A FIRST COURSE IN TURBULENCEPDF电子书下载

1.INTRODUCTION 1

1.1The nature of turbulence 1

Irregularity 1

Diffusivity 2

Large Reynolds numbers 2

Three-dimensional vorticity fluctuations 2

Dissipation 3

Continuum 3

Turbulent flows are flows 3

1.2Methods of analysis 4

Dimensional analysis 5

Asymptotic invariance 5

Local invariance 6

1.3The origin of turbulence 7

1.4Diffusivity of turbulence 8

Diffusion in a problem with an imposed length scale 8

Eddy diffusivity 10

Diffusion in a problem with an imposed time scale 11

1.5Length scales in turbulent flows 14

Laminar boundary layers 14

Diffusive and convective length scales 15

Turbulent boundary layers 16

Laminar and turbulent friction 17

Small scales in turbulence 19

An inviscid estimate for the dissipation rate 20

Scale relations 21

Molecular and turbulent scales 23

1.6Outline of the material 24

2.TURBULENT TRANSPORT OF MOMENTUM AND HEAT 27

2.1The Reynolds equations 27

The Reynolds decomposition 28

Correlated variables 29

Equations for the mean flow 30

The Reynolds stress 32

Turbulent transport of heat 33

2.2Elements of the kinetic theory of gases 34

Pure shear flow 34

Molecular collisions 35

Characteristic times and lengths 38

The correlation between v1 and v2 38

Thermal diffusivity 39

2.3Estimates of the Reynolds stress 40

Reynolds stress and vortex stretching 40

The mixing-length model 42

The length-scale problem 44

A neglected transport term 45

The mixing length as an integral scale 45

The gradient-transport fallacy 47

Further esti-mates 49

Recapitulation 49

2.4Turbulent heat transfer 50

Reynolds’ analogy 51

The mixing-length model 51

2.5Turbulent shear flow near a rigid wall 52

A flow with constant stress 54

Nonzero mass transfer 55

The mixing-length approach 55

The limitations of mixing-length theory 57

3.THE DYNAMICS OF TURBULENCE 59

3.1Kinetic energy of the mean flow 59

Pure shear flow 60

The effects of viscosity 62

3.2Kinetic energy of the turbulence 63

Production equals dissipation 64

Taylor microscale 65

Scale relations 67

Spectral energy transfer 68

Further estimates 69

Wind-tunnel turbu-lence 70

Pure shear flow 74

3.3Vorticity dynamics 75

Vorticity vector and rotation tensor 76

Vortex terms in the equations of motion 76

Reynolds stress and vorticity 78

The vorticity equation 81

Vorticity in turbulent flows 84

Two-dimensional mean flow 85

The dynamics of ΩiΩi 86

The equation for ωiωi 86

Turbulence is rota-tional 87

An approximate vorticity budget 88

Multiple length scales 92

Stretching of magnetic field lines 93

3.4The dynamics of temperature fluctuations 95

Microscales in the temperature field 95

Buoyant convection 97

Richardson numbers 98

Buoyancy time scale 99

Monin-Oboukhov length 100

Convec-tion in the atmospheric boundary layer 100

4.BOUNDARY-FREE SHEAR FLOWS 104

4.1Almost parallel，two-dimensional flows 104

Plane flows 104

The cross-stream momentum equation 106

The streamwise momentum equation 108

Turbulent wakes 109

Turbulent jets and mixing layers 110

The momentum integral 111

Momentum thickness 112

4.2Turbulent wakes 113

Self-preservation 113

The mean-velocity profile 115

Axisymmetric wakes 118

Scale relations 119

The turbulent energy budget 120

4.3The wake of a self-propelled body 124

Plane wakes 125

Axisymmetric wakes 127

4.4Turbulent jets and mixing layers 127

Mixing layers 128

Plane jets 129

The energy budget in a plane jet 131

4.5Comparative structure of wakes，jets，and mixing layers 133

4.6Thermal plumes 135

Two-dimensional plumes 136

Self-preservation 141

The heat-flux inte-gral 142

Further results 142

5.WALL-BOUNDED SHEAR FLOWS 146

5.1The problem of multiple scales 146

Inertial sublayer 147

Velocity-defect law 147

