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| Van Dyke M. — Perturbation methods in fluid mechanics |
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| Ïðåäìåòíûé óêàçàòåëü |
Nonuniformity in high-aspect-ratio wing theory 170 176
Nonuniformity in supersonic airfoil theory 106—109
Nonuniformity of coordinate perturbations 81
Nonuniformity region of see "Region of nonuniformity"
Nonuniformity, model equation 78—80
Nonuniformity, multiple 82
Nonuniformity, physical criterion 80—83 168
Nonuniformity, prediction of 78
Nonuniformity, source of 78—80
Nonuniqueness see "Eigensolutions"
Nonuniqueness of Blasius solution for flat plate 131—132
Nonuniqueness of thin-airfoil solution 52—54
Nose-correction rules, bodies of revolution 74
Nose-correction rules, round edge 59—68 71—73
Nose-correction rules, sharp edge 68—70 74
Nose-correction rules, two edges 97
Optimal coordinates 141 144—146 200
Order symbols O and o 23—29
Order symbols Î and o, operations with 25—26
Order symbols Î and o, relation to physical order of magnitude 25
Osculating parabola 56 59—60 63—64 66 67 73
Oseen approximation 5 153—156
Oseen approximation for boundary layer 156
Oseen approximation for flat plate 165 198
Oseen approximation for paraboloid 165
Oseen approximation for plane wake 165
Oseen approximation for sphere 5 155 206 209—210
Oseen expansion 156 157—158 159 165
Oseen solution 5 155 206 209—210
Oseen solution, pulsating 43
Oseen solution, second approximation at low Reynolds number 159—161
Oseen solution, separation 150 159—160
Oseenlet 158 162
Outer expansion 64
Outer expansion for boundary layer on flat plate 124—126
Outer expansion for entropy layer 185
Outer expansion for lifting-line theory 171 173
Outer expansion, definition 85
Outer expansion, distinction from inner expansion 93
Outer limit 85
outer variables 64 85
Overlap domain 89 90 92
Parabola, boundary layer 6 204 208 211—212
Parabola, drag 55—56
Parabola, exact complex velocity 71
Parabola, Janzen — Rayleigh expansion 212
Parabola, osculating 56 59—60 63—64 66 67 73
Parabola, potential flow 88
Parabola, skin friction 6 204 208 213
Parabola, surface speed 60
Parabola, thin-airfoil approximation 60 71
Parabolic coordinates 142 203 206 209 211
Parabolic equations, direct coordinate expansion 38
Parabolic equations, inverse coordinate expansion 41
Parabolic equations, method of strained coordinates 100 118—119 167
Parabolic shear, circle in 19 98
Paraboloid of revolution 75 165
Paraboloidal shock wave 6 40 203—204 206 208—209
Paradox, d'Alembert's 153
Paradox, Stokes' 152
Paradox, Whitehead's 152—153
Parameter perturbation 3
Parameter perturbation, convergence of 31
Parameter perturbation, joining 212—213
Parameter perturbation, regular 81
Parameter perturbation, singular 81—82
Parameter, artificial 75 132
Particular integral 12 36
Particular integral, finding 36
Particular integral, general 36 75
Patching 54 89 140 211 212
Perturbation expansion, examples 4—6
Perturbation expansion, regular 6—8 9—20
Perturbation expansion, singular 6—8 33
Perturbation quantity 2 22—23
Perturbation quantity, choice of 22—23
Physical criterion for uniformity 80—83 168
Pi, series for 202—203
Plate see "Finite flat plate" "Flat
PLK method see "Strained coordinates method
