流体动力学稳定性（第2版）

foreword by john miles

preface

1 introduction

1 introduction

2 mechanisms of instability

3 fundamental concepts of hydrodynamic stability

4 kelvin-helmholtz instability

5 break-up of a liquid jet in air

problems for chapter 1

2 thermal instability

6 introduction

7 the equations of motion

the exact equations, 34; the boussinesq equations,35

8 the stability problem

the linearized equations, 37; the boundary condi-tions, 40; normalmodes, 42

9 general stability characteristics

exchange of stabilities, 44; a variational principle,45

10 particular stability characteristics

free-free boundaries, 50; rigid-rigid boundaries,51; free-rigidboundaries, 52

11 the cells

12 experimental results

13 some applications

problems for chapter 2

3 centrifugal instability

14 introduction

15 instability of an inviscid fluid

three-dimensional disturbances, 73; axisymmetric disturbances, 77,two-dimensional disturbances, 80

16 instability of couette flow of an inviscid fluid

17 the taylor problem

axisymmetric disturbances, 90; two-dimensional disturbances, 103;three-dimensional disturbances,104; some experimental results,104

18 the dean problem

the dean problem, 108; the taylor-dean prob-lem, 113

19 the g6rtler problem

problems for chapter 3

4 parallel shear flows

20 introduction

the inviscid theory

21 the governing equations

22 general criteria for instability

23 flows with piecewise-linear velocity profiles

unbounded vortex sheet, 145; unbounded shear layer, 146; boundedshear layer, 147

24 the initial-value problem

the viscous theory

25 the governing equations

26 the eigenvalue spectrum for small reynolds numbers

a perturbation expansion, 159; sufficient conditions for stability,161

27 heuristic methods of approximation

the reduced equation and the inviscid approxima-tions, 165; theboundary-layer approximation near a rigid wa!l, 167; the wkbjapproximations,167; the local turning-point approximations,171; thetruncated equation and tollmien's improved viscous approximat...

correction to the singular inviscid solution, 177

28 approximations to the eigenvalue relation

symmetrical flows in a channel, 181; flows of the boundary-layertype, 183; the boundary-layer approximation to φ3(z), 184; the wkbjapproxi-mation to φ3(z), 185; the local turning-point approximationto φ3(z), 188; tollmien's improved approximation to φ3...

29 the long-wave approximation for unbounded flows

30 numerical methods of solution

expansions in orthogonal functions, 203; finite-difference methods,206; initial-value methods (shooting), 207

31 stability characteristics of various basic flows

plane couette flow, 212; poiseuiile flow in a circular pipe, 216;plane poiseuille flow, 221; combined plane couette and planepoiseuille flow, 223; the blasius boundary-layer profile, 224; theasymptotic suction boundary-layer profile, 227; boundary laye...

32 experimental results

problems for chapter 4

5 uniform asymptotic approximations

33 introduction

plane couette flow

34 the integral representations of the solutions

35 the differential,equation method

general velocity profiles

36 a preliminary transformation

37 the inner and outer expansions

the inner expansions, 268; the outer expansions,271; the centralmatching problem, 276; com- posite approximations, 278

38 uniform approximations

the solution of well-balanced type, 280; the solu- tions ofbalanced type, 280; the solutions of dominant-recessive type,283

39 a comparison with lin's theory

40 preliminary simplification of the eigenvalue relation

41 the uniform approximation to the eigenvalue relation

a computational form of the first approximation to the eigenvaluerelation, 299; results for plane poiseuille flow, 301

42 a comparision with the heuristic approximations to theeigenvalue relation

the local turning-point approximation to φ3(z), 305;tolimien'simproved approximation to φ3(z), 306;the uniform approximation toφ3(z) based on the truncated equation, 308; the uniformapproxima-tion to φ3(z) based on the orr-sommerfeldequation,3o9

43 a numerical treatment of the orr-sommerfeld problem usingcompound matrices

symmetrical flows in a channel, 315; boundary-layer flows,316

problems for chapter 5

6 additional topics in linear stability theory

44 instability of parallel flow of a stratified fluid

introduction, 320; internal gravity waves and ray-leigh-taylorinstability, 324; kelvin-helmholtz instability, 325

45 baroclinic instability

46 instability of the pinch

47 development of linear instability in time and space

initial-value problems, 345; spatially growing modes, 349

48 instability of unsteady flows

introduction, 353; instability of periodic flows, 354;instabilityof other unsteady basic flows, 361

problems for chapter 6

7 nonlinear stability

49 introduction

landau's theory, 370; discussion, 376

so the derivation of ordinary differential systems governingstability

sl resonant wave interactions

internal resonance of a double pendulum, 387;resonant waveinteractions, 392

s2 fundamental concepts of nonlinear stability

introduction to ordinary differential equations, 398;introductionto bifurcation theory, 402; structural stability, 407; spatialdevelopment of nonlinear stability, 416; critical layers inparallel flow, 420

s3 additional fundamental concepts of nonlinear stability

the energy method, 424; maximum and minimum energy in vortexmotion, 432; application of boun-dary-layer theory to cellularinstability, 434

s4 some applications of the nonlinear theory

benard convection, 435; couette flow, 442;parallel shear flows,450

problems for chapter 7

appendix. a class of generalized airy functions

a1 the airy functions ak(z)

a2 the functions an(z, p), bo(z, p) and bk(z, p)

a3 the functions ak(z, p, q) and bk(z, p, q)

a4 the zeros of at(z,p)

addendum: weakly non-parallel theories for the blasius boundarylayer

solutions

bibliography and author index

motion picture index

subject index