Two-dimensional turbulence a physicist approach [Review]

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1、PhysicsReports362(2002)1–62Two-dimensionalturbulence:aphysicistapproachPatrickTabelingLaboratoiredePhysiqueStatistique,EcoleNormaleSuperieure,24rueLhomond,75231Paris,FranceReceivedJune2001;editor:I:ProcacciaContents1.Introduction27.Dispersionofpairsintheinversecascade402.Exactresults48

2、.Condensedstates423.Coherentstructures89.Enstrophycascade454.Statisticsofthecoherentstructuresin10.Coherentstructuresvs.cascades52decayingtwo-dimensionalturbulence1611.Conclusions565.Equilibriumstatesoftwo-dimensional12.Uncitedreferences57turbulence22Acknowledgements576.Inverseenergycas

3、cade29References57AbstractMuchprogresshasbeenmadeontwo-dimensionalturbulence,theselasttwodecades,butstill,anumberoffundamentalquestionsremainunanswered.Theobjectiveofthepresentreviewistocollectandorganizetheavailableinformationonthesubject,emphasizingonaspectsaccessibletoexperiment,ando

4、utliningcontributionsmadeonsimple9owcon:gurations.Wheneverpossible,openquestionsaremadeexplicit.Varioussubjectsarepresented:coherentstructures,statisticaltheories,inversecascadeofenergy,condensedstates,Richardsonlaw,directcascadeofenstrophy,andtheinter-playbetweencascadesandcoherentstru

5、ctures.Thereviewo=ersaphysicist’sviewontwo-dimensionalturbulenceinthesensethatexperimentalfactsplayanimportantroleinthepresentation,technicalissuesaredescribedwithoutmuchdetail,sometimesinanoversimpli:edform,andphysicalargumentsaregivenwheneverpossible.Ihopethisbiasdoesnotjeopardizethei

6、nterestofthepresentationforwhoeverwishestovisitthefascinatingworldofFlatland.
c2002ElsevierScienceB.V.Allrightsreserved.PACS:47.27.Ak;47.27.Eq;05.45.−a0370-1573/02/$-seefrontmatterc2002ElsevierScienceB.V.Allrightsreserved.PII:S0370-1573(01)00064-32P.Tabeling/PhysicsReports362(2002)1–62

7、1.IntroductionSeveralmotivationsorprospectsmayleadtogetinvolvedinstudiesontwo-dimensionalturbulence.Onemotivation,probablysharedbyalltheinvestigators,isthathydrodynamictur-bulence,despiteitspracticalinterest,itsomnipresence,andtheseriesofassaultsithasbeensubmittedtofordecades,i