流体动力稳定性 : 第2版

Foreword by John Miles

Preface

1 INTRODUCTION

1 Introduction

2 Mechanisms of instability

3 Fundamental concepts of hydrodynamic stability

4 KeMn-Helmholtzinstability

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

The Boussinesq equations

8 The stability problem

The linearized equations

The boundary conditions

Normal modes

9 General stability characteristics

Exchange of stabilities

A variational principle

10 Particular stability characteristics

Free-free boundaries

Rigid-rigid boundaries

free-rigid boundaries

11 The cells

12 Experimentalresults

13 Some applications

Problems for chapter 2

3 CENTRIFUGAL INSTABILITY

14 Introduction

15 Instability of an inviscid fluid

Three-dimensional disturbances

Axisymmetric disturbances

Two-dimensionaldisturbances

16 Instability of Couette flow of an inviscid fluid

17 The Taylor problem

Axisymmctric disturbances

Two-dimensional disturbances

Three-dimensional disturbances

Some experimental results

18 The Dean proble

The Dean problem

The Taylor-Dean problem

19 The Gortler 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

Unbounded shear layer

Bounded shear layer

24 The initial-value problem

The viscous theory

25 The governing equations

26 The eigenvalue spectrum for small Reynolds numbers

A perturbation expansion

Sufficient conditions for stability

27 Heuristic methods of approximation

……

5 UNIFORM ASYMPTOTIC APPROXIMATIONS

6 ADDITIONAL TOPICS IN LINEAR STABILITY THEORY

7 NONLINEAR STABILITY

APPENDIX. A CLASS OF GENERALIZED AIRY FUNCTIONS

The study of hydrodynamic stability goes back to the theoretical work of Helmhoitz （1868）， KeMn （1871） and Rayleigh （1879，1880） on inviscid flows and， above all， the experimental investi gations of Reynolds （1883）， which initiated the systematic study of viscous shear flows. Reynolds's work stimulated the theoretical investigations of Orr （1907） and Sommerfeld （1908）， who inde~pendently considered small， traveling-wave disturbances of an otherwise steady， parallel flow and derived （what is now known as） the Orr-Sommerfeld equation.