流体动力学稳定性 第2版PDF电子书下载

1 INTRODUCTION 1

1 Introduction 1

2 Mechanisms of instability 4

3 Fundamental concepts of hydrodynamic stability 8

4 Kelvin-Helmholtz instability 14

5 Break-up of a liquid jet in air 22

Problems for chapter 1 27

2 THERMAL INSTABILITY 32

6 Introduction 32

7 The equations of motion 34

The exact equations 34

The Boussinesq equations 35

8 The stability problem 37

The linearized equations 37

The boundary condi-tions 40

Normal modes 42

9 General stability characteristics 44

Exchange of stabilities 44

A variational principle 45

10 Particular stability characteristics 50

Free-free boundaries 50

Rigid-rigid boundaries 51

free-rigid boundaries 52

11 The cells 52

12 Experimental results 59

13 Some applications 62

Problems for chapter 2 63

3 CENTRIFUGAL INSTABILITY 69

14 Introduction 69

15 Instability of an inviscid fluid 71

Three-dimensional disturbances 73

Axisymmetric disturbances 77

Two-dimensional disturbances 80

16 Instability of Couette flow of an inviscid fluid 82

17 The Taylor problem 88

Axisymmetric disturbances 90

Two-dimensional disturbances 103

Three-dimensional disturbances 104

Some experimental results 104

18 The Dean problem 108

The Dean problem 108

The Taylor-Dean prob-lem 113

19 The G？rtler problem 116

Problems for chapter 3 121

4 PARALLEL SHEAR FLOWS 124

20 Introduction 124

The inviscid theory 126

21 The governing equations 126

22 General criteria for instability 131

23 Flows with piecewise-linear velocity profiles 144

Unbounded vortex sheet 145

Unbounded shear layer 146

Bounded shear layer 147

24 The initial-value problem 147

The viscous theory 153

25 The governing equations 153

26 The eigenvalue spectrum for small Reynolds numbers 158

A perturbation expansion 159

Sufficient conditions for stability 161

27 Heuristic methods of approximation 164

The reduced equation and the inviscid approxima-tions 165

The boundary-layer approximation near a rigid wall 167

The WKBJ approximations 167

The local turning-point approximations 171

The truncated equation and Tollmien's improved viscous approximations 175

The viscous correction to the singular inviscid solution 177

28 Approximations to the eigenvalue relation 180

Symmetrical flows in a channel 181

Flows of the boundary-layer type 183

The boundary-layer approximation to φ3(z) 184

The WKBJ approxi-mation to φ3(z) 185

The local turning-point approximation to φ3(z) 188

Tollmien's improved approximation to φ3(z) 191

29 The long-wave approximation for unbounded flows 196

30 Numerical methods of solution 202

Expansions in orthogonal functions 203

Finite-difference methods 206

Initial-value methods(shooting) 207

31 Stability characteristics of various basic flows 211

Plane Couette flow 212

Poiseuille flow in a circular pipe 216

Plane Poiseuille flow 221

Combined plane Couette and plane Poiseuille flow 223

The Blasius boundary-layer profile 224

The asymptotic suction boundary-layer profile 227

Boundary layers at separation 229

The Falkner-Skan profiles 231

The Bickley jet 233

The hyper-bolic-tangent shear layer 237

32 Experimental results 239

Problems for chapter 4 245

5 UNIFORM ASYMPTOTIC APPROXIMATIONS 251

33 Introduction 251

Plane Couette flow 256

34 The integral representations of the solutions 256

35 The differential equation method 263

General velocity profiles 265

36 A preliminary transformation 265

37 The inner and outer expansions 267

The inner expansions 268

The outer expansions 271

The central matching problem 276

Com-posite approximations 278

38 Uniform approximations 280

The solution of well-balanced type 280

The solu-tions of balanced type 280

The solutions of dominant-recessive type 283

39 A comparison with Lin's theory 285

40 Preliminary simplification of the eigenvalue relation 290

41 The uniform approximation to the eigenvalue relation 295

A computational form of the first approximation to the eigenvalue relation 299

Results for plane Poiseuille flow 301

42 A comparision with the heuristic approximations to the eigenvalue relation 305

The local turning-point approximation to φ3(z) 305

Tollmien's improved approximation to φ3(z) 306

The uniform approximation to φ3(z)based on the truncated equation 308

The uniform approxima-tion to φ3(z)based on the Orr-Sommerfeld equation 309

43 A numerical treatment of the Orr-Sommerfeld problem using compound matrices 311

Symmetrical flows in a channel 315

Boundary-layer flows 316

Problems for chapter 5 317

6 ADDITIONAL TOPICS IN LINEAR STABlLITY THEORY 320

44 Instability of parallel flow of a stratified fluid 320

Introduction 320

Internal gravity waves and Ray-leigh-Taylor instability 324

Kelvin-Helmholtz instability 325

45 Baroclinic instability 333

46 Instability of the pinch 339

47 Development of linear instability in time and space 345

Initial-value problems 345

Spatially growing modes 349

48 Instability of unsteady flows 353

Introduction 353

Instability of periodic flows 354

Instability of other unsteady basic flows 361

Problems for chapter 6 363

7 NONLINEAR STABILITY 370

49 Introduction 370

Landau's theory 370

Discussion 376

50 The derivation of ordinary differential systems governing stability 380

51 Resonant wave interactions 387

Internal resonance of a double pendulum 387

Resonant wave interactions 392

52 Fundamental concepts of nonlinear stability 398

Introduction to ordinary differential equations 398

Introduction to bifurcation theory 402

Structural stability 407

Spatial development of nonlinear stability 416

Critical layers in parallel flow 420

53 Additional fundamental concepts of nonlinear stability 423

The energy method 424

Maximum and minimum energy in vortex motion 432

Application of boun-dary-layer theory to cellular instability 434

54 Some applications of the nonlinear theory 435

Bénard convection 435

Couette flow 442

Parallel shear flows 450

Problems for chapter 7 458

APPENDIX.A CLASS OF GENERALIZED AIRY FUNCTIONS 465

A1 The Airy functions Ak(z) 465

A2 The functions Ak(z,p),B0(z,p)and Bk(z,p) 466

A3 The functions Ak(z,p,q)and Bk(z,p,q) 472

A4 The zeros of At(z,p) 477

Addendum:Weakly non-parallel theories for the Blasius boundary layer 479

Solutions 481

Bibliography and author index 559

Motion picture index 595

Subject index 597