湍流研究的動(dòng)力系統(tǒng)方法

定　價(jià)：￥45.00

作　者：	（英）Tomas Bohr等著
出版社：	清華大學(xué)出版社
叢編項(xiàng)：	劍橋非線性科學(xué)系列
標(biāo)　簽：	暫缺

購(gòu)買這本書可以去

當(dāng)當(dāng)網(wǎng) (￥38.30)

ISBN：	9787302039051	出版時(shí)間：	2000-01-01	包裝：
開本：	25cm	頁(yè)數(shù)：	350頁(yè)	字?jǐn)?shù)：

內(nèi)容簡(jiǎn)介

暫缺《湍流研究的動(dòng)力系統(tǒng)方法》簡(jiǎn)介

作者簡(jiǎn)介

暫缺《湍流研究的動(dòng)力系統(tǒng)方法》作者簡(jiǎn)介

圖書目錄

TothememoryofGiovannivii
Prefaceix
Introductionxi
Chapter1Turbulenceanddynamicalsystems1
1.1Whatdowemeanbyturbulence?1
1.2Examplesofturbulentphenomena3
1.2.1Fluids3
1.2.2Chemicalturbulence7
1.2.3Flamefronts9
1.3Whyadynamicalsystemapproach?11
1.4Examplesofdynamicalsystemsforturbulence11
1.4.1Shellmodels11
1.4.2Coupledmaplattices12
1.4.3Cellularautomata13
1.5Characterizationofchaosinhighdimensionality14
1.5.1Lyapunovexponentsinextendedsystems14
1.5.2Lyapunovspectraanddimensiondensities15
1.5.3Characterizationofchaosindiscretemodels18
1.5.4Thecorrelationlength18
1.5.5Scalinginvarianceandchaos19
Chapter2Phenomenologyofhydrodynamicturbulence21
2.1Turbulenceasastatisticaltheory21
2.1.1Statisticalmechanicsofaperfectfluid22
2.1.2Basicfactsandideasonfullydevelopedturbulence24
2.1.3Theclosureproblem28
2.2Scalinginvafianceinturbulence31
2.3Multifractaldescriptionoffullydevelopedturbulence34
2.3.1Scalingofthestructurefunctions34
2.3.2Multiplicativemodelsforintermittency36
2.3.3Probabilitydistributionfunctionofthevelocitygradients40
2.3.4Multiscaling43
2.3.5Numberofdegreesoffreedomofturbulence44
2.4Two-dimensionalturbulence45
Chapter3Reducedmodelsforhydrodynamicturbulence48
3.1Dynamicalsystemsasmodelsoftheenergycascade48
3.2Abriefoverviewonshellmodels49
3.2.1ThemodelofDesnyanskyandNovikov51
3.2.2ThemodelofGledzer,OhkitaniandYamada(theGOYmodel)52
3.2.3Hierarchicalshellmodels56
3.2.4Continuumlimitoftheshellmodels57
3.3DynamicalpropertiesoftheGOYmodels58
3.3.1Fixedpointsandscaling58
3.3.2Transitionfromastablefixedpointtochaos60
3.3.3TheLyapunovspectrum65
3.4MultifractalityintheGOYmodel68
3.4.1Anomalousscalingofthestructurefunctions68
3.4.2Dynamicalintermittency71
3.4.3Constructionofa3Dincompressiblevelocityfieldfromtheshellmodels73
3.5AclosuretheoryfortheGOYmodel74
3.6Shellmodelsfortheadvectionofpassivescalars78
3.7Shellmodelsfortwo-dimensionalturbulence83
3.8Low-dimensionalmodelsforcoherentstructures88
Chapter4Turbulenceandcoupledmaplattices91
4.1Introductiontocoupledchaoticmaps92
4.1.1Linearstabilityofthecoherentstate93
4.1.2Spreadingofperturbations94
4.2Scalingatthecriticalpoint97
4.2.1ScalingoftheLyapunovexponents97
4.2.2Scalingofthecorrelationlength99
4.2.3Spreadingoflocalizedperturbations101
4.2.4Renormalizationgroupresults104
4.3Lyapunovspectra106
4.3.1Coupledmaplatticeswithconservationlaws107
4.3.2Analyticresults110
4.4Coupledmapswithlaminarstates112
4.4.1Spatio-temporalintermittency112
4.4.2lnvariantmeasuresandPerron-FrobeniusequationofCML114
4.4.3Meanfieldapproximationandphasediagram115
4.4.4Directiteratesandfinitesizescaling118
4.4.5Spatialcorrelationsandhyperscaling121
4.5Coupledmaplatticeswithanisotropiccouplings123
4.5.1Convectiveinstabilitiesandturbulentspots123
4.5.2Coherentchaosinanisotropicsystems128
4.5.3Aboundarylayerinstabilityinananisotropicsystem131
4.5.4Acoupledmaplatticeforaconvectivesystem134
Chapter5TurbulenceinthecomplexGinzburg-Landauequation138
5.1ThecomplexGinzburg-Landauequation139
5.2Thestabilityofthehomogeneousperiodicstateamithephaseequation143
