旋度与湍流

旋度与湍流
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作者:
2005-01
版次: 1
ISBN: 9787302102045
定价: 24.00
装帧: 平装
开本: 16开
纸张: 胶版纸
页数: 174页
正文语种: 英语
分类: 自然科学
12人买过
  • Thisbookprovidesanintroductiontothetheoryofturbulenceinfluidsbasedontherepresentationoftheflowbymeansofitsvorticityfield.Ithaslongbeenunderstoodthat,atleastinthecaseofincompressibleflow,thevorticityrepresentationisnaturalandphysicallytransparent,yetthedevelopmentofatheoryofturbulenceinthisrepresentationhasbeenslow.ThepioneeringworkofOnsagerandofJoyceandMontgomeryonthestatisticalmechanicsoftwo-dimensionalvortexsystemshasonlyrecentlybeenputonafirmmathematicalfooting,andthethree-dimensionaltheoryremainsinpartsspeculativeandevencontroversial.
    Somepracticalinformationaboutapproximationproceduresisprovidedinthebook,aswellastoolsforassessingtheplausibilityofapproximationschemes.Theemphasis,however,isontheunderstandingofturbulence——-itsorigin,mechanics,spectra,organizedstructures,energybudget,andrenormalization.Thephysicalspacemethodologyisnatural,andmakesthereasoningparticularlystraightforward.Openquestionsareindicatedassuchthroughoutthebook. Preface
    Introduction
    1.TheEquationsofMotion
    1.1TheEulerandNavier-StokesEquations
    1.2VorticityFormoftheEquations
    1.3DiscreteVortexRepresentations
    1.4MagnetizationVariables
    1.5FourierRepresentationforPeriodicFlow

    2.RandomFlowandItsSpectra
    2.1IntroductiontoProbabilityTheory
    2.2RandomFields
    2.3RandomSolutionsoftheNavier-StokesEquations
    2.4RandomFourierTransformofaHomogeneousFlowField
    2.5BrownianMotionandBrownianWalks

    3.TheKolmogorovTheory
    3.1TheGoalsofTurbulenceTheory:UniversalEquilibrium
    3.2KolmogorovTheory:DimensionalConsiderations
    3.3TheKolmlgorovSpectrumandanEnergyCascade
    3.4FractalDimension
    3.5AFirstDiscussionofIntermittency
    4.EquilibriumFlowinSpectralVariablesandinTwoSpaceDimensions
    4.1StatisticalEquilibrium
    4.2The“Absolute”StatisticalEquilibriuminWaveNumberSpace
    4.3TheCombinatorialMethod:TheApproachtoEquilibriumandNegativeTemperatures
    4.4TheOnsagerTheoryandtheJoyce-MontgomeryEquation
    4.5TheContinuumLimitandtheRoleofInvariants
    4.6TheApproachtoEquilibrium,Viscosity,andInertialPowerLaws

    5.VortexStretching
    6.Polymers,Percolation,Renormalization
    7.VortexEquilibriaainThree-DimensionalSpace
    Bibliography
    Index
  • 内容简介:
    Thisbookprovidesanintroductiontothetheoryofturbulenceinfluidsbasedontherepresentationoftheflowbymeansofitsvorticityfield.Ithaslongbeenunderstoodthat,atleastinthecaseofincompressibleflow,thevorticityrepresentationisnaturalandphysicallytransparent,yetthedevelopmentofatheoryofturbulenceinthisrepresentationhasbeenslow.ThepioneeringworkofOnsagerandofJoyceandMontgomeryonthestatisticalmechanicsoftwo-dimensionalvortexsystemshasonlyrecentlybeenputonafirmmathematicalfooting,andthethree-dimensionaltheoryremainsinpartsspeculativeandevencontroversial.
    Somepracticalinformationaboutapproximationproceduresisprovidedinthebook,aswellastoolsforassessingtheplausibilityofapproximationschemes.Theemphasis,however,isontheunderstandingofturbulence——-itsorigin,mechanics,spectra,organizedstructures,energybudget,andrenormalization.Thephysicalspacemethodologyisnatural,andmakesthereasoningparticularlystraightforward.Openquestionsareindicatedassuchthroughoutthebook.
  • 目录:
    Preface
    Introduction
    1.TheEquationsofMotion
    1.1TheEulerandNavier-StokesEquations
    1.2VorticityFormoftheEquations
    1.3DiscreteVortexRepresentations
    1.4MagnetizationVariables
    1.5FourierRepresentationforPeriodicFlow

    2.RandomFlowandItsSpectra
    2.1IntroductiontoProbabilityTheory
    2.2RandomFields
    2.3RandomSolutionsoftheNavier-StokesEquations
    2.4RandomFourierTransformofaHomogeneousFlowField
    2.5BrownianMotionandBrownianWalks

    3.TheKolmogorovTheory
    3.1TheGoalsofTurbulenceTheory:UniversalEquilibrium
    3.2KolmogorovTheory:DimensionalConsiderations
    3.3TheKolmlgorovSpectrumandanEnergyCascade
    3.4FractalDimension
    3.5AFirstDiscussionofIntermittency
    4.EquilibriumFlowinSpectralVariablesandinTwoSpaceDimensions
    4.1StatisticalEquilibrium
    4.2The“Absolute”StatisticalEquilibriuminWaveNumberSpace
    4.3TheCombinatorialMethod:TheApproachtoEquilibriumandNegativeTemperatures
    4.4TheOnsagerTheoryandtheJoyce-MontgomeryEquation
    4.5TheContinuumLimitandtheRoleofInvariants
    4.6TheApproachtoEquilibrium,Viscosity,andInertialPowerLaws

    5.VortexStretching
    6.Polymers,Percolation,Renormalization
    7.VortexEquilibriaainThree-DimensionalSpace
    Bibliography
    Index
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