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Introduction to Interactive Boundary Layer Theory : Oxford Texts in Applied and Engineering Mathematics - Ian John Sobey

Introduction to Interactive Boundary Layer Theory

Oxford Texts in Applied and Engineering Mathematics


Published: 1st December 2000
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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 Introductionp. 1
Introductionp. 1
The Navier-Stokes equationsp. 3
Boundary conditionsp. 5
Asymptotic methodsp. 5
The Euler equations and potential flowp. 9
Stokes flowp. 10
Oseen's approximationp. 11
Basic boundary layer theoryp. 13
Dragp. 17
Summary and overviewp. 20
The Triple Deck
The Boundary Layer on a Flat Platep. 25
Introductionp. 25
Semi-infinite plate--Rectangular coordinatesp. 26
Semi-infinite plate - Parabolic coordinatesp. 36
The drag on a section of semi-infinite platep. 45
The wake behind a finite length platep. 49
Near wake regionp. 50
Far wake expansionp. 59
The drag on a finite platep. 69
Summaryp. 74
The Triple Deckp. 76
Introductionp. 76
Formulationp. 82
The middle deckp. 83
The outer deckp. 85
The inner deckp. 86
Computed resultsp. 88
Dragp. 90
Numerical solution of the Navier-Stokes equationsp. 91
Summaryp. 96
Numerical Solution of Triple Deck Equationsp. 97
Introductionp. 97
Numerical solution in rectangular coordinatesp. 98
Solution using sublayer coordinatesp. 103
A spectral methodp. 104
Channel flowp. 106
Introduction to Separationp. 111
Separated Flow about a Cylinderp. 115
Observation at moderate Reynolds numberp. 115
Free streamline theoryp. 122
Boundary layer with a variable pressure gradientp. 149
Combined boundary layer--free streamline modelsp. 164
Goldstein's hypothesis of a boundary layer singularityp. 169
Direct numerical solution of boundary layer equationsp. 176
Reprisep. 183
Numerical solution of Navier-Stokes equationsp. 184
Attempts to resolve Goldstein's singularityp. 194
Summaryp. 198
Prediction of Separation from a Cylinderp. 199
Introductionp. 199
Sychev's hypothesis for separationp. 204
Smith's solution near separationp. 206
Separation from a cylinderp. 208
Comparison with numerical solutionsp. 210
Prandtl-Batchelor flowp. 212
Summaryp. 218
Channel Flow
Introduction to Channel Flowp. 223
Introductionp. 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] 1p. 233
Free streamline theoryp. 234
Computed examplesp. 246
Numerical solution of the Navier-Stokes equationsp. 250
Flow near a cornerp. 252
Summaryp. 261
Upstream Influencep. 263
Introductionp. 263
Asymmetric channels: [Set membership] [similar] R[superscript -1/7]p. 263
Upstream influencep. 266
A numerical examplep. 276
Symmetric channelsp. 277
Prandtl-Batchelor flow in channelsp. 282
Summaryp. 282
Coanda Effectp. 284
Introductionp. 284
Symmetry and bifurcationp. 284
Bifurcation solutions from Navier-Stokes equationsp. 290
Application of interactive boundary layer theoryp. 292
Summaryp. 298
Problems and Computer Programsp. 299
Chapter 1--Introductionp. 299
Chapter 2--Flat platep. 300
Chapter 3 and 4--Triple deckp. 300
Chapter 5 and 6--Separationp. 301
Chapter 7--Prediction of separation from a cylinderp. 303
Chapter 8--Channel flowp. 303
Chapter 9--Upstream influencep. 304
Chapter 10--Coanda effectp. 306
Bibliographyp. 307
Author Indexp. 323
Subject Indexp. 327
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780198506751
ISBN-10: 0198506759
Series: Oxford Texts in Applied and Engineering Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 346
Published: 1st December 2000
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 24.1 x 16.1  x 2.3
Weight (kg): 0.63