剪切流中的稳定性和转换 英文版PDF|Epub|txt|kindle电子书版本网盘下载

剪切流中的稳定性和转换 英文版PDF格式电子书版下载

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1 Introduction and General Results1

1.1 Introduction1

1.2 Nonlinear Disturbance Equations2

1.3 Definition of Stability and Critical Reynolds Numbers3

1.3.1 Definition of Stability3

1.3.2 Critical Reynolds Numbers5

1.3.3 Spatial Evolution of Disturbances6

1.4 The Reynolds-Orr Equation7

1.4.1 Derivation of the Reynolds-Orr Equation7

1.4.2 The Need for Linear Growth Mechanisms9

Ⅰ Temporal Stability of Parallel Shear Flows15

2 Linear Inviscid Analysis15

2.1 Inviscid Linear Stability Equations15

2.2 Modal Solutions17

2.2.1 General Results17

2.2.2 Dispersive Effects and Wave Packets33

2.3 Initial Value Problem38

2.3.1 The Inviscid Initial Value Problem38

2.3.2 Laplace Transform Solution42

2.3.3 Solutions to the Normal Vorticity Equation46

2.3.4 Example:Couette Flow48

2.3.5 Localized Disturbances50

3 Eigensolutions to the Viscous Problem55

3.1 Viscous Linear Stability Equations55

3.1.1 The Velocity-Vorticity Formulation55

3.1.2 The Orr-Sommerfeld and Squire Equations56

3.1.3 Squire's Transformation and Squire's Theorem58

3.1.4 Vector Modes59

3.1.5 Pipe Flow61

3.2 Spectra and Eigenfunctions64

3.2.1 Discrete Spectrum64

3.2.2 Neutral Curves71

3.2.3 Continuous Spectrum74

3.2.4 Asymptotic Results78

3.3 Further Results on Spectra and Eigenfunctions85

3.3.1 Adjoint Problem and Bi-Orthogonality Condition85

3.3.2 Sensitivity of Eigenvalues89

3.3.3 Pseudo-Eigenvalues93

3.3.4 Bounds on Eigenvalues94

3.3.5 Dispersive Effects and Wave Packets96

4 The Viscous Initial Value Problem99

4.1 The Viscons Initial Value Problem99

4.1.1 Motivation99

4.1.2 Derivation of the Disturbance Equations102

4.1.3 Disturbance Measure102

4.2 The Forced Squire Equation and Transient Growth103

4.2.1 Eigenfunction Expansion103

4.2.2 Blains Boundary Layer Flow105

4.3 The Complete Solution to the Initial Value Problem106

4.3.1 Continuous Formulation106

4.3.2 Discrete Formulation108

4.4 Optimal Growth111

4.4.1 The Matrix Exponential111

4.4.2 Maximum Amplification112

4.4.3 Optimal Disturbances119

4.4.4 Reynolds Number Dependence of Optimal Growth120

4.5 Optimal Response and Optimal Growth Rate126

4.5.1 The Forced Problem and the Resolvent126

4.5.2 Maximum Growth Rate131

4.5.3 Response to Stochastic Excitation133

4.6 Estimates of Growth139

4.6.1 Bounds on Matrix Exponential139

4.6.2 Conditions for No Growth141

4.7 Localized Disturbances144

4.7.1 Choice of Initial Disturbances144

4.7.2 Examples147

4.7.3 Asymptotic Behavior149

5 Nonlinear Stability153

5.1 Motivation153

5.1.1 Introduction153

5.1.2 A Model Problem154

5.2 Nonlinear Initial Value Problem155

5.2.1 The Velocity-Vorticity Equations155

5.3 Weakly Nonlinear Expansion160

5.3.1 Multiple-Scale Analysis160

5.3.2 The Landau Equation164

5.4 Three-Wave Interactions167

5.4.1 Resonance Conditions167

5.4.2 Derivation of a Dynamical System168

5.4.3 Triad Interactions172

5.5 Solutions to the Nonlinear Initial Value Problem177

5.5.1 Formal Solutions to the Nonlinear Initial Value Problem177

5.5.2 Weakly Nonlinear Solutions and the Center Manifold179

5.5.3 Nonlinear Equilibrium States180

5.5.4 Numerical Solutions for Localized Disturbances185

5.6 Energy Theory188

5.6.1 The Energy Stability Problem188

5.6.2 Additional Constraints191

Ⅱ Stability of Complex Flows and Transition197

6 Temporal Stability of Complex Flows197

6.1 Effect of Pressure Gradient and Crossflow198

6.1.1 Falkner-Skan(FS)Boundary Layers198

6.1.2 Falkner-Skan-Cooke(FSC) Boundary layers203

6.2 Effect of Rotation and Curvature207

6.2.1 Curved Channel Flow207

6.2.2 Rotating Channel Flow211

6.2.3 Combined Effect of Curvature and Rotation213

6.3 Effect of Surface Tension216

6.3.1 Water Table Flow216

6.3.2 Energy and the Choice of Norm218

