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1、217WaveletanalysisofthebreakdownofapulsedvortexflowPSAddisonDepartmentofCivilandTransportationEngineering,MechistonCampus,NapierUniversity,10ColintonRoad,Edinburgh,ScotlandEH105DT,UKAbstract:Thepaperprovidesanintroductiontothepropertiesanduseofthecontinuouswavelettransform.Itthe
2、ndescribesthewaveletanalysisofthebreakdownofaconfinedvortexflowwheretimeseriesdataofthecentre-linevelocitiesfromapulsedvortexflowatapipeorificeareexaminedusingtheMexicanhatwavelettransform.Thedevelopmentofthesignalfromtheperiodic,vortexflowviaanenergeticturbulentbreakdownregiontoaflo
3、wcomposedoflow-frequencycoherentstructuresatintermittenttemporalscalesismonitoredusingwavelettransformplots,waveletenergyplotsandwaveletpowerspectra.Keywords:wavelettransform,vortexflow,fluidturbulence,MexicanhatwaveletNOTATIONpopularitystemsfromitsabilitytoexaminefeatureswithint
4、hesignalbothinfrequencyandlocation.awaveletdilationparameterApplicationshaveburgeonedinmanyfields:medicalbwaveletlocationparameterscience,e.g.theanalysisofECGandEEGsignalsCadmissibilityconstantandDNAsequences[1–3];geophysics,e.g.seismicgDpipeinternaldiameterdata,oceanwaves,hydra
5、ulicconductivitydistri-pEenergybutionsinthesubsurface,seafloorbathymetry,etc.ffrequencyofthepassbandcentreofthewavelet(see,forexample,Foufoula-GeorgiouandKumar[4],cg()waveletfunctionandmorespecificallyforseismicanalysisseeGrubbgˆ(v)Fouriertransformofg(t)andWalden[5]andChakraborty
6、andOkaya[6];P(v)powerspectrumnon-destructivetesting[7,8];speechsignalcharac-ttimeterization[9];fluidturbulence(dealtwithindetailinT(a,b)wavelettransformusingwaveletscaleaatthenextsection);ecologicalstructures[10];evenlocationbstockmarketpriceindices[11].(Acomprehensive,Utemporal
7、meanvelocityatthepipecentre-lineelementaryaccountofthemathematicalandhistori-Upipecentre-line(temporalmean)velocityforcalbackgroundofthewavelettransformmaybeHPunpulsedHagen–Poiseuilleflowfoundinreference[12].)Thispapergivesanintro-xsignalvariable(hereinvelocity)ductorytutorialin
8、thepropertiesofthewavelettrans-Zdownstreamdistancefrom
