,resultinginadiffusioninadirectionperpendiculartoshore.Thelateraldiffusionofmomentumalsoenablesthemomentumfluxinsidethesurfzonetodrivelongshorecurrentsoutsidethesurfzone.30/33Chapter4TheinclusionofhorChapter431/333.NumericalmodelingChapter431/333.NumericalmoChapter432/33Chapter432/33THANKYOU“CoastalHydrodynamics”——chapter4THANKYOU“CoastalHydrodynamic注：文档资料素材和资料部分来自网络，如不慎侵犯了您的权益，请联系文库客服，我们将做删除处理，感谢您的理解。注：文档资料素材和资料部分来自网络，如不慎侵犯了您的权益，请36CoastalHydrodynamicsCoastalHydrodynamicsChapter4NEARSHORECURRENTS

StatingtypesofcurrentsStatingconceptofradiationstressStatingphenomenaofwaveset-upandwaveset-downStatingcharacteristicsoflongshorecurrents1/33Chapter4NEARSHORECURRENTSSDefinitionChapter4§4.2RadiationStress2.Expressions3.Applications2/33DefinitionChapter4§4.2RadChapter4Thereisastressfieldinwaterwaves,whichissimilartotheReynoldsstressinturbulence.Thisforceisusuallycalledmomentumflux,sinceitisresultedfromtheexchangeofmomentumamongthewaterparticles.1.Definition3/33Chapter4ThereisastressfiChapter4Radiationstressisdefinedastheexcessmomentumfluxinducedbytheexistenceofwavemotion.Itequalsthedifferencebetweenthetotalmomentumfluxesandthehydrostaticpressureintheabsenceofwaves.4/33Chapter4RadiationstressisChapter4Theradiationstressacrosstheplanex=constantinthedirectionofwaveadvanceisTheradiationstressofy-momentumacrosstheplaney=constantThetransverseradiationstressinthedirectionofwavesis5/33Chapter4TheradiationstressChapter4Ifthex-axisisplacedinthedirectionofwaveadvanceandthey-axisparalleltothewavecrests,thentherearetwononzerocomponentstotheradiationstress:thex-andy-fluxesof

x-momentumandy-momentum.2.Expressions6/33Chapter4Ifthex-axisisplaChapter4Inthemoregeneralcase,whenalinearwaveispropagatingatsomeangleα

tothex-axis,theradiationstresscanbeexpressedas7/33Chapter4InthemoregeneralChapter4Radiationstresshasbeenprovedtobeaverypowerfultoolinthestudyofavarietyofoceanographicphenomena.Inthecontextoflittoralprocesses,ithasbeenusedtopredictchangesinthemeanwaterlevel(set-upandset-down)inthenearshoreregionandtoanalyzethegenerationoflongshorecurrents.Otherapplicationshavebeentothegenerationofsurfbeat,theinteractionofwaveswithsteadycurrents.3.Applications8/33Chapter4RadiationstresshasWaveset-downChapter4§4.3WaveSet-downandWaveSet-up2.Waveset-up

