美赛培训论文

FormationandVariationoftheGreatPacificGarbagePatchAbstractInthispaper,webuildamodelbyutilizedynamicanalogtoexpoundtheformationoftheoceangarbagepatch.Ourdestinationistotrackthelitterdebrisandforecastitsfutureconditionstohelpmanagingit.Aftertheanalysis,wefindthatthevelocityoftrashalleviatesastimegoeson.Trashdoesitsmotionintwoprobableways,oneisduetoresistancesgivenbyseawater,andanotherisduetodampedvibration.Byusingclassicphysicaltheories,wecapturemainmotivespropellingtrashintotheSouthPacificGyre.That’showthegreatgarbagepatchforms.Accordingtothemodelandtheitsresult,weformulatethemonitoringprogram.Comparedwiththephysicaltruth,themodelalsohassomeunsatisfactoryaspects,butithassomereference.IntroductionWhereeveristheworld’slargestdump?ItislocatedinthePacificOcean,aboutonethousandsixhundredkilometerswestofCalifornia,calledtheGreatPacificOceanGarbagePatch.Accordingtopertinentdata[1],itistenmilliontonsofdebrislitterthatispilingupthere,likeaplasticsoupwhenpeoplearelookingahead.And80percentofthetrashisfrommaincontinents,10percentconsistsofusednetsorotherfishingtoolsandtheother10percentoftrashisfrompassing-byships.Mostofthegarbageislandsareinoceanicgyres.Nowadays,awidevarietyoftechnicalandscientificproblemsassociatedwiththisdebrismassarecomingtolight.Butuntilnow,noonecanreasonoutit’scoverageareaexactlyandthegreateconomiclossesecologicalimpactandthePacificOceanGyrehascaused.Long-termeffectivemethodsaresearchedtoobjectivelycharacterizetheGyre.TheoceancurrentisthemechanismoftheGreatPacificOceanGarbagePatch.Inourpaper,wewilltakethesouthpacificoceangarbagepatchforexample,focusingonhowthedebrislitterdriftsinthefluid,assemblesinquantity,distributesundertheeffectofoceancurrentsin.Afterwards,inaccordancewithourmodel,weprojectprocessreasonablesuggestionstomonitortheGyre,trackingit’sgrowth.Assumptions1.Regardlessoftimeandgeographicalposition’simpactsonthespeedoftheoceancurrents,weconsiderthespeedasconstantvalue.2.Accordingtothedatum[2],wedesignatethespeedofthewestwinddriftvp1as1.4km/h,thatofPeruCurrentvp2as1km/h,thatofthesouthequatorialwarmcurrentasvp33km/h,thatofthenorthAustraliacurrentasvp41.4km/h.3.RegardtheflowofthecurrentsasstationaryflowandtheseawaterasNewtonianfluid,whichmeanstheviscosityoftheseawaterisconstant.4.Considertheleveloftheseaisinlaminarflow.5.Themasspoint’smotionintheseacanbeinfluencedbytheoceancurrentnomatterhowfarthemallpointisawayfromit.6.Themasspoint’smotionissynthesizedbythesub-movementofperoceancurrentregardlessofeffectsofotherfactors.TheModelInourmodel,wewillutilizedynamicanalogtoexpoundtheformationoftheoceangarbagepatch.Themodelsubstitutesstraightlinesforoceancurrentswhichformthegyre,inthemodeltheorientationofthestraightlinerepresentativeoftheflowdirectionandthespeedvalueretrospecttotheassumptionNo.4.Sequentially,wesimplifythephysicaltruthasthatshowninthefigure1.(DuetothechangeofthedirectionofthePeruCurrentonpassage,thesimplifiedmodelreplacestowstraightlines,whichareofthesamespeedbutdifferentdirection,ofthePeruCurrent.)Figure1:theDistributionoftheOceanCurrentsintheSouthPacificOceanThen,ourmodeltalksoverhowtheoceancurrenteffectthemasspoint’smovement,morespecifically,theeffectonthevelocityofthedirectionparalleltothelineandperpendiculartotheline.Let’sdiscusstheeffectonthemasspoint’svelocityofthedirectionparalleltothelinefirstly.AccordingtotheassumptionNo.3andNo.4andtherelativeinformation[3],wecandescribetheoceancurrentflowasone-dimensionalsteadyflow.OnthebasisofNavier-StokesEquationshowbelow2222221()yyyyuuudupYxxyzdtYmeansthemassforceofthedirectionY-axis,inourmodel0Y;ρmeansthedensityofseawater;νmeansthekinematicviscosityofseawater,,μmeansthedynamicviscosityofseawater.Wecansimplifytheequationaboveandgettheonebelow221xdudpdydxIntegrateandget21212xdpuycycdx(1)Soweplugtowboundaryconditions(2)shownbelowintotheformula(1)0::0xcurrentxyuuyuintegralconstant12cc、isdetermined112dpcdx,2currentcuSince0dpdx,socurrentvu(2)Wecanmakeaconclusionthatthemasspoint’svelocityinthedirectionparalleltotheoceancurrentisthesameasthatoftheoceancurrent.Secondlywefocusonthemasspoint’velocityinthedirectionperpendiculartotheoceancurrent’sdirection.Havingconsultedsomematerials[4],wedecidethattheoceancurrent’simpactonfloatersinthedirectionperpendiculartotheoceancurrent’sdirectionisequivalenttowavedampedoscillation.Thefartherawayfromthewavesource,theweakertheoscillationis,whichmeansinourmodelthatthesmallerthefloater’svelocityinthedirectionperpendiculartotheoceancurrent’sdirectionis.AndthevelocityvalueisdcvAe(3)Ameansoscillationrange,1A;βmeansthedampingcoefficient,0.2;dmeansthedistancethepointfromthesourceortheline;theevolutionmeansvelocityistheenergy’sevolution.Thedistancedisdeterminedbytheformulabelow0022||axbycdab(4)Thenweshoulddecidetheequationsofthestraightlinesoftheoceancurrents.Accordingtothefigure1andourestimationoftheintercepts,theequationsareshownbelow111:tanlyx222:tan(8200)lyx333:tan4000lyx444:tan(1000)lyx555:tan(7700)lyxSothedistancesthatanypointawayfromthelinesare100121|