Introduction to Interactive Boundary Layer Theory

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Overview

One of the major achievements in fluid mechanics in the last quarter of the twentieth century has been the development of an asymptotic description of perturbations to boundary layers known generally as 'triple deck theory'. These developments have had a major impact on our understanding of laminar fluid flow, particularly laminar separation. It is also true that the theory rests on three quarters of a century of development of boundary layer theory which involves analysis, experimentation and computation. All these parts go together, and to understand the triple deck it is necessary to understand which problems the triple deck resolves and which computational techniques have been applied. This book presents a unified account of the development of laminar boundary layer theory as a historical study together with a description of the application of the ideas of triple deck theory to flow past a plate, to separation from a cylinder and to flow in channels. The book is intended to provide a graduate level teaching resource as well as a mathematically oriented account for a general reader in applied mathematics, engineering, physics or scientific computation.
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Editorial Reviews

Booknews
This graduate-level text draws together basic boundary layer theory, which has proven to be a remarkable advance in theoretical fluid mechanics but which has been scattered through the literature and so can be hard to follow. The text provides an overview of the subject, with an emphasis on the theory's historical development. It's divided into three sections: early general ideas, the application of matched asymptotic analysis techniques, and modern "triple-deck" structures of the Navier-Stokes equations. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Meet the Author

St John's College, Oxford
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Table of Contents

1 Mathematical and Fluid Mechanical Introduction 1
1.1 Introduction 1
1.2 The Navier-Stokes equations 3
1.3 Boundary conditions 5
1.4 Asymptotic methods 5
1.5 The Euler equations and potential flow 9
1.6 Stokes flow 10
1.7 Oseen's approximation 11
1.8 Basic boundary layer theory 13
1.9 Drag 17
1.10 Summary and overview 20
I The Triple Deck
2 The Boundary Layer on a Flat Plate 25
2.1 Introduction 25
2.2 Semi-infinite plate--Rectangular coordinates 26
2.3 Semi-infinite plate - Parabolic coordinates 36
2.4 The drag on a section of semi-infinite plate 45
2.5 The wake behind a finite length plate 49
2.6 Near wake region 50
2.7 Far wake expansion 59
2.8 The drag on a finite plate 69
2.9 Summary 74
3 The Triple Deck 76
3.1 Introduction 76
3.2 Formulation 82
3.3 The middle deck 83
3.4 The outer deck 85
3.5 The inner deck 86
3.6 Computed results 88
3.7 Drag 90
3.8 Numerical solution of the Navier-Stokes equations 91
3.9 Summary 96
4 Numerical Solution of Triple Deck Equations 97
4.1 Introduction 97
4.2 Numerical solution in rectangular coordinates 98
4.3 Solution using sublayer coordinates 103
4.4 A spectral method 104
4.5 Channel flow 106
II Separation
5 Introduction to Separation 111
6 Separated Flow about a Cylinder 115
6.1 Observation at moderate Reynolds number 115
6.2 Free streamline theory 122
6.3 Boundary layer with a variable pressure gradient 149
6.4 Combined boundary layer--free streamline models 164
6.5 Goldstein's hypothesis of a boundary layer singularity 169
6.6 Direct numerical solution of boundary layer equations 176
6.7 Reprise 183
6.8 Numerical solution of Navier-Stokes equations 184
6.9 Attempts to resolve Goldstein's singularity 194
6.10 Summary 198
7 Prediction of Separation from a Cylinder 199
7.1 Introduction 199
7.2 Sychev's hypothesis for separation 204
7.3 Smith's solution near separation 206
7.4 Separation from a cylinder 208
7.5 Comparison with numerical solutions 210
7.6 Prandtl-Batchelor flow 212
7.7 Summary 218
III Channel Flow
8 Introduction to Channel Flow 223
8.1 Introduction 223
8.2 Asymmetric channels: R[superscript -1] [double less-than sign] [Set membership] [double less-than sign] R[superscript -1/7] 228
8.3 Symmetric channels: R[superscript -1] [double less-than sign] [Set membership] [double less-than sign] 1 233
8.4 Free streamline theory 234
8.5 Computed examples 246
8.6 Numerical solution of the Navier-Stokes equations 250
8.7 Flow near a corner 252
8.8 Summary 261
9 Upstream Influence 263
9.1 Introduction 263
9.2 Asymmetric channels: [Set membership] [similar] R[superscript -1/7] 263
9.3 Upstream influence 266
9.4 A numerical example 276
9.5 Symmetric channels 277
9.6 Prandtl-Batchelor flow in channels 282
9.7 Summary 282
10 Coanda Effect 284
10.1 Introduction 284
10.2 Symmetry and bifurcation 284
10.3 Bifurcation solutions from Navier-Stokes equations 290
10.4 Application of interactive boundary layer theory 292
10.5 Summary 298
Appendix A Problems and Computer Programs 299
A.1 Chapter 1--Introduction 299
A.2 Chapter 2--Flat plate 300
A.3 Chapter 3 & 4--Triple deck 300
A.4 Chapter 5 & 6--Separation 301
A.5 Chapter 7--Prediction of separation from a cylinder 303
A.6 Chapter 8--Channel flow 303
A.7 Chapter 9--Upstream influence 304
A.8 Chapter 10--Coanda effect 306
Bibliography 307
Author Index 323
Subject Index 327
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