9/33Waveset-downChapter4§4.3Chapter4Ifoneconsiderswavesarrivingatthebeachwiththeircrestsparalleltotheshoreline,therewillbeashorewardfluxofmomentum.Thismomentumfluxenteringthenearshorezonewiththeincomingwavescannotsimplydisappearbutrathermustbebalancedbyopposingforceswhichwilldissipatethemomentum.10/33Chapter4IfoneconsiderswavChapter4Consideratrainofwavesencounteringthecoastwithnormalincidence.Forashortdistancedx,aforcebalancecanbedeveloped.Thepressuregradientoftheslopingwatersurfacebalancesthechangeoftheincomingmomentum.Thereisthereforeachangeinmeanwatersurfaceslopewheneverthereisachangeintheradiationstress.11/33Chapter4ConsideratrainofChapter4Waveset-downisaphenomenonthatthemeansealevelfallsbelowthestillwaterlevelfromoffshoretothebreakingpoint.Basedontheradiationstressconcept,theamountofwaveset-downisfoundtobe1.Waveset-down12/33Chapter4Waveset-downisapChapter4Thisrelationshipdescribesagradualreductionofthemeanwaterlevelastheshorelineisapproached.Themeandisplacementinwaterlevelfromthestillwaterlevelisalwaysnegative,becomingmoresoasthewaveentersshallowwateruntilbreakingcommences.Thatistosay,themeansealevelfallsbelowthestillwaterlevel.13/33Chapter4ThisrelationshipdeChapter4Atthebreakingpoint,themaximumamountofwaveset-downisTheset-downislessthan5%ofthebreakingdepthbecausethebreakingcriterionequals0.78.14/33Chapter4AtthebreakingpoinChapter4Waveset-upisaphenomenonthatthemeansealevelrisesabovethestillwaterlevelinsidethesurfzone.Insidethesurfzone,basedonaspillingbreakermodel,theamountofwaveset-upcanbeexpressedas2.Waveset-up15/33Chapter4Waveset-upisapheChapter4Theaboveexpressionindicatesthatthemeanwatersurfacedisplacementincreaseslinearlywithdepthsastheshoreisapproached.Inthesurfzone,themeansealevelslopeisconstantandproportionaltothebeachslope.Thewatersurfaceslopeprovidesahydrostaticpressuregradientdirectedoffshoretocounterthechangeofwavemomentumbybreakingacrosstheshoreline.16/33Chapter4TheaboveexpressionChapter4Themaximumvalueofwaveset-upattheshorelineisForγ=0.8,themaximumamountofset-upisabout15%ofthebreakerdepthorabout25%ofthebreakerheight.17/33Chapter4ThemaximumvalueofChapter4Waveset-downandset-up18/33Chapter4Waveset-downandseMeanvelocityChapter4§4.4LongshoreCurrents2.Horizontalvelocitydistribution19/333.NumericalmodelingMeanvelocityChapter4§4.4Chapter419/33Longshorecurrent&longshoredriftChapter419/33LongshorecurreChapter4Bowen(1969)hassuggestedthatthelongshorecurrentduetoanobliquewaveapproachmaybegeneratedbythelongshorecomponentoftheradiationstress.1.Meanvelocity20/33Chapter4Bowen(1969)hassugChapter4FollowingBowen’ssuggestionanddevelopment,Longuet-Higgins(1970)derivedthefollowingrelationshipThisderivationisbasedontheassumptionthat

Sxy

isdissipatedinthenearshorezonebytheproductionofthelongshorecurrentanditsassociatedbottomdrag.

21/33Chapter4FollowingBowen’ssuChapter4ThesandtransportstudiesofKomarandInman(1970)hadearliersuggestedthatThiswaspromptedbytheagreementbetweentwoseeminglyindependentestimatesofthelittoralsandtransport,theagreementonlybeingpossibleifthelongshorecurrentduetoanobliquewaveapproachisgivenbytherelationshipoftheaboveequation.22/33Chapter4ThesandtransportsChapter4Itwasfoundthattheremaininglaboratorymeasurementsaswellasallthefielddataareinagreementwiththeaboveequation.Sincetheagreementismuchbetterthanwiththeotherexistingtheories,andsinceithasthebesttheoreticalbasis,beingderivablefromradiationstressconcepts,thisequationoffersthebestavailablepredictionofthelongshorecurrentvelocityatmid-surfgeneratedbywavesbreakingatanangletotheshoreline.23/33Chapter4ItwasfoundthatthChapter4Inordertoestablisharelationshipbetweenthelongshorecurrentandcoastalsedimentphenomena,itisnecessarytoknowthehorizontalandverticallongshorecurrentvelocitydistributionsinthenearshorearea.Extensiveanalyseshavebeencarriedoutonthehorizontaldistribution.However,theverticaldistributionisstillaproblemtobesolvedinthefuture.2.Velocitydistribution24/33Chapter4InordertoestablisChapter4ConsiderthelocalspatialchangeofSxyasthedrivingthrust,andincludeahorizontaleddyviscosity,ahorizontalmixingeffectwh