List of tables Preface Nomenclature PART ONE: FUNDAMENTALS 1 Introduction 1.1 The nature of turbulent flows 1.2 The study of turbulent flows 2 The equations of fluid motion 2.1 Continuum fluid properties 2.2 Eulerian and Lagrangian fields 2.3 The continuity equation 2.4 The momentum equation 2.5 The role of pressure 2.6 Conserved passive scalars 2.7 The vorticity equation osm in 2.8 Rates of strain and rotation 2.9 Transformation properties 3 The statistical description of turbulent flows 3.1 The random nature of turbulence 3.2 Characterization of random variables 3.3 Examples of probability distributions 3.4 Joint random variables 3.5 Normal and joint-normal distributions 3.6 Random processes 3.7 Random fields 3.8 Probability and averaging 4 Mean-fow equations 4.1 Reynolds equations 4.2 Reynolds stresses 4.3 The mean scalar equation 4.4 Gradient-diffusion and turbulent-viscosity hypotheses 5 Free shear flows 5.1 The round jet:experimental observations 5.1.1 A description of the flow 5.1.2 The mean velocity field 5.1.3 Reynolds stresses 5.2 The round jet:mean momentum 5.2.1 Boundary-layer equations 5.2.2 Flow rates of mass,momentum,and energy 5.2.3 Self-similarity 5.2.4 Uniform turbulent viscosity 5.3 The round jet:kinetic energy 5.4 Other self-similar flows 5.4.1 The plane jet 5.4.2 The plane mixing layer 5.4.3 The plane wake 5.4.4 The axisymmetric wake 5.4.5 Homogeneous shear flowqorg biuh ctuuciigo? 5.4.6 Grid turbulence 5.5 Further observations
5.5.1 A conserved scalar 5.5.2 Intermittency 5.5.3 PDFs and higher moments 5.5.4 Large-scale turbulent motion ups uioittov od 6 The scales of turbulent motion 6.1 The energy cascade and Kolmogorov hypotheses 6.1.1 The energy cascade dus to noiiqinsesb lasthei 6.1.2 The Kolmogorov hypotheses isn mobast s 6.1.3 The energy spectrum obnsn lo noilnsinsioensr 6.1.4 Restatement of the Kolmogorov hypotheses 6.2 Structure functions 6.3 Two-point correlation 6.4 Fourier modes 6.4.1 Fourier-series representation 6.4.2 The evolution of Fourier modes …… PART TWO: MODELLING AND SIMULATION PART THREE: APPENDICES
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