waveguide model of coherent structures in the ：在相干结构的波导模型

,1,23,45,2/U,U/L|IMK,|/U,|IMK,|K,60/U,10/,20/21331,26,3N,214N,21,1,1B7R104105,2T1T/1T1,T1,T1,T1,U,V,W,1A1B1A3,B,0,12IIK1K21,27,31,20093022BORODULINVI,KACHANOVYS,ROSCHEKTAYEVAPEXPERIMENTALDETECTIONOFDETERMINISTICTURBULENCE/JOURNALOFTURBULENCEVOL12,N232011P1343GKHUJADZE,RNGUYENVANYEN,KSCHNEIDER,MOBERLACKANDMFARGECOHERENTVORTICITYEXTRACTIONINTURBULENTBOUNDARYLAYERSUSINGORTHOGONALWAVELETSIN13THEUROPEANTURBULENCECONFERENCEWARSAW,1215SEPTEMBER2011UNIVERSITYOFWARSAW,POLANDBOOKOFABSTRACTS4LANDAHLMTAWAVEGUIDEMODELFORTURBULENTSHEARFLOWJFLUIDMECH,1967,VOL29,PT3,P4414595ZHAROVVAWEAKLYNONLINEARPULSATIONMODELSINLAMINARANDTURBULENTBOUNDARYLAYERSWESTEASTHIGHSPEEDFLOWFIELDCONFERENCE1922NOVEMBER2007MOSCOW,RUSSIA6DAVIDSONRCMETHODINNONLINEARPLASMATHEORY,NYLACADPRESS,1972PUREANDAPPLIEDPHYSICSVOL377,1974WAVEGUIDEMODELOFCOHERENTSTRUCTURESINTHEDEVELOPEDTURBULENTBOUNDARYLAYERINONEMODEAPPROXIMATIONVLADIMIRZHAROVDEPARTMENTOFTHEORETICALRESEARCH,CENTRALAEROHYDRODYNAMICINSTITUTETSAGI,ZHUKOVSKI,MOSCOWREGION,RUSSIANFEDERATIONTHEEARLYHIGHACCURACYEXPERIMENTALSTUDIES1HAVESHOWNTHEDEVELOPEDTURBULENTBOUNDARYLAYERCONTAINSTHEORGANIZEDVORTICALSTRUCTURESWHICHDEFINEMANYPHYSICALPROPERTIESOFTHESEFLOWSLASTEXPERIMENTAL2ANDNUMERICAL3RESEARCHESCONFIRMTHEEXISTENCEOFTHECOHERENTSTRUCTURESITISINTERESTINGTOCONSTRUCTASIMPLIFIEDMATHEMATICALMODELFORTHISPHENOMENONFROMTHENAVIERSTOKESEQUATIONSTHEWAVEGUIDEMODELOFDEVELOPEDBOUNDARYLAYER4ISONEOFTHEMEANINGFULAPPROACHTOSOLVETHISPROBLEMBYANALOGYTOTHISMODELTHENONLINEAREQUATIONFORFOURIERCOMPONENTSOFTHEVERTICALVELOCITYOFTOLLMIENSCHLICHTINGTSWAVESWASOBTAINED5FROMNAVIERSTOKESEQUATIONSFORPULSATIONSINTHEBOUNDARYLAYERUPTOTHIRDPOWERBYAMPLITUDEATONEMODEAPPROXIMATIONTHEEQUATIONCONTAINSTHESMALLPARAMETER2/UWHEREISTHEMOMENTUMTHICKNESS,UISTHEFREESTREAMVELOCITYTHEINTERRELATIONSCALINGLAW/L|IMK,|INTRODUCEDFORMATCHINGOFTHEEQUATIONMEMBERS,WHERE|IMK,|ISTHEMINIMUM,BYK,DECREMENTOFTHEMAINMODEOFTSWAVETHEAMPLITUDESOFTHEWAVESREPRESENTEDASTHESUMOFCOHERENTANDINCOHERENTPARTSGOVERNEDBYSYSTEMOFEQUATIONSWITHSMALLPARAMETERFIGURE1AFIGURE1BFIGURE1ATHE3WAVERESONANCECURVE,BTHEREGIONOFTHEWAVEVECTORS,0,12IIK1KWHERETHEWEIGHTINGFACTORSAREPOSITIVEATDIFFERENT0THEMULTISCALEMETHOD6WASUSEDFORSOLVINGTHISSYSTEM0/U,10/,20/2ASARESULTTHEEQUATIONOFMULTIPLE3WAVERESONANCEWASOBTAINEDFORTHECOHERENTSTRUCTUREAT1SCALEA3WAVERESONANCECURVE,ISTHEEIGENVALUEOFTHEMAINMODEOF012RRRKK012KRERTSWAVESISDEPICTEDUPONTHEFIGURE1AANDTHEPICTURESHOWSTHEAPPEARANCEOFLONGITUDINALVORTICESINTHETURBULENTBOUNDARYLAYERFLOWFORTHETWOPOINTCORRELATIONFUNCTIONOFTHEINCOHERENTPARTWEGOTCLOSEDINTEGRODIFFERENTIALEQUATIONINTHE2SCALETHECLOSUREOFTHECHAINOFTHEMULTIPOINTCORRELATIONEQUATIONSISDEFINEDBYTHEEXISTENCEOFSMALLPARAMETER6THISEQUATIONCONTAINSTHESOURCEMEMBERDEFINEDBYTHECOHERENTSTRUCTUREITISSHOWNTHATDYNAMICSOFMULTIPLE3WAVERESONANCESYSTEMINTHEDISCRETEREPRESENTATIONOFNTRIPLETSSATISFIESINVARIANTQUADRATICFORMOFCOMPLEXWAVEAMPLITUDESWITHREALWEIGHTINGFACTORSIFTHEWEIGHTINGFACTORSAREPOSITIVETHESYSTEMISGOVERNEDBYFINITEMOTIONATTHESURFACEOFTHEUNITSPHEREOF214NDIMENSIONATPROPERNORMALIZATIONOFTHEAMPLITUDESTHENORMALIZATIONOFTHEQUADRATICFORMISPOSSIBLEDUETOTHEEXISTENCEOFTHETRANSFORMATIONOFAMPLITUDESANDTIMEWHICHLEAVETHEMULTIPLE3WAVERESONANCEEQUATIONUNVARIEDTHEFACTOROFTHISTRANSFORMATIONSATISFIESTHEEQUATIONAT2SCALETHENUMERICALANALYSISONTHEBASISOFTHEMUSKERPROFILEOFTHELONGITUDINALVELOCITYOFTHETURBULENTBOUNDARYLAYERSHOWSTHEEXISTENCEOFTHEWAVENUMBERREGIONWHERETHESEWEIGHTINGFACTORAREPOSITIVETHEWAVENUMBERREGIONOFINCLINEDWAVESWHERETHESEFACTORSAREPOSITIVEISSHOWNINFIGURE1BTHEREFORETHISREGIONCANBEBROUGHTINCORRESPONDENCEWITHTHECOHERENTSTRUCTURECOMPARISONOFTHESCALINGLAWWITHEXPERIMENTALDATA7ATTHERANGEOFREYNOLDSNUMBERR104105,ISTHEBOUNDARYLAYERTHICKNESSBYVELOCITY,SHOWSGOODCOINCIDENCEFIGURE2MEANVALUES,T1,T1,T1,T1,HERE,ANDU,V,W,ARECOMPONENTSOFVELOCITYDEFINEDBYTHECOHERENTSTRUCTURE,AREDEFINEDTOO1/TTHEWORKISSUPPORTEDBYRFBRPROJECTN110800832FIGURE2COMPARISONOFTHESCALELAWWITHEXPERIMENTALDATA1,27,3THEPRESENTTHEORYREFERENCES1BELOTSERKOVSKIIOM,KHLOPKOVYUI,ZHAROVVA,GORELOVSL,KHLOPKOVAYUORGANIZEDSTRUCTURESINTURBULENTFLOWSANALYSISOFEXPERIMENTALWORKSDEVOTEDTOBOUNDARYLAYERMMIPT,2009302P2BORODULINVI,KACHANOVYS,ROSCHEKTAYEVAPEXPERIMENTALDETECTIONOFDETERMINISTICTURBULENCE/JOURNALOFTURBULENCEVOL12,N232011P1343GKHUJADZE,RNGUYENVANYEN,KSCHNEIDER,MOBERLACKANDMFARGECOHERENTVORTICITYEXTRACTIONINTURBULENTBOUNDARYLAYERSUSINGORTHOGONALWAVELETSIN13THEUROPEANTURBULENCECONFERENCEWARSAW,1215SEPTEMBER2011UNIVERSITYOFWARSAW,POLANDBOOKOFABSTRACTS4LANDAHLMTAWAVEGUIDEMODELFORTURBULENTSHEARFLOWJFLUIDMECH,1967,VOL29,PT3,P4414595ZHAROVVAWEAKLYNONLINEARPUL