Environmentaldispersioninwetlandflow

EnvironmentaldispersioninwetlandflowL.Zenga,G.Q.Chena,*,H.S.Tangb,Z.WuaaStateKeyLaboratoryofTurbulenceandComplexSystems,DepartmentofMechanicsandAerospaceTechnology,CollegeofEngineering,PekingUniversity,Beijing100871,ChinabDepartmentofCivilEngineering,CityCollege,CityUniversityofNewYork,NY10031,USAarticleinfoArticlehistory:Received12January2010Accepted19February2010Availableonline24February2010Keywords:WetlandflowEnvironmentaldispersionContaminantemissionEnvironmentalfluidmechanicsabstractForthetypicalcaseofapulsedcontaminantemissionintoashallowwetlandchannel,atheoreticalanalysisispresentedinthispaperforthedecayofthewidth-averagedmeanconcentrationunderenvironmentaldispersion.Thevelocityprofileofafullydevelopedsteadyflowthroughthewetlandchannelisobtainedwiththatforthewell-knownplanePoiseuilleflowasaspecialcase.Anenvironmentaldispersionmodelforthemeanconcen-trationisdevisedasanextensionofTaylor’sclassicanalysisondispersion,andcorrespond-ingenvironmentaldispersivityisobtainedbyAris’smethodofmomentsandillustratedwithanasymptotictimevariationwithstemdominated,transitional,andwidth-stemdominatedstages.Analyticalsolutionforthelongitudinaldecayofmeanconcentrationduetoenvironmentaldispersionisrigorouslyderivedandcharacterizedwithmultipletimescales.2010ElsevierB.V.Allrightsreserved.1.IntroductionWetlandshavereceivedincreasingattention,duetotheirsignificantecosystemservices[1–3],intermsofwatersupply,climateregulation,biodiversityconservation,contaminantdegradation,etc.[4,5].Forecologicalriskassessment,ecologicalrestorationandwastewatertreatmentengineeringassociatedwithwetlands[6–8],whatofprimaryinterestmightbetheenvironmentaldispersionofsolutes[9,10].Flowandmasstransportinwetlandsarecharacteristicofmulti-scales[11,12].Complexastheyare,thedetailsoftheflowandsolutetransferinthedomainofirregularvicinitybeloworatthescaleofstemarethemselvesnotinterestingforprac-ticalapplications.Instead,superficialtransportfieldsatthephaseaveragedscale,outofthephaseaverage[13,14]tosmearoutthediscontinuitybetweenthefluidintheirregularvicinityandthesolidframe(i.e.vegetationandmedia),asacontin-uousdistributionintheentiredomainofconcernisconcerned.Environmentaldispersionisduetothecross-sectionalvariationofthesuperficialvelocity[15].Inenvironmentalhydrau-licdesignandassessment,superficialvelocityisusuallymodelledbyDarcy’slaworManning’sequations[16].However,theDarcy’slawisvalidonlyforseepageinporousmediaatlowReynoldsnumbernotupto10[17],whichisnotthetypicalcaseofthewetlandswithacharacteristiclengthassociatedwithstemdiameterofthevegetationplant[18].ThoughManning’sequations,originallyusedforflowinopenchannels,maytakethespecialcasewithsubmergedaquaticvegetationintocon-siderationtoacertainextentwithamodificationtoaccountforthefrictioneffect,theextensiveinteractionbetweenthewatercolumn,andtheemergentandfloatingvegetationcannotbereasonablyreflected.Toaccountfortheresistancetoflowduetoemergentplants,peatandlitter,amodifiedSaint-Venantequationswasproposedtodescribethevelocitythroughanidealizedwetlandwithvegetationrepresentedbyanaggregateofrigidcylinders[19].However,themodelneglectsthe1007-5704/$-seefrontmatter2010ElsevierB.V.Allrightsreserved.doi:10.1016/j.cnsns.2010.02.019*Correspondingauthor.Tel.:[phone];fax:[phone].E-mailaddress:[e-mail](G.Q.Chen).CommunNonlinearSciNumerSimulat16(2011)206–215ContentslistsavailableatScienceDirectCommunNonlinearSciNumerSimulatjournalhomepage:fieldexperiments[11,20–22].Basedonanassumptionofbalancebetweenvegetationdragandpressuredifference,aformuladependentonvegetationmorphologywasdevelopedtopredicttheverticalvariationofsuperficialflowinsaltmarshwetland[11].Sincetheformulaneglectstheviscousstressinwatercolumnandbedfrictiontoflow,itisnotappli-cableforwetlandswithsparseemergentvegetation.Thoughlateraldistributionoflongitudinalvelocityhasimportantef-fectsonenvironmentaldispersion,todatetheanalyticalsolutiontocharacterizeitisstillpoorlydeveloped.Todescribeenvironmentaldispersioninwetlandsattheholisticscale,classicstudiesonTaylordispersion[23]inpurefluidflowscanbeveryillustrative,sinceTaylor’sclassicanalysisfordispersionofsolublematterinsolventflowingslowlythroughanemptytubehasbeenwidelyextendedtoavarietyofenvironmentalflows,suchasflowsinopenchannels,rivers,estuariesetc.[24–35].Fortheenvironmentaldispersioninthewetlands,someendeavorshavebeenmade,focusingontheimpactsofverticaldistributionoflongitudinalsuperficialvelocityonenvironmentaldispersivity.BasedonTaylor’sconceptofdispersionregardingtoenvironmentaltransport,LightbodyandNepfestimatedtheenvironmentaldispersivityinanemergentcanopyasasumofthestem-scaledispersioncoefficientduetowake-shearandthedepth-scaledispersioncoef-ficientduetotheverticalvariationofvelocity[11,36].Byuseoftwo-zonemodelortwo-boxmodel,environmentaldisper-sioninwetlandswithsubmergedaquaticvegetationisexplored[8,9,37].Theseenvironmentaldispersivities,however,werederivedforanidealize