stratification of suspended sediment in open 在开放的悬浮泥沙分层

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1、Rte-bookSuspSedStrat.docSTRATIFICATIONOFSUSPENDEDSEDIMENTINOPENCHANNELFLOWGaryParkerThisdocumentisacompaniontotheExcelworkbookRte-bookSuspSedDensityStrat.xls.DefinitionsConsidersteady,equilibriumopenchannelflowoveranerodiblebedinawidechannelwithupwardnormalprofiles

2、ofstreamwisevelocityandvolumesuspendedsedimentconcentration,wherezdenotesacoordinateupwardnormalfrombed.TheflowhasdepthH,shearvelocityandshearvelocityduetoskinfriction.Thebedhascompositeroughnesskc,wherekcisgivenaswhereUdenotesdepth-averagedflowvelocity.Intheabsenc

3、eofbedformskcbecomesequaltothegrainroughnessks.Intheaboverelations,.Thewaterhasdensityrandkinematicviscosityn.ThesedimentisassumedtobeuniformwithsizeD,densityrsandfallvelocityvs.ThesubmergedspecificgravityofthesedimentisgivenasandtheexplicitparticleReynoldsnumberRe

4、pisgivenaswheregdenotesgravitationalacceleration.ParticlefallvelocityvsisspecifiedbyadimensionlessrelationoftheformwhereandthefunctionalrelationshipitselfisgivenbyDietrich(1982).Basicforms5Rte-bookSuspSedStrat.docTheequationofmomentumconservationfortheflowtakesthef

5、orm(1)wherentdenotesakinematiceddyviscosity.Thecorrespondingformforconservationofsuspendedsedimentis(2)Eddyviscosityntisspecifiedinthefollowingform:(3)wherekdenotestheKarmanconstant,F1andF2arespecifiedfunctions,andRidenotesthegradientRichardsonnumber,givenby(4)Theb

6、ottomboundaryconditionforvelocityisdeterminedbyamatchtotheroughlogarithmiclawatnormalizedreferencebedelevationzr:(5)wherekdenotestheKarmanconstant(0.4).Thebottomboundaryconditionforconcentrationofsuspendedsedimentislikewisegivenintermsofaspecificationofreferencebed

7、concentrationatzr.Intheimplementationoftheworkbookzrissetequalto0.05.DimensionlessformsDefinedimensionlessvelocityandconcentrationasfollows:5Rte-bookSuspSedStrat.docEquations(1),(2),(4)and(5)canthenbereducedto(6)(7)(8)(9)where(10a,b)Inaddition,thenear-bedconditionf

8、ornormalizedconcentrationcbecomes(11)FormsforthefunctionsF1andF2ThestandardformforthefunctionF1istheparabolicone(12)SmithandMcLean(1977)offerthea