Fluid Mechanics and Singular Perturbations

Fluid Mechanics and Singular Perturbations

1st Edition - January 1, 1967

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  • Editor: Paco Lagerstrom
  • eBook ISBN: 9780323152822

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Fluid Mechanics and Singular Perturbations: A Collection of Papers by Saul Kaplun focuses on the works and contributions of Saul Kaplun to the studies of fluid mechanics and singular perturbations. The book first discusses the role of coordinate system in boundary-layer theory. Boundary-layer approximations as limits of exact solutions; comparison of different boundary-layer solutions; and comparison with exact solution and choice of optimal are discussed. The text also looks at asymptotic experiment of Navier-Stokes solution for small Reynolds numbers; basic concepts in the theory of singular perturbations and their applications to flow at small Reynolds numbers; and low Reynolds number flow. The book discusses as well a generalization of Poiseuille and Couette flows and nature of solutions of the boundary-layer equations. Numerical solutions and analyses are presented. The text also looks at compatibility condition for boundary layer equation at a point of zero skin friction. Intuitive background; the past-like solution and its principal asymptotic expansions; and class of compatible profiles are discussed. The book is a valuable source of information for readers who want to study fluid mechanics.

Table of Contents

  • 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


    Subject Index

Product details

  • No. of pages: 384
  • Language: English
  • Copyright: © Academic Press 1967
  • Published: January 1, 1967
  • Imprint: Academic Press
  • eBook ISBN: 9780323152822

About the Editor

Paco Lagerstrom

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