数学物理学百科全书(第5卷·英文版·s-y)-[法]费朗克斯-elsevier出版-2007

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1、StabilityofFlowsSFriedlander,UniversityofIllinois-Chicago,(FriedlanderandSerre2003)andthecompendiumChicago,IL,USAofarticlesonhydrodynamicsandnonlinearª2006ElsevierLtd.Allrightsreserved.instabilitiesinGodrecheandManeville(1998).TheEquationsofMotionIntroductionTheNavier–Stokesequationsf

2、orthemotionofanThisarticlegivesabriefdiscussionofatopicwithincompressible,constantdensity,viscousfluidareanenormousliterature,namelythestability/instabil-@q12ityoffluidflows.Followingtheseminalobserva-þðq
rÞq¼rPþrq½1a@ttionsandexperimentsofReynoldsin1883,theissueofstabilityofafluid

3、flowbecameoneofthecentraldivq¼0½1bproblemsinfluiddynamics:stableflowsarerobustunderinevitabledisturbancesintheenvironment,whereq(x,t)denotesthevelocityvector,P(x,t)thewhileunstableflowsmaybreakup,sometimespressure,andtheconstantsandarethedensityrapidly.Thesepossibilitiesweredemonstr

4、atedinaandkinematicviscosity,respectively.Thissystemisrelativelysimpleexperimentwhereflowinapipeisconsideredinthree(orsometimestwo)spatialexaminedatincreasingspeeds.Asadimensionlessdimensionswithaspecifiedinitialvelocityfieldparameter(nowknownastheReynoldsnumber)qðx;0Þ¼q0ðxÞ½1cincreas

5、es,theflowcompletelychangesitsnaturefromastableflowtoacompletelydifferentregimeandphysicallyappropriateboundaryconditions:forthatisirregularinspaceandtime.Reynoldscalledexample,zerovelocityonarigidboundary,orthis‘‘turbulence’’andobservedthatthetransitionperiodicityconditionsforflowona

6、torus.Thisfromthesimpleflowtothechaoticflowwascausednonlinearsystemofpartialdifferentialequationsbythephenomenonofinstability.(PDEs)hasprovedtoberemarkablychallenging,Eventhoughthetopichasbeenthesubjectofandinthreedimensionsthefundamentalissuesofintensestudyovermorethanacentury,Reynol

7、dsexistenceanduniquenessofphysicallyreasonableexperimentisstillnotfullyexplainedbycurrentsolutionsarestillopenproblems.theory.AlthoughthereisnorigorousproofofItisoftenusefultoconsidertheNavier–Stokesstabilityofthesimpleflow(knownasPoiseuilleequationsinnondimensionalformbyscalingtheflo

8、winac