5.2Turbulent flows in pipes and channels 149

Channel flow 149

The surface layer on a smooth wall 152

The core region 153

Inertial sublayer 153

Logarithmic friction law 156

Turbulent pipe flow 156

Experimental data on pipe flow 157

The viscous sub-layer 158

Experimental data on the law of the wall 161

Experimental data on the velocity-defect law 162

The flow of energy 163

Flow over rough surfaces 164

5.3Planetary boundary layers 166

The geostrophic wind 166

The Ekman layer 167

The velocity-defect law 167

The surface layer 168

The logarithmic wind profile 169

Ekman layers in the ocean 170

5.4The effects of a pressure gradient on the flow in surface layers 171

A second-order correction to pipe flow 174

The slope of the logarithmic velocity profile 175

5.5The downstream development of turbulent boundary layers 177

The potential flow 179

The pressure inside the boundary layer 181

The boundary-layer equation 182

Equilibrium flow 184

The flow in the wall layer 185

The law of the wall 185

The logarithmic friction law 186

The pressure-gradient parameter 186

Free-stream velocity distributions 188

Boundary layers in zero pressure gradient 190

Transport of scalar contam-inants 194

6.THE STATISTICAL DESCRIPTION OF TURBULENCE 197

6.1The probability density 197

6.2Fourier transforms and characteristic functions 201

The effects of spikes and discontinuities 203

Parseval’s relation 205

6.3Joint statistics and statistical independence 207

6.4Correlation functions and spectra 210

The convergence of averages 211

Ergodicity 212

The Fourier transform of ρ（τ） 214

6.5The central limit theorem 216

The statistics of integrals 218

A generalization of the theorem 220

More statistics of integrals 220

7.TURBULENT TRANSPORT 223

7.1Transport in stationary，homogeneous turbulence 223

Stationarity 223

Staticnary，homogeneous turbulence without mean veloc- ity 224

The probability density of the Lagrangian velocity 226

The Lagrangianintegral scale 229

The diffusion equation 230

7.2Transport in shear flows 230

Uniform shear flow 230

Joint statistics 232

Longitudinal dispersion in channel flow 233

Bulk velocity measurements in pipes 235

7.3Dispersion of contaminants 235

The concentration distribution 235

The effects of molecular transport 237

The effect of pure，steady strain 238

Transport at large scales 241

7.4Turbulent transport in evolving flows 241

Thermal wake in grid turbulence 242

Self-preservation 243

Dispersion rela-tive to the decaying turbulence 245

The Gaussian distribution 246

Disper-sion in shear flows 246

8.SPECTRAL DYNAMICS 248

8.1One- and three-dimensional spectra 248

Aliasing in one-dimensional spectra 248

The three-dimensional spec-trum 250

The correlation tensor and its Fourier transform 250

Two common one-dimensional spectra 251

Isotropic relations 253

Spectra of isotropic simple waves 254

8.2The energy cascade 256

Spectral energy transfer 258

A simple eddy 258

The energy cascade 260

8.3The spectrum of turbulence 262

The spectrum in the equilibrium range 262

The large-scale spectrum 264

The inertial subrange 264

8.4The effects of production and dissipation 267

The effect of dissipation 269

The effect of production 271

Approximate spectra for large Reynolds numbers 272

8.5Time spectra 274

The inertial subrange 277

The Lagrangian integral time scale 277

An approximate Lagrangian spectrum 278

8.6Spectra of passive scalar contaminants 279

One- and three-dimensional spectra 280

The cascade in the temperature spectrum 281

Spectra in the equilibrium range 282

The inertial-diffusive subrange 283

The viscous-convective subrange 284

The viscous-diffusive subrange 285

Summary 286

Bibliography and references 288

Index 295