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| Ïîèñê ïî óêàçàòåëÿì |
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| Van Dyke M. — Perturbation methods in fluid mechanics |
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| Ïðåäìåòíûé óêàçàòåëü |
"Impossible" inner problem 85 101 173
 —expansion method see "Janzen — Rayleigh approximation"
Accuracy of asymptotic series 30—32
Accuracy, effect of logarithmic terms 202
Accuracy, improvement of 202—210
Additive composition 94 190
Airfoil integral 49 172
Airfoil theory, singular perturbation problems 45—76
Airfoil, supersonic 106—117
Analytic continuation 31—32 210
Angle of attack, effective 172 173
Angles, ratio of 83
Approximations, irrational 2
Approximations, rational 2
Approximations, role of in fluid mechanics 1—8
Artificial parameter 75 132
Asymptotic expansion see "Asymptotic series"
Asymptotic form 26 90
Asymptotic matching principle 64 90 128 161 186
Asymptotic representation 26 90
Asymptotic sequence for thin-airfoil theory 47 73
Asymptotic sequence, alternative 28
Asymptotic sequence, choice of 29—30 35 125
Asymptotic sequence, definition 28
Asymptotic sequence, difference between inner and outer 84 104
Asymptotic sequence, logarithms in 5 29 30 33 35 47 57 59 69 200—202 207
Asymptotic series, accuracy of 30—32
Asymptotic series, convergence of 27 30—32
Asymptotic series, definition 26
Asymptotic series, error in 31
Asymptotic series, power series 27
Asymptotic series, properties of 32—34
Asymptotic series, uniqueness of 33—34
Asymptotic solution 3
Axisymmetric see "Body of revolution" "Blunt-body "Paraboloid
Backward influence 38 39 42
Basic solution 4 93
Biconvex airfoil 56—59 68 74 97
Blasius series for boundary layer, inverse for parabola 41 211
Blasius series for boundary layer, on circle 18—19
Blasius series for boundary layer, on parabola 6 39 204 208
Blasius solution for flat plate 129—131
Blasius solution for flat plate, uniqueness 131—132
Block matching 74
Blunt-body problem 6 39 40 203 206 207 208—209
Blunted wedge in hypersonic flow 182—192
Body of revolution, nose-correction rules for incompressible flow 74
Body of revolution, paraboloid 75 165
Body of revolution, slender-body theory 74
Boundary conditions, discontinuities in 42
Boundary conditions, loss of 80 88 126
Boundary conditions, perturbation of 9 11 13
Boundary conditions, transfer of 36—37 43 47
Boundary layer in Oseen approximation 156
Boundary layer, change of coordinates 140—145
Boundary layer, coordinates 17
Boundary layer, first-order equation 128
Boundary layer, higher approximations 121
Boundary layer, on circle 17—19
Boundary layer, on flat plate 129—140 142—145 196—197
Boundary layer, on parabola 6 204 208 211—212
Boundary layer, theory 17 121—147
Boundary layer, thickness 127
Boundary layer, unsteady growth 38—39
Change of characteristics 42 43—44
Change of type 42 129
Characteristics, change of 42 43—44
Circular cylinder 9—20
Circular cylinder in parabolic shear 19 98
Circular cylinder in uniform shear flow 11—13
Circular cylinder, at low Reynolds number 161—164
Circular cylinder, boundary layer on 17—19
Circular cylinder, compressible flow 4 15—16 214
Circular cylinder, corrugated 19
Circular cylinder, distorted 13—14
Circular cylinder, drag at low Reynolds number 164
Circular cylinder, inviscid irrotational flow 10—11
Circular cylinder, Janzen — Rayleigh approximation 4 15—16
Circular cylinder, porous 19
Circular cylinder, pulsating 19
Circular cylinder, separation 19 121—122 150 214
Circular cylinder, skin friction 18
Circular cylinder, Stokes approximation 152—153
Circular cylinder, viscous flow 16—19
Complementary solution 12
Composite expansion 83—85 98 163 197—198 199
Composite expansion for blunted wedge 190—192
Composite expansion, construction of 94—97
Composite expansions, method of 197—198 213
Composition, additive 94 190
Composition, multiplicative 96 190
Compressible flow see "Hypersonic flow" "Subsonic "Supersonic "Transonic
Cone in slightly supersonic flow 176—182
Cone, circular perturbation of solution for supersonic flow 9
Conservation principle, global 53
Convergence of asymptotic series 27 30—32
Convergence of Janzen — Rayleigh expansion 4
Convergence, improvement of 202—210
Convergence, radius of 32 206 207—208
