1300 187 187
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.
This book provides various physical/engineering/historical insights on this topic. EMS Sobey includes recent work in a seamless manner ... a very readable book. New Scientist
| Mathematical and Fluid Mechanical Introduction | p. 1 |
| Introduction | p. 1 |
| The Navier-Stokes equations | p. 3 |
| Boundary conditions | p. 5 |
| Asymptotic methods | p. 5 |
| The Euler equations and potential flow | p. 9 |
| Stokes flow | p. 10 |
| Oseen's approximation | p. 11 |
| Basic boundary layer theory | p. 13 |
| Drag | p. 17 |
| Summary and overview | p. 20 |
| The Triple Deck | |
| The Boundary Layer on a Flat Plate | p. 25 |
| Introduction | p. 25 |
| Semi-infinite plate--Rectangular coordinates | p. 26 |
| Semi-infinite plate - Parabolic coordinates | p. 36 |
| The drag on a section of semi-infinite plate | p. 45 |
| The wake behind a finite length plate | p. 49 |
| Near wake region | p. 50 |
| Far wake expansion | p. 59 |
| The drag on a finite plate | p. 69 |
| Summary | p. 74 |
| The Triple Deck | p. 76 |
| Introduction | p. 76 |
| Formulation | p. 82 |
| The middle deck | p. 83 |
| The outer deck | p. 85 |
| The inner deck | p. 86 |
| Computed results | p. 88 |
| Drag | p. 90 |
| Numerical solution of the Navier-Stokes equations | p. 91 |
| Summary | p. 96 |
| Numerical Solution of Triple Deck Equations | p. 97 |
| Introduction | p. 97 |
| Numerical solution in rectangular coordinates | p. 98 |
| Solution using sublayer coordinates | p. 103 |
| A spectral method | p. 104 |
| Channel flow | p. 106 |
| Separation | |
| Introduction to Separation | p. 111 |
| Separated Flow about a Cylinder | p. 115 |
| Observation at moderate Reynolds number | p. 115 |
| Free streamline theory | p. 122 |
| Boundary layer with a variable pressure gradient | p. 149 |
| Combined boundary layer--free streamline models | p. 164 |
| Goldstein's hypothesis of a boundary layer singularity | p. 169 |
| Direct numerical solution of boundary layer equations | p. 176 |
| Reprise | p. 183 |
| Numerical solution of Navier-Stokes equations | p. 184 |
| Attempts to resolve Goldstein's singularity | p. 194 |
| Summary | p. 198 |
| Prediction of Separation from a Cylinder | p. 199 |
| Introduction | p. 199 |
| Sychev's hypothesis for separation | p. 204 |
| Smith's solution near separation | p. 206 |
| Separation from a cylinder | p. 208 |
| Comparison with numerical solutions | p. 210 |
| Prandtl-Batchelor flow | p. 212 |
| Summary | p. 218 |
| Channel Flow | |
| Introduction to Channel Flow | p. 223 |
| Introduction | p. 223 |
| Asymmetric channels: R[superscript -1] [double less-than sign] [Set membership] [double less-than sign] R[superscript -1/7] | p. 228 |
| Symmetric channels: R[superscript -1] [double less-than sign] [Set membership] [double less-than sign] 1 | p. 233 |
| Free streamline theory | p. 234 |
| Computed examples | p. 246 |
| Numerical solution of the Navier-Stokes equations | p. 250 |
| Flow near a corner | p. 252 |
| Summary | p. 261 |
| Upstream Influence | p. 263 |
| Introduction | p. 263 |
| Asymmetric channels: [Set membership] [similar] R[superscript -1/7] | p. 263 |
| Upstream influence | p. 266 |
| A numerical example | p. 276 |
| Symmetric channels | p. 277 |
| Prandtl-Batchelor flow in channels | p. 282 |
| Summary | p. 282 |
| Coanda Effect | p. 284 |
| Introduction | p. 284 |
| Symmetry and bifurcation | p. 284 |
| Bifurcation solutions from Navier-Stokes equations | p. 290 |
| Application of interactive boundary layer theory | p. 292 |
| Summary | p. 298 |
| Problems and Computer Programs | p. 299 |
| Chapter 1--Introduction | p. 299 |
| Chapter 2--Flat plate | p. 300 |
| Chapter 3 and 4--Triple deck | p. 300 |
| Chapter 5 and 6--Separation | p. 301 |
| Chapter 7--Prediction of separation from a cylinder | p. 303 |
| Chapter 8--Channel flow | p. 303 |
| Chapter 9--Upstream influence | p. 304 |
| Chapter 10--Coanda effect | p. 306 |
| Bibliography | p. 307 |
| Author Index | p. 323 |
| Subject Index | p. 327 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
ISBN: 9780198506751
ISBN-10: 0198506759
Series: Oxford Texts in Applied & Engineering Mathematics
Audience:
Tertiary; University or College
Format:
Hardcover
Language:
English
Number Of Pages: 346
Published: 30th November 2000
Publisher: Oxford University Press
Dimensions (cm): 23.4 x 15.6
x 2.3
Weight (kg): 0.626
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