6.3.3 Results221

6.4 Stability of Unsteady Flow223

6.4.1 Oscillatory Flow223

6.4.2 Arbitrary Time Dependence229

6.5 Effect of Compressibility237

6.5.1 The Compressible Initial Value Problem237

6.5.2 Inviscid Instabilities and Rayleigh's Criterion240

6.5.3 Viscous Instability246

6.5.4 Nonmodal Growth249

7 Growth of Disturbances in Space253

7.1 Spatial Eigenvalue Analysis253

7.1.1 Introduction253

7.1.2 Spatial Spectra255

7.1.3 Gaster's Transformation264

7.1.4 Harmonic Point Source266

7.2 Absolute Instability270

7.2.1 The Concept of Absolute Instability270

7.2.2 Briggs'Method273

7.2.3 The Cusp Map278

7.2.4 Stability of a Two-Dimensional Wake281

7.2.5 Stability of Rotating Disk Flow284

7.3 Spatial Initial Value Problem290

7.3.1 Primitive Variable Formulation290

7.3.2 Solution of the Spatial Initial Value Problem291

7.3.3 The Vibrating Ribbon Problem294

7.4 Nonparallel Effects300

7.4.1 Asymptotic Methods301

7.4.2 Parabolic Equations for Steady Disturbances309

7.4.3 Parabolized Stability Equations(PSE)318

7.4.4 Spatial Optimal Disturbances329

7.4.5 Global Instability337

7.5 Nonlinear Effects344

7.5.1 Nonlinear Wave Interactions344

7.5.2 Nonlinear Parabolized Stability Equations346

7.5.3 Examples349

7.6 Disturbance Environment and Receptivity351

7.6.1 Introduction351

7.6.2 Nonlocalized and Localized Receptivity353

7.6.3 An Adjoint Approach to Receptivity363

7.6.4 Receptivity Using Parabolic Evolution Equations367

8 Secondary Instability373

8.1 Introduction373

8.2 Secondary Instability of Two-Dimensional Waves374

8.2.1 Derivation of the Equations374

8.2.2 Numerical Results378

8.2.3 Elliptical Instability381

8.3 Secondary Instability of Vortices and Streaks383

8.3.1 Governing Equations383

8.3.2 Examples of Secondary Instability of Streaks and Vortices389

8.4 Eckhaus Instability394

8.4.1 Secondary Instability of Parallel Flows394

8.4.2 Parabolic Equations for Spatial Eckhaus Instability397

9 Transition to Turbulence401

9.1 Transition Scenarios and Thresholds401

9.1.1 Introduction401

9.1.2 Three Transition Scenarios403

9.1.3 The Most Likely Transition Scenario411

9.1.4 Conclusions413

9.2 Breakdown of Two-Dimensional Waves414

9.2.1 The Zero Pressure Gradient Boundary Layer414

9.2.2 Breakdown of Mixing Layers420

9.3 Streak Breakdown425

9.3.1 Streaks Forced by Blowing or Suction425

9.3.2 Freestream Turbulence429

9.4 Oblique Transition436

9.4.1 Experiments and Simulations in Blasius Flow436

9.4.2 Transition in a Separation Bubble441

9.4.3 Compressible Oblique Transition445

9.5 Transition of Vortex-Dominated Flows446

9.5.1 Transition in Flows with Curvature446

9.5.2 Direct Numerical Simulations of Secondary Instability of Crossflow Vortices450

9.5.3 Experimental Investigations of Breakdown of Crossflow Vortices455

9.6 Breakdown of Localized Disturbances456

9.6.1 Experimental Results for Boundary Layers459

9.6.2 Direct Numerical Simulations in Boundary Layers460

9.7 Transition Modeling465

9.7.1 Low-Dimensional Models of Subcritical Transition465

9.7.2 Traditional Transition Prediction Models469

9.7.3 Transition Prediction Models Based on Nonmodal Growth471

9.7.4 Nonlinear Transition Modeling474

Ⅲ Appendix479

A Numerical Issues and Computer Programs479

A.1 Global versus Local Methods479

A.2 Runge-Kutta Methods480

A.3 Chebyshev Expansions483

A.4 Infinite Domain and Continuous Spectrum486

A.5 Chebyshev Discretization of the Orr-Sommerfeld Equation487

A.6 MATLAB Codes for Hydrodynamic Stability Calculations489

A.7 Eigenvalues of Parallel Shear Flows503

B Resonances and Degeneracies509

B.1 Resonances and Degeneracies509

B.2 Orr-Sommerfeld-Squire Resonance511

C Adjoint of the Linearized Boundary Layer Equation515

C.1 Adjoint of the Linearized Boundary Layer Equation515

D Selected Problems on Part Ⅰ519

Bibliography529

Index551