5.3Planewavesandtheirstability146
5.3.1Thestabilityofplanewaves146
5.3.2Convectiveversusabsolutestability148
5.4Large-scalesimulationsandthecoupledmapapproximation148
5.5Spiralsandwavenumberselection150
5.6Theonsetofturbulence152
5.6.1Transientturbulenceandnucleation155
5.7Glassystatesofboundvortices158
5.8Vortexinteractions161
5.8.1Microscopictheoryofshocks162
5.8.2Asymptoticproperties163
5.8.3Weakshocks167
5.9PhaseturbulenceandtheKuramoto-Sivashinskyequation168
5.9.1CorrelationsintheKuramoto-Sivashinskyequation170
5.9.2Dimensiondensitiesandcorrelationsinphaseturbulence171
5.10Anisotropicphaseequation172
5.10.1Theshapeofaspreadingspot173
5.10.2Turbulentspotsandpulses178
5.10.3Anisotropicturbulentspotsintwodimensions181
Chapter6Predictabilityinhigh-dimensionalsystoms183
6.1Predictabilityinturbulence185
6.1.1MaximumLyapunovexponentofaturbulentfiow185
6.1.2Theclassicaltheoryofpredictabilityinturbulence186
6.2Predictabilityinsystemswithmanycharacteristictimes188
6.3ChaosandbutterflyeffectintheGOYmodel191
6.3.1Growthofinfinitesimalperturbationsanddynamicalintermittency191
6.3.2Statisticsofthepredictabilitytimeanditsrelationwithintermittency195
6.3.3Growthofnon-infinitesimalperturbations197
6.4Predictabilityinextendedsystems200
6.5Predictabilityinnoisysystems202
6.6Finalremarks209
Chapter7Dynamicsofinterfaces211
7.1Turbulenceandinterfaces211
7.2TheBurgersequation212
7.3TheLangevinapproachtodynamicalinterfaces:theKPZequation215
7.4Deterministicinterfacedynamics:theKuramoto-Sivashinskyequation219
7.4.1Cross-overtoKPZbehaviour222
7.4.2TheKuramoto-Sivashinskyequationin2+1dimensions225
7.4.3Interfacesincoupledmaplattices227
7.5Depinningmodels231
7.5.1Quenchedrandomnessanddirectedpercolationnetworks231
7.5.2Self-organized-criticaldynamics:theSneppenmodel232
7.5.3Colouredactivity235
7.5.4AscalingtheoryfortheSneppenmodel:mappingtodirectedpercolation237
7.5.5Ageometricdescriptionoftheavalanchedynamics240
7.5.6Multiscaling241
7.6Dynamicsofamembrane243
Chapter8Lagrangianchaos244
8.1Generalremarks244
8.1.1ExamplesofLagrangianchaos247
8.1.2Stretchingofmateriallinesandsurfaces251
8.2EulerianversusLagrangianchaos253
8.2.1OnsetofLagrangianchaosintwo-dimensionalflows255
8.2.2Eulerianchaosandfluidparticlemotion258
8.2.3AcommentonLagrangianchaos264
8.3Statisticsofpassivefields265
8.3.1Thegrowthofscalargradients265
8.3.2Themultifractalstructureforthedistributionofscalargradients266
8.3.3Thepowerspectrumofscalarfelds268
8.3.4SomeremarksonthevalidityoftheBatchelorlaw270
8.3.5Intermittencyandmultifractalityinmagneticdynamos272
Chapter9Chaoticdiffusion277
9.1Diffusioninincompressibleflows279
9.1.1StandarddiffusioninthepresenceofLagrangianchaos279
9.1.2Standarddiffusioninsteadyvelocityfields281
9.1.3Anomalousdiffusioninrandomvelocityfields283
9.1.4Anomalousdiffusioninsmoothvelocityfields284
9.2Anomalousdiffusioninfieldsgeneratedbyextendedsystems285
9.2.1AnomalousdiffusionintheKuramoto-Sivashinskyequation286
9.2.2Multidiffusionalonganintermittentmembrane290
AppendixAHopfbifurcation292
AppendixBHamiltoniansystems294
AppendixCCharacteristicandgeneralizedLyapunovexponents301
AppendixDConvectiveinstabilitiesandlinearfrontpropagation309
AppendixEGeneralizedfractaldimensionsandmultifractals315
AppendixFMultiaffinefields320
AppendixGReductiontoafinite-dimensionaldynamicalsystem325
AppendixHDirectedpercolation329
References332
Index347