Convergence, value of 30
Coordinate perturbation 3
Coordinate perturbation for elliptic equations 39—40
Coordinate perturbation, boundary layer on flat plate 123
Coordinate perturbation, convergence of 31
Coordinate perturbation, direct expansion 37—40
Coordinate perturbation, inverse expansion 41—42
Coordinate perturbation, joining of 210—212
Coordinate perturbation, nonuniformity of 81
Coordinate perturbation, replacement by parameter perturbation 82—83
Coordinate perturbation, singular 82
Coordinates, alternative for flat plate 142—144
Coordinates, change of in boundary layer 140—145
Coordinates, natural 203—204
Coordinates, optimal 141 144—146 200
Coordinates, parabolic 142 203 206 209 211
Coordinates, semicharacteristic 108
Coordinates, semioptimal 144 146
Coordinates, shrinking rectangular 143—144
Corner on supersonic airfoil 112—115
Correlation theorem 142 147
Corrugated quasi cylinder 19
Critical Mach number 4 214
Cumulative effect 106 107
Direct coordinate expansion 37—40
Disparate lengths 81 82 168 189 198
Displacement thickness flow due to 132—135 137 138 139
Displacement thickness for wake of finite flat plate 136—137
Displacement thickness of entropy layer 1 89
Distorted circle 13—14
Divortex 173
Double limit process 21 189
Drag of circle at low Reynolds number 164
Drag of sphere at low Reynolds number 5 149 161 206 209—210
Drag, leading-edge 54—56 138
Eddy, behind circle and sphere 150 156 159—160
Effective angle of attack 1 72 173
Eigensolutions in flat-plate boundary layer 131—132
Eigensolutions in inverse coordinate expansions 41 42
Eigensolutions in thin-airfoil theory 52—54 58 62—67 73 89
Ellipsoid of revolution 74 192
Elliptic airfoil, block matching 74
Elliptic airfoil, composite solution 96—97
Elliptic airfoil, incompressible thin-airfoil solution 50—52 72
Elliptic airfoil, inner and outer solutions 94
Elliptic airfoil, inviscid complex velocity 73
Elliptic airfoil, inviscid surface speed 52
Elliptic airfoil, local solution near edge 62
Elliptic airfoil, shifting correction 72—73
Elliptic airfoil, subsonic thin-airfoil expansion 5
Elliptic equations, direct coordinate expansion 39
| Elliptic equations, initial-value problem 39
Elliptic equations, inverse coordinate expansion 41
Elliptic equations, method of strained coordinates 100 118—119 167
Elliptic wing 6 168 174—176 207 213
Entropy layer 182 186—189
Entropy layer, displacement effect 189
Euler transformation 32 33—34 207—210
Exponential decay of vorticity 131 139—140 201
Exponential terms in asymptotic sequence 29
Extension theorem 92
Finite flat plate, first-order boundary layer 123—124 129 130
Finite flat plate, inclined in potential flow 169—170
Finite flat plate, second-order boundary layer 136—137
Finite flat plate, skin friction 137 139
First approximation 4
First-order solution 4
Flat plate in viscous flow, alternative coordinates 142—144
Flat plate in viscous flow, alternative interpretations of Blasius solution 122—124
Flat plate in viscous flow, boundary-layer solution 129—140 142—145 196—197
Flat plate in viscous flow, finite 123—124 129 130 136—137
Flat plate in viscous flow, flow due to displacement thickness 132—134
Flat plate in viscous flow, leading edge 39 138—139
Flat plate in viscous flow, method of composite equations 196—197
Flat plate in viscous flow, optimal coordinates 144 145
Flat plate in viscous flow, Oseen approximation 165 198
Flat plate in viscous flow, second-order boundary layer 134—136
Flat plate in viscous flow, skin friction 137—139 140
Flat plate in viscous flow, third-order boundary layer 139—140
Flow due to displacement thickness 132—135 137 138 139
Free-streamline flow 42
Gauge Functions 23—28
Gauge functions, choice of 24—25
General particular integral 36 75
Generalized asymptotic expansion see "Composite expansion"
Global conservation principle 53
Group property 129 131 146
Hyperbolic equations, change of characteristics 42
Hyperbolic equations, direct coordinate expansion 38
Hyperbolic equations, inverse coordinate expansion 41
Hyperbolic shock wave 183
Hypersonic flow, blunt body 6 40 208—209
Hypersonic flow, blunted wedge 182—192
Hypersonic flow, similarity rule 22 43
Hypersonic small-disturbance theory 22 35 185
Improvement of series 202—210
