湍流 英文版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

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PART ONE:FUNDAMENTALS1

1 Introduction3

1.1 The nature of turbulent flows3

1.2 The study of turbulent flows7

2 The equations of fluid motion10

2.1 Continuum fluid properties10

2.2 Eulerian and Lagrangian fields12

2.3 The continuity equation14

2.4 The momentum equation16

2.5 The role of pressure18

2.6 Conserved passive scalars21

2.7 The vorticity equation22

2.8 Rates of strain and rotation23

2.9 Transformation properties24

3 The statistical description of turbulent flows34

3.1 The random nature of turbulence34

3.2 Characterization of random variables37

3.3 Examples of probability distributions43

3.4 Joint random variables54

3.5 Normal and joint-normal distributions61

3.6 Random processes65

3.7 Random fields74

3.8 Probability and averaging79

4 Mean-flow equations83

4.1 Reynolds equations83

4.2 Reynolds stresses86

4.3 The mean scalar equation91

4.4 Gradient-diffusion and turbulent-viscosity hypotheses92

5 Free shear flows96

5.1 The round jet:experimental observations96

5.1.1 A description of the flow96

5.1.2 The mean velocity field97

5.1.3 Reynolds stresses105

5.2 The round jet:mean momentum111

5.2.1 Boundary-layer equations111

5.2.2 Flow rates of mass,momentum,and energy115

5.2.3 Self-similarity116

5.2.4 Uniform turbulent viscosity118

5.3 The round jet:kinetic energy122

5.4 Other self-similar flows134

5.4.1 The plane jet134

5.4.2 The plane mixing layer139

5.4.3 The plane wake147

5.4.4 The axisymmetric wake151

5.4.5 Homogeneous shear flow154

5.4.6 Grid turbulence158

5.5 Further observations161

5.5.1 A conserved scalar161

5.5.2 Intermittency167

5.5.3 PDFs and higher moments173

5.5.4 Large-scale turbulent motion178

6 The scales of turbulent motion182

6.1 The energy cascade and Kolmogorov hypotheses182

6.1.1 The energy cascade183

6.1.2 The Kolmogorov hypotheses184

6.1.3 The energy spectrum188

6.1.4 Restatement of the Kolmogorov hypotheses189

6.2 Structure functions191

6.3 Two-point correlation195

6.4 Fourier modes207

6.4.1 Fourier-series representation207

6.4.2 The evolution of Fourier modes211

6.4.3 The kinetic energy of Fourier modes215

6.5 Velocity spectra219

6.5.1 Definitions and properties220

6.5.2 Kolmogorov spectra229

6.5.3 A model spectrum232

6.5.4 Dissipation spectra234

6.5.5 The inertial subrange238

6.5.6 The energy-containing range240

6.5.7 Effects of the Reynolds number242

6.5.8 The shear-stress spectrum246

6.6 The spectral view of the energy cascade249

6.7 Limitations,shortcomings,and refinements254

6.7.1 The Reynolds number254

6.7.2 Higher-order statistics255

6.7.3 Internal intermittency258

6.7.4 Refined similarity hypotheses260

6.7.5 Closing remarks263

7 Wall flows264

7.1 Channel flow264

7.1.1 A description of the flow264

7.1.2 The balance of mean forces266

7.1.3 The near-wall shear stress268

7.1.4 Mean velocity profiles271

7.1.5 The friction law and the Reynolds number278

7.1.6 Reynolds stresses281

7.1.7 Lengthscales and the mixing length288

7.2 Pipe flow290

7.2.1 The friction law for smooth pipes290

7.2.2 Wall roughness295

7.3 Boundary layers298

7.3.1 A description of the flow299

7.3.2 Mean-momentum equations300

7.3.3 Mean velocity profiles302

7.3.4 The overlap region reconsidered308

7.3.5 Reynolds-stress balances313

7.3.6 Additional effects320

7.4 Turbulent structures322

PART TWO:MODELLING AND SIMULATION333

8 An introduction to modelling and simulation335

8.1 The challenge335

8.2 An overview of approaches336

8.3 Criteria for appraising models336

9 Direct numerical simulation344

9.1 Homogeneous turbulence344

9.1.1 Pseudo-spectral methods344

9.1.2 The computational cost346

9.1.3 Artificial modifications and incomplete resolution352

9.2 Inhomogeneous flows353

9.2.1 Channel flow353

9.2.2 Free shear flows354

9.2.3 Flow over a backward-facing step355

9.3 Discussion356

10 Turbulent-viscosity models358

10.1 The turbulent-viscosity hypothesis359

10.1.1 The intrinsic assumption359

10.1.2 The specific assumption364

10.2 Algebraic models365

10.2.1 Uniform turbulent viscosity365

10.2.2 The mixing-length model366

10.3 Turbulent-kinetic-energy models369

10.4 The κ-εmodel373

10.4.1 An overview373

10.4.2 The model equation for ε375

10.4.3 Discussion382

10.5 Further turbulent-viscosity models383

10.5.1 The κ-ω model383

10.5.2 The Spalart-Allmaras model385

11 Reynolds-stress and related models387

11.1 Introduction387

11.2 The pressure-rate-of-strain tensor388

