Fluid Mechanics and Singular Perturbations

Foreword

Part One Theory of Singular Perturbations with Applications to the Asymptotic Theory of the Navier-Stokes Equations

Introduction to Part I

Chapter I The Role of Coordinate Systems in Boundary-Layer Theory, Reprint from Journal of Applied Mathematics and Physics, Vol. V, pp. 111-135, 1954

§ 1. Introduction

§ 2. Boundary-Layer Approximations as Limits of Exact Solutions

§ 3. Comparison of Different Boundary-Layer Solutions

§ 4. Comparison with Exact Solution. Choice of Optimal Coordinates

§ 5. Examples

§ 6. Discussion

Chapter II Asymptotic Expansions of Navier-Stokes Solutions for Small Reynolds Numbers, Reprint from Journal of Mathematics and Mechanics, Vol. 6, No. 5, September, 1957, pp. 585-593

§ 1. Introduction

§ 2. Outer and Inner Limits and Expansions

§ 3. Intermediate Limits

§ 4. Matching. Intermediate Expansions

§ 5. Application to Flow Past a Sphere

§ 6. Composite Expansion

§ 7. Drag

§ 8. Explicit Expression for for the Sphere

Chapter III Low Reynolds Number Flow Past a Circular Cylinder, Reprint from Journal of Mathematics and Mechanics, Vol. 6, No. 5, September 1957, pp. 595-603

§ 1. Result

§ 2. Derivation of u0

§ 3. Derivation of g1 and u1

§ 4. Composite Expansion. Lamb's Solution

§ 5. Influence of Non-Linear Terms: u2 and g2

§ 6. Cylinder of Arbitrary Cross-Section

§ 7. Numerical Aspects

Editors' Notes to Chapters II and III

Chapter IV Basic Concepts in the Theory of Singular Perturbations and Their Applications to Flow at Small Reynolds Numbers

§ 1. Limits and Expansions

§ 2. Matching Conditions

Editors' Notes to Chapter IV

Chapter V Low Reynolds Number Flow: Two-Dimensional Lifting Case

§ 1. Characteristic Solution; Characteristic Directions; Equivalent Diameter

§ 2. Lift Perturbation

Editors' Notes to Chapter V

Chapter VI Further Remarks on Orders

§ 1. The Function Space J and Its Quotient Spaces

§ 2. Uniform Approximation. Sets of J Validity

§ 3. Topological Structure of

Editors' Notes to Chapter VI

Part Two Separation in Laminar Boundary Layers

Introduction to Part II

Chapter I A Generalization of Poiseuille and Couette Flows

§ 1. Preliminaries

§ 2. The Expansion for Small ε

§ 3. The Expansion for ε Fixed

Editors' Notes to Chapter I

Chapter II On Nature of Solutions of the Boundary-Layer Equations Near Zeroes of υ

§ 1. Preliminaries

§ 2. Simple Zero

§ 3. Double Zero

Editors' Notes to Chapter II

Chapter III Compatibility Conditions for the Boundary-Layer Equations at a Point of Zero Skin Friction

§ 1. Intuitive Background

§ 2. The Past-Like Solution and Its Principal Asymptotic Expansions

§ 3. A Class of Compatible Profiles

Editors' Notes to Chapter III

Bibliography

Subject Index