Impulsive motion, blunt body at hypersonic speed 40 206—207
Impulsive motion, circle in viscous flow 214
Impulsive motion, cylinder in viscous flow 214
Indeterminacy see also "Eigensolutions"
Indeterminacy in boundary-layer solution 132
Indeterminacy in inverse coordinate expansions 41
Initial-value problem for elliptic equations 39
Inner and outer expansions see "Matched asymptotic expansions method
Inner expansion 64 84
Inner expansion for boundary layer 127
Inner expansions for boundary layer on semi-infinite flat plate 140
Inner expansions for entropy layer 187—189
Inner expansions for lifting-line theory 172
Inner expansions, definition 85
Inner expansions, distinction from outer expansion 93
Inner limit 85
Inner variables 64 84
Inner variables for entropy layer 187
Inner variables for lifting wing of high aspect ratio 169
Inner variables, choice of 85—88
Inner variables, definition 85
Intermediate limit 91 161
Intermediate matching 91—93
Intermediate matching principle 92—93 161
Intermediate problem 91
Intermediate solution 92
Intermediate variable 91
Inverse Blasius series 41 211
Inverse coordinate expansion 41—42
Irrational approximation 2—4
Iteration 15 34—35
Janzen — Rayleigh approximation 4
Janzen — Rayleigh approximation for circle 4 15—16 35 36
Janzen — Rayleigh approximation for parabola 212
Joining of coordinate expansions 210—212
Joining of parameter expansions 212—213
Joukowski airfoil 54—56
Kutta — joukowski condition 42 169
Leading edge, round-nosed airfoil 52 53 54—56 59—68 71—73
Leading edge, sharp-nosed airfoil 56—57 68—70 74
Leading edge, square-nosed airfoil 57—59 73
Leading edge, viscous flow over flat plate 39 138—139
Leading-edge drag 54—56 138
Leading-edge thrust 56
Least degeneracy, principle of 86 127
Lifting-line theory 6 167—176 192
Lighthill's rule 61
Lighthill's technique see "Strained coordinates method
Limit matching principle 90 161
Limit process 21—23
Limit process, double 21 189
Limit process, multiple 21 82
Log log 25 29 201
Logarithms 5 200—202
Logarithms as gauge functions 25
Logarithms in asymptotic expansions 5 29 30 33 35 47 57 59 68 69 73 140 160—161 162 200—202 207
Logarithms in inverse coordinate expansions 41 42
Logarithms in lifting-line theory 173 176
Logarithms in thin-airfoil theory 57 59 68 69 73
Logarithms in viscous-flow solutions 140 160—161 162
Logarithms, log log 25 29 201
Logarithms, relation to algebraic companion 201—202
Logarithms, source of 68 201
Mach lines, revised 110—111
Mach number, critical 4 214
Mass on spring 98
Matched asymptotic expansions, blunted wedge in hypersonic flow 183—192
Matched asymptotic expansions, circle at low Reynolds number 161—164
Matched asymptotic expansions, failure 213
Matched asymptotic expansions, lifting wing of high aspect ratio 167—176
Matched asymptotic expansions, method of 7 77—98
Matched asymptotic expansions, sphere at low Reynolds number 156—161
Matching 88—89 89—90 210
Matching and principle of minimum singularity 73 88
Matching condition for boundary layer 128 129
Matching in thin-airfoil theory 64—70
Matching of circulation in lifting-line theory 171
Matching order 93—94
Matching principle 89—90
Matching principle, asymptotic 64 90 128 161 186
Matching principle, intermediate 92—93 161
Matching principle, limit 90 161
Matching to determine eigensolutions 53
Method of matched asymptotic expansions see "Matched asymptotic expansions method
Method of strained coordinates 82 97 183 186—191 see method
Middle expansion 82 97 183 186—191
Middle variable 186
Minimum singularity, principle of 53 64 65 73 88 132 158 163
Multiple limit process 21 82 189
Multiple scales, method of 198—200 213
Multiplicative composition 96 190
Multiplicative correction, round edges 59—61 74
Multiplicative correction, sharp edges 74
Natural coordinates 203—204
Navier — Stokes equations 124 153 165
Newton — Busemann theory 6 22 23
Newtonian approximation 43 208
Nonequilibrium flow over wavy wall 192—193
Nonuniformity 33 see
Nonuniformity at sharp stagnation edge 57
Nonuniformity at square edge 58
Nonuniformity for blunted wedge in hypersonic flow 185 187
Nonuniformity for elliptic airfoil 50
Nonuniformity in conical flow 83
Nonuniformity in direct coordinate expansions 39
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