《A FIRST COURSE IN TURBULENCE》求取 ⇩

1.INTRODUCTION1

1.1The nature of turbulence1

Irregularity1

Diffusivity2

Large Reynolds numbers2

Three-dimensional vorticity fluctuations2

Dissipation3

Continuum3

Turbulent flows are flows3

1.2Methods of analysis4

Dimensional analysis5

Asymptotic invariance5

Local invariance6

1.3The origin of turbulence7

1.4Diffusivity of turbulence8

Diffusion in a problem with an imposed length scale8

Eddy diffusivity10

Diffusion in a problem with an imposed time scale11

1.5Length scales in turbulent flows14

Laminar boundary layers14

Diffusive and convective length scales15

Turbulent boundary layers16

Laminar and turbulent friction17

Small scales in turbulence19

An inviscid estimate for the dissipation rate20

Scale relations21

Molecular and turbulent scales23

1.6Outline of the material24

2.TURBULENT TRANSPORT OF MOMENTUM AND HEAT27

2.1The Reynolds equations27

The Reynolds decomposition28

Correlated variables29

Equations for the mean flow30

The Reynolds stress32

Turbulent transport of heat33

2.2Elements of the kinetic theory of gases34

Pure shear flow34

Molecular collisions35

Characteristic times and lengths38

The correlation between v1 and v238

Thermal diffusivity39

2.3Estimates of the Reynolds stress40

Reynolds stress and vortex stretching40

The mixing-length model42

The length-scale problem44

A neglected transport term45

The mixing length as an integral scale45

The gradient-transport fallacy47

Further esti-mates49

Recapitulation49

2.4Turbulent heat transfer50

Reynolds’ analogy51

The mixing-length model51

2.5Turbulent shear flow near a rigid wall52

A flow with constant stress54

Nonzero mass transfer55

The mixing-length approach55

The limitations of mixing-length theory57

3.THE DYNAMICS OF TURBULENCE59

3.1Kinetic energy of the mean flow59

Pure shear flow60

The effects of viscosity62

3.2Kinetic energy of the turbulence63

Production equals dissipation64

Taylor microscale65

Scale relations67

Spectral energy transfer68

Further estimates69

Wind-tunnel turbu-lence70

Pure shear flow74

3.3Vorticity dynamics75

Vorticity vector and rotation tensor76

Vortex terms in the equations of motion76

Reynolds stress and vorticity78

The vorticity equation81

Vorticity in turbulent flows84

Two-dimensional mean flow85

The dynamics of ΩiΩi86

The equation for ωiωi86

Turbulence is rota-tional87

An approximate vorticity budget88

Multiple length scales92

Stretching of magnetic field lines93

3.4The dynamics of temperature fluctuations95

Microscales in the temperature field95

Buoyant convection97

Richardson numbers98

Buoyancy time scale99

Monin-Oboukhov length100

Convec-tion in the atmospheric boundary layer100

4.BOUNDARY-FREE SHEAR FLOWS104

4.1Almost parallel，two-dimensional flows104

Plane flows104

The cross-stream momentum equation106

The streamwise momentum equation108

Turbulent wakes109

Turbulent jets and mixing layers110

The momentum integral111

Momentum thickness112

4.2Turbulent wakes113

Self-preservation113

Themean-velocity profile115

Axisymmetric wakes118

Scale relations119

The turbulent energy budget120

4.3The wake of a self-propelled body124

Plane wakes125

Axisymmetric wakes127

4.4Turbulent jets and mixing layers127

Mixing layers128

Plane jets129

The energy budget in a plane jet131

4.5Comparative structure of wakes，jets，and mixing layers133

4.6Thermal plumes135

Two-dimensional plumes136

Self-preservation141

The heat-flux inte-gral142

Further results142

5.WALL-BOUNDED SHEAR FLOWS146

5.1The problem of multiple scales146

Inertial sublayer147

Velocity-defect law147

5.2Turbulent flows in pipes and channels149

Channel flow149

The surface layer on a smooth wall152

The core region153

Inertial sublayer153

Logarithmic friction law156

Turbulent pipe flow156

Experimental data on pipe flow157

The viscous sub-layer158

Experimental data on the law of the wall161

Experimental data on the velocity-defect law162

The flow of energy163

Flow over rough surfaces164

5.3Planetary boundary layers166

The geostrophic wind166

The Ekman layer167

The velocity-defect law167

The surface layer168

The logarithmic wind profile169

Ekman layers in the ocean170

5.4The effects of a pressure gradient on the flow in surface layers171

A second-order correction to pipe flow174

The slope of the logarithmic velocity profile175

5.5The downstream development of turbulent boundary layers177

The potential flow179

The pressure inside the boundary layer181

The boundary-layer equation182

Equilibrium flow184

The flow in the wall layer185

The law of the wall185

The logarithmic friction law186

The pressure-gradient parameter186

Free-stream velocity distributions188

Boundary layers in zero pressure gradient190

Transport of scalar contam-inants194

6.THE STATISTICAL DESCRIPTION OF TURBULENCE197

6.1The probability density197

6.2Fourier transforms and characteristic functions201

The effects of spikes and discontinuities203

Parseval’s relation205

6.3Joint statistics and statistical independence207

6.4Correlation functions and spectra210

The convergence of averages211

Ergodicity212

The Fourier transform of ρ（τ）214

6.5The central limit theorem216

The statistics of integrals218

A generalization of the theorem220

More statistics of integrals220

7.TURBULENT TRANSPORT223

7.1Transport in stationary，homogeneous turbulence223

Stationarity223

Staticnary，homogeneous turbulence without mean veloc- ity224

The probability density of the Lagrangian velocity226

The Lagrangianintegral scale229

The diffusion equation230

7.2Transport in shear flows230

Uniform shear flow230

Joint statistics232

Longitudinal dispersion in channel flow233

Bulk velocity measurements in pipes235

7.3Dispersion of contaminants235

The concentration distribution235

The effects of molecular transport237

The effect of pure，steady strain238

Transport at large scales241

7.4Turbulent transport in evolving flows241

Thermal wake in grid turbulence242

Self-preservation243

Dispersion rela-tive to the decaying turbulence245

The Gaussian distribution246

Disper-sion in shear flows246

8.SPECTRAL DYNAMICS248

8.1One- and three-dimensional spectra248

Aliasingin one-dimensional spectra248

The three-dimensional spec-trum250

The correlation tensor and its Fourier transform250

Two common one-dimensional spectra251

Isotropic relations253

Spectra of isotropic simple waves254

8.2The energy cascade256

Spectral energy transfer258

A simple eddy258

The energy cascade260

8.3The spectrum of turbulence262

The spectrum in the equilibrium range262

The large-scale spectrum264

The inertial subrange264

8.4The effects of production and dissipation267

The effect of dissipation269

The effect of production271

Approximate spectra for large Reynolds numbers272

8.5Time spectra274

The inertial subrange277

The Lagrangian integral time scale277

An approximate Lagrangian spectrum278

8.6Spectra of passive scalar contaminants279

One- and three-dimensional spectra280

The cascade in the temperature spectrum281

Spectra in the equilibrium range282

The inertial-diffusive subrange283

The viscous-convective subrange284

The viscous-diffusive subrange285

Summary286

Bibliography and references288

Index295