湍流（影印版）

Preface
CHAPTER1
Introduction
1.1Turbulenceandsymmetries
1.2Outlineofthebook
CHAPTER2
Symmetriesandconservationlaws
2.1Periodicboundaryconditions
2.2Symmetries
2.3Conservationlaws
2.4Energybudgetscale-by-scale
CHAPTER3
Whyaprobabilisficdescriptionofturbulence?
3.1Thereissomethingpredictableinaturbulentsignal
3.2Amodelfordeterministicchaos
3.3Dynamicalsystems
3.4TheNavier-Stokesequationasadynamicalsystem
CHAPTER4
Probabilistictools:asurvey
4.1Randomvariables
4.2Randomfunctions
4.3Statisticalsymmetries
4.4Ergodicresults
4.5Thespectrumofstationaryrandomfunctions
CHAPTER5
Twoexperimentallawsoffullydevelopedturbulence
5.1Thetwo-thirdslaw
5.2Theenergydissipationlaw
CHAPTER6
TheKolmogorov1941theory
6.1Kolmogorov1941andsymmetries
6.2Koimogorov'sfour-fifthslaw
6.2.1TheKfirmfin-Howarth-Moninrelationforanisotropic
turbulence
6.2.2Theenergyfluxforhomogeneousturbulence
6.2.3Theenergyfluxforhomogeneousisotropicturbulence
6.2.4Fromtheenergyfluxrelationtothefour-fifthslaw
6.2.5RemarksonKolmogorov'sfour-fifthslaw
6.3MainresultsoftheKolmogorov1941theory
6.3.1TheKolmogorov-Obukhovlawandthestructurefunc-tions
6.3.2Effectofafiniteviscosity:thedissipationrange
6.4KoimogorovandLandau:thelackofuniversality
6.4.1TheoriginalformulationofLandau'sobjection
6.4.2AmodernreformulationofLandau'sobjection
6.4.3KolmogorovandLandaureconciled?
6.5HistoricalremarksontheKolmogorov1941theory
CHAPTER7
PhenomenologyofturbulenceinthesenseofKolmogorov1941
7.1Introduction
7.2Basictoolsofphenomenology
7.3TheRichardsoncascadeandtheIocalnessofinteractions
7.4Reynoldsnumbersanddegreesoffreedom
7.5Microscopicandmacroscopicdegreesoffreedom
7.6Thedistributionofvelocitygradients
7.7Thelawofdecayoftheenergy
7.8Beyondphenomenology:finite-timeblow-upofidealflow
CHAPTER8
Intermitteney
8.1Introduction
8.2Self-similarandintermittentrandomfunctions
8.3Experimentalresultsonintermittency
8.4Exactresultsonintermittency
8.5Intermittencymodelsbasedonthevelocity
8.5.1The/B-model
8.5.2Thebiffactalmodel
8.5.3Themultiffactalmodel
8.5.4Aprobabilisticreformulationofthemultiffactalmodel
8.5.5Theintermediatedissipationrangeandmultiffactaluniversality
8.5.6Theskewnessandtheflatnessofvelocityderivativesaccordingtothemultiffactalmodel
8.6Intermittencymodelsbasedonthedissipation
8.6.1Multifractaldissipation
8.6.2Bridgingmultifractalitybasedonthevelocityandmul-tifractalitybasedonthedissipation
8.6.3Randomcascademodels
8.6.4Largedeviationsandmultifractality
8.6.5Thelognormalmodelanditsshortcomings
8.7Shellmodels
8.8Historicalremarksonfractalintermittencymodels
8.9Trendsinintermittencyresearch
8.9.1Vortexfilaments:thesinewsofturbulence?
8.9.2Statisticalsignatureofvortexfilaments:dogortail?
8.9.3Thedistributionofvelocityincrements
CHAPTER9
Furtherreading:aguidedtour
9.1Introduction
9.2Booksonturbulenceandfluidmechanics
9.3Mathematicalaspectsoffullydevelopedturbulence
9.4Dynamicalsystems,fractalsandturbulence
9.5Closure,functionalanddiagrammaticmethods
9.5.1TheHopfequation
9.5.2Functionalanddiagrammaticmethods
9.5.3Thedirectinteractionapproximation
9.5.4Closuresandtheirshortcomings
9.6Eddyviscosity,multiscalemethodsandrenormalization
9.6.1Eddyviscosity:averyoldidea
9.6.2Multiscalemethods
9.6.3Applicationsofmultiscalemethodsinturbulence
9.6.4Renormalizationgroup(RG)methods
9.7Two-dimensionalturbulence
9.7.1Cascadesandvortices
9.7.2Two-dimensional.turbulenceandstatisticalmechanics
9.7.3Conservativedynamics'punctuated'bydissipativeevents
9.7.4FromFlatlandtothree-dimensionalturbulence
References
Authorindex
Subjectindex