
| 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 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-flow 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 5.2 the round jet: mean momentum 5.3 the round jet: kinetic energy 5.4 other self-similar flows 5.5 further observations 6 the scales of turbulent motion 6.1 the energy cascade and kolmogorov hypotheses 6.2 structure functions 6.3 two-point correlation 6.4 fourier modes 6.5 velocity spectra 6.6 the spectral view of the energy cascade 6.7 limitations, shortcomings, and refinements 7 wall flows 7.1 channel flow 7.2 pipe flow 7.3 boundary layers 7.4 turbulent structures part two: modelling and simulation 8 an introduction to modelling and simulation 8.1 the challenge 8.2 an overview of approaches 8.3 criteria for appraising models 9 direct numerical simulation 9.1 homogeneous turbulence 9.2 inhomogeneous flows 9.3 discussion 10 turbulent-viscosity models 10.1 the turbulent-viscosity hypothesis 10.2 algebraic models 10.3 turbulent-kinetic-energy models 10.4 the k-εmodel 10:5 further turbulent-viscosity models 11 reynolds-stress and related models 11.1 introduction 11.2 the pressure-rate-of-strain tensor 11.3 return-to-isotropy models 11.4 rapid-distortion theory 11.5 pressure-rate-of-strain models 11.6 extension to inhomogeneous flows 11.7 near-wall treatments 11.8 elliptic relaxation models 11.9 algebraic stress and nonlinear viscosity models 11.10 discussion 12 pdf methods 12.1 the eulerian pdf of velocity 12.2 the model velocity pdf equation 12.3 langevin equations 12.4 turbulent dispersion 12.5 the velocity-frequency joint pdf 12.6 the lagrangian particle method 12.7 extensions 12.8 discussion 13 large-eddy simulation 13.1 introduction 13.2 filtering 13.3 filtered conservation equations 13.4 the smagorinsky model 13.5 les in wavenumber space 13.6 further residual-stress models 13.7 discussion part three: appendices appendix .4 cartesian tensors a.1 cartesian coordinates and vectors a.2 the definition of cartesian tensors a.3 tensor operations a.4 the vector cross product a.5 a summary of cartesian-tensor suffix notation appendix b properties of second-order tensors appendix c dirac delta functions c.1 the definition of δ(x) c.2 properties of rs(x) c.3 derivatives of rs(x) c.4 taylor series c.5 the heaviside function c.6 multiple dimensions appendix d fourier transforms appendix e spectral representation of stationary random processes e.1 fourier series e.2 periodic random processes e.3 non-periodic random processes e.4 derivatives of the-process appenthix f the discrete fourier transform appendix g power-law spectra appendix h derivation of eulerian pdf equations appendix i characteristic functions appendix j diffusion processes bibliography author index subject index |
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