Foreword
Preface
Introduction
Chapter1 Dimensional analysis and physical similarity
1.1 Dimensions
1.1.1 Mesurement of physical quantities, units of measurement, Systems of units
1.1.2 Classes of systems of units
1.1.3 Dimension of a physical quantity
1.1.4 The dimension function is always a power-law monomial
1.1.5 Quantities with indepandent dimensions
1.2 Dimensional analysis
1.2.1 Governing parameters
1.2.2 Transfomation to dimensionaless parameters, Generalized homogeneity.П-theorem
1.2.3 Problems
1.3 Physical similarity
1.3.1 Physically similar phenomena
1.3.2 The rule for scaling the results for a physically similar model up to the prototype
1.3.3 Choosing the governing parameters of the model
1.3.4 Problems
Chapter2 Self-similarity and intermadiate asympotics
2.1 Gently sioping groundwater flow. A mathematical model
2.2 Very intense concentrated flooding: the self-similar solution
2.3 The intermediate asymptotics
2.4 Problem:very intense groundwater pulse flow-the self-similar intermediate-asympototic solition
Chapter3 Scaling laws and self-similar solutions that cannot be obtained by dimensional analysis
Chapter4 Complete and incomplete simiarity.Self-similar solitions of the first and second kind
Chapter5 Scaling and transformation groups. Renormalization group
Chapter6 Self-similar phenomena and travelling waves
Chapter7 Scaling laws and fractals
7.1 Mandelbrot fractals and incomplete similarity
7.1.1 The concept of fractals. Fracrtal curves
7.2 Incomplete similarity of fractals
7.3 Scaling relationship between the breathing rate of animals and their mass.Fractality of respiratory organs
Chapter8 Scaling laws for turbulent wall-bounded shear flows at very large Reynolds numbers
8.1 Turbulence at very large Reynolds numbres
8.2 Chorin's mathematical example
8.3 Steady shear flows ay very large Reynolds numbers.The intermadiate region in pipe flow
8.4 Modification of Izakson-Millikan-von Mises derivation of the velocity distibution in the intermadiate region.The vanishing-viscosity asymptotics
8.5 Turbulent boundary layers
Preface
Introduction
Chapter1 Dimensional analysis and physical similarity
1.1 Dimensions
1.1.1 Mesurement of physical quantities, units of measurement, Systems of units
1.1.2 Classes of systems of units
1.1.3 Dimension of a physical quantity
1.1.4 The dimension function is always a power-law monomial
1.1.5 Quantities with indepandent dimensions
1.2 Dimensional analysis
1.2.1 Governing parameters
1.2.2 Transfomation to dimensionaless parameters, Generalized homogeneity.П-theorem
1.2.3 Problems
1.3 Physical similarity
1.3.1 Physically similar phenomena
1.3.2 The rule for scaling the results for a physically similar model up to the prototype
1.3.3 Choosing the governing parameters of the model
1.3.4 Problems
Chapter2 Self-similarity and intermadiate asympotics
2.1 Gently sioping groundwater flow. A mathematical model
2.2 Very intense concentrated flooding: the self-similar solution
2.3 The intermediate asymptotics
2.4 Problem:very intense groundwater pulse flow-the self-similar intermediate-asympototic solition
Chapter3 Scaling laws and self-similar solutions that cannot be obtained by dimensional analysis
Chapter4 Complete and incomplete simiarity.Self-similar solitions of the first and second kind
Chapter5 Scaling and transformation groups. Renormalization group
Chapter6 Self-similar phenomena and travelling waves
Chapter7 Scaling laws and fractals
7.1 Mandelbrot fractals and incomplete similarity
7.1.1 The concept of fractals. Fracrtal curves
7.2 Incomplete similarity of fractals
7.3 Scaling relationship between the breathing rate of animals and their mass.Fractality of respiratory organs
Chapter8 Scaling laws for turbulent wall-bounded shear flows at very large Reynolds numbers
8.1 Turbulence at very large Reynolds numbres
8.2 Chorin's mathematical example
8.3 Steady shear flows ay very large Reynolds numbers.The intermadiate region in pipe flow
8.4 Modification of Izakson-Millikan-von Mises derivation of the velocity distibution in the intermadiate region.The vanishing-viscosity asymptotics
8.5 Turbulent boundary layers