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