11.3 Return-to-isotropy models392

11.3.1 Rotta's model392

11.3.2 The characterization of Reynolds-stress anisotropy393

11.3.3 Nonlinear return-to-isotropy models398

11.4 Rapid-distortion theory404

11.4.1 Rapid-distortion equations405

11.4.2 The evolution of a Fourier mode406

11.4.3 The evolution of the spectrum411

11.4.4 Rapid distortion of initially isotropic turbulence415

11.4.5 Final remarks421

11.5 Pressure-rate-of-strain models422

11.5.1 The basic model(LRR-IP)423

11.5.2 Other pressure-rate-of-strain models425

11.6 Extension to inhomogeneous flows428

11.6.1 Redistribution428

11.6.2 Reynolds-stress transport429

11.6.3 The dissipation equation432

11.7 Near-wall treatments433

11.7.1 Near-wall effects433

11.7.2 Turbulent viscosity434

11.7.3 Model equations for κ and ε435

11.7.4 The dissipation tensor436

11.7.5 Fluctuating pressure439

11.7.6 Wall functions442

11.8 Elliptic relaxation models445

11.9 Algebraic stress and nonlinear viscosity models448

11.9.1 Algebraic stress models448

11.9.2 Nonlinear turbulent viscosity452

11.10 Discussion457

12 PDF methods463

12.1 The Eulerian PDF of velocity464

12.1.1 Definitions and properties464

12.1.2 The PDF transport equation465

12.1.3 The PDF of the fluctuating velocity467

12.2 The model velocity PDF equation468

12.2.1 The generalized Langevin model469

12.2.2 The evolution of the PDF470

12.2.3 Corresponding Reynolds-stress models475

12.2.4 Eulerian and Lagrangian modelling approaches479

12.2.5 Relationships between Lagrangian and Eulerian PDFs480

12.3 Langevin equations483

12.3.1 Stationary isotropic turbulence484

12.3.2 The generalized Langevin model489

12.4 Turbulent dispersion494

12.5 The velocity-frequency joint PDF506

12.5.1 Complete PDF closure506

12.5.2 The log-normal model for the turbulence frequency507

12.5.3 The gamma-distribution model511

12.5.4 The model joint PDF equation514

12.6 The Lagrangian particle method516

12.6.1 Fluid and particle systems516

12.6.2 Corresponding equations519

12.6.3 Estimation of means523

12.6.4 Summary526

12.7 Extensions529

12.7.1 Wall functions529

12.7.2 The near-wall elliptic-relaxation model534

12.7.3 The wavevector model540

12.7.4 Mixing and reaction545

12.8 Discussion555

13 Large-eddy simulation558

13.1 Introduction558

13.2 Filtering561

13.2.1 The general definition561

13.2.2 Filtering in one dimension562

13.2.3 Spectral representation565

13.2.4 The filtered energy spectrum568

13.2.5 The resolution of filtered fields571

13.2.6 Filtering in three dimensions575

13.2.7 The filtered rate of strain578

13.3 Filtered conservation equations581

13.3.1 Conservation of momentum581

13.3.2 Decomposition of the residual stress582

13.3.3 Conservation of energy585

13.4 The Smagorinsky model587

13.4.1 The definition of the model587

13.4.2 Behavior in the inertial subrange587

13.4.3 The Smagorinsky filter590

13.4.4 Limiting behaviors594

13.4.5 Near-wall resolution598

13.4.6 Tests of model performance601

13.5 LES in wavenumber space604

13.5.1 Filtered equations604

13.5.2 Triad interactions606

13.5.3 The spectral energy balance609

13.5.4 The spectral eddy viscosity610

13.5.5 Backscatter611

13.5.6 A statistical view of LES612

13.5.7 Resolution and modelling615

13.6 Further residual-stress models619

13.6.1 The dynamic model619

13.6.2 Mixed models and variants627

13.6.3 Transport-equation models629

13.6.4 Implicit numerical filters631

13.6.5 Near-wall treatments634

13.7 Discussion635

13.7.1 An appraisal of LES635

13.7.2 Final perspectives638

PART THREE:APPENDICES641

Appendix A Cartesian tensors643

A.1 Cartesian coordinates and vectors643

A.2 The definition of Cartesian tensors647

A.3 Tensor operations649

A.4 The vector cross product654

A.5 A summary of Cartesian-tensor suffix notation659

Appendix B Properties of second-order tensors661

Appendix C Dirac delta functions670

C.1 The definition of δ（x）670

C.2 Properties of δ（x）672

C.3 Derivatives of δ（x）673

C.4 Taylor series675

C.5 The Heaviside function675

C.6 Multiple dimensions677

Appendix D Fourier transforms678

Appendix E Spectral representation of stationary random processes683

E.1 Fourier series683

E.2 Periodic random processes686

E.3 Non-periodic random processes689

E.4 Derivatives of the process690

Appendix F The discrete Fourier transform692

Appendix G Power-law spectra696

Appendix H Derivation of Eulerian PDF equations702

Appendix I Characteristic functions707

Appendix J Diffusion processes713

Bibliography727

Author index749

Subject index754