Introduction to Interactive Boundary Layer Theory Book

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