标度.自相似性和中间渐近

Preface
Foreword
0Introduction
0.1Dimensionalanalysisandphysicalsimilarity
0.2Assumptionsunderlyingdimensionalanalysis
0.3Self-similarphenomena
0.4Self-similarsolutionsasintermediateasymptotics.
Thesolutionsofthefirstandsecondkind.
Renormalizationgroup
0.5Self-similaritiesandtravellingwaves
1Dimensions,dimensionalanalysisandsimilarity
1.1Dimensions
1.2DimensionalAnalysis
1.3Similarity
2Theconstructionofintermediate-asymptoticsolutions
usingdimensionalanalysis.Self-similarsolutions
2.1Heatpropagationfromaconcentratedinstantaneoussource
2.2Phenomenaattheinitialstageofanuclearexplosion
2.3Self-similarity.Intermediateasymptotics
3Self-similaritiesofthesecondkind:firstexamples
3.1Flowofanidealfluidpastawedge
3.2Filtrationinanelasto-plasticporousmedium:themodified
instantaneousheatsourceproblem
4Self-similaritiesofthesecondkind:
furtherexamples
41Modifiedveryintenseexplosionproblem
4.2TheyonWeizsiicker-Zeldovichproblem:animpulsive
loading
5Classifcationofsimilarityrulesandself-similarity
solutions.Arecipefortheapplicationofsimilarity
analysis
5.1Completeandincompletesimilarity
6Scalingandtransformationgroups.Renormalization
group
6.1Dimensionalanalysisandtransformationgroups
6.2Therenormalisationgroupandincompletesimilarity
7Self-similarsolutionsandtravellingwaves
7.1Solutionsoftravelling-wavetype
7.2Burgersshockwave-steadytravellingwaveofthe
firstkind
7.3Flame:steadytravellingwaveofthesecondkind
7.4Nonlineareigenvalueproblem
7.5Flamepropagationinareactingmixture:anintermediate
asymptotics
8Invariantsolutions:asymptoticconservationlaws,
spectrumofeigenvalues,andstability
81Asymptoticconservationlaws
8.2Spectrumofeigenvalues
8.3Stabilityofinvariantsolutions
9Scalinginthedeformationandfractureofsolids
9.1Transitionfromself-similarityofthefirstkindto
self-similarityofthesecond;alinearelasticityproblem
9.2Similaritylawsforbrittleandquasi-brittlefracture
10Scalinginturbulence
10.1Homogeneousandisotropicturbulence
10.2Turbulentshearflows
11Scalingingeophysicalfluiddynamics
11.1Scalinglawsfortheatmosphericsurfacelayer
11.2Flowswithstronglystablestratification
11.3Theregimeoflimitingsaturationofaturbulentshearflow
ladenwithsediment
11.4Upperthermoclineintheocean-thetravellingthermal
wavemodel
11.5Stronginteractionofturbulencewithinternalwaves.
Deepeningoftheturbulentregion
11.6Thebreakingofinternalwavesandextensionof
mixed-fluidpatchesinastablystratifiedfluid
11.7Severalphenomenarelatedtoturbulenceinastably
stratifiedfluid
12Scaling:miscellaneousspecialproblems
12.1Mandelbrotfractalsandincompletesimilarity
12.2Example:scalingrelationshipbetweenthebreathingrateof
animalsandtheirmass.Fractalityofrespiratoryorgans
12.3Thespreadingofaground-watermound
Afterword
References
Index