流体动力学稳定性 第2版【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

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1 INTRODUCTION1

1 Introduction1

2 Mechanisms of instability4

3 Fundamental concepts of hydrodynamic stability8

4 Kelvin-Helmholtz instability14

5 Break-up of a liquid jet in air22

Problems for chapter 127

2 THERMAL INSTABILITY32

6 Introduction32

7 The equations of motion34

The exact equations34

The Boussinesq equations35

8 The stability problem37

The linearized equations37

The boundary condi-tions40

Normal modes42

9 General stability characteristics44

Exchange of stabilities44

A variational principle45

10 Particular stability characteristics50

Free-free boundaries50

Rigid-rigid boundaries51

free-rigid boundaries52

11 The cells52

12 Experimental results59

13 Some applications62

Problems for chapter 263

3 CENTRIFUGAL INSTABILITY69

14 Introduction69

15 Instability of an inviscid fluid71

Three-dimensional disturbances73

Axisymmetric disturbances77

Two-dimensional disturbances80

16 Instability of Couette flow of an inviscid fluid82

17 The Taylor problem88

Axisymmetric disturbances90

Two-dimensional disturbances103

Three-dimensional disturbances104

Some experimental results104

18 The Dean problem108

The Dean problem108

The Taylor-Dean prob-lem113

19 The G？rtler problem116

Problems for chapter 3121

4 PARALLEL SHEAR FLOWS124

20 Introduction124

The inviscid theory126

21 The governing equations126

22 General criteria for instability131

23 Flows with piecewise-linear velocity profiles144

Unbounded vortex sheet145

Unbounded shear layer146

Bounded shear layer147

24 The initial-value problem147

The viscous theory153

25 The governing equations153

26 The eigenvalue spectrum for small Reynolds numbers158

A perturbation expansion159

Sufficient conditions for stability161

27 Heuristic methods of approximation164

The reduced equation and the inviscid approxima-tions165

The boundary-layer approximation near a rigid wall167

The WKBJ approximations167

The local turning-point approximations171

The truncated equation and Tollmien's improved viscous approximations175

The viscous correction to the singular inviscid solution177

28 Approximations to the eigenvalue relation180

Symmetrical flows in a channel181

Flows of the boundary-layer type183

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 flows196

30 Numerical methods of solution202

Expansions in orthogonal functions203

Finite-difference methods206

Initial-value methods(shooting)207

31 Stability characteristics of various basic flows211

Plane Couette flow212

Poiseuille flow in a circular pipe216

Plane Poiseuille flow221

Combined plane Couette and plane Poiseuille flow223

The Blasius boundary-layer profile224

The asymptotic suction boundary-layer profile227

Boundary layers at separation229

The Falkner-Skan profiles231

The Bickley jet233

The hyper-bolic-tangent shear layer237

32 Experimental results239

Problems for chapter 4245

5 UNIFORM ASYMPTOTIC APPROXIMATIONS251

33 Introduction251

Plane Couette flow256

34 The integral representations of the solutions256

35 The differential equation method263

General velocity profiles265

36 A preliminary transformation265

37 The inner and outer expansions267

The inner expansions268

The outer expansions271

The central matching problem276

Com-posite approximations278

38 Uniform approximations280

The solution of well-balanced type280

The solu-tions of balanced type280

The solutions of dominant-recessive type283

39 A comparison with Lin's theory285

40 Preliminary simplification of the eigenvalue relation290

41 The uniform approximation to the eigenvalue relation295

A computational form of the first approximation to the eigenvalue relation299

Results for plane Poiseuille flow301

42 A comparision with the heuristic approximations to the eigenvalue relation305

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 equation308

The uniform approxima-tion to φ3(z)based on the Orr-Sommerfeld equation309

43 A numerical treatment of the Orr-Sommerfeld problem using compound matrices311

Symmetrical flows in a channel315

Boundary-layer flows316

Problems for chapter 5317

6 ADDITIONAL TOPICS IN LINEAR STABlLITY THEORY320

44 Instability of parallel flow of a stratified fluid320

Introduction320

Internal gravity waves and Ray-leigh-Taylor instability324

Kelvin-Helmholtz instability325

45 Baroclinic instability333

46 Instability of the pinch339

47 Development of linear instability in time and space345

Initial-value problems345

Spatially growing modes349

48 Instability of unsteady flows353

Introduction353

Instability of periodic flows354

Instability of other unsteady basic flows361

Problems for chapter 6363

7 NONLINEAR STABILITY370

49 Introduction370

Landau's theory370

Discussion376

50 The derivation of ordinary differential systems governing stability380

51 Resonant wave interactions387

Internal resonance of a double pendulum387

Resonant wave interactions392

52 Fundamental concepts of nonlinear stability398

Introduction to ordinary differential equations398

Introduction to bifurcation theory402

Structural stability407

Spatial development of nonlinear stability416

Critical layers in parallel flow420

53 Additional fundamental concepts of nonlinear stability423

The energy method424

Maximum and minimum energy in vortex motion432

Application of boun-dary-layer theory to cellular instability434

54 Some applications of the nonlinear theory435

Bénard convection435

Couette flow442

Parallel shear flows450

Problems for chapter 7458

APPENDIX.A CLASS OF GENERALIZED AIRY FUNCTIONS465

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 layer479

Solutions481

Bibliography and author index559

Motion picture index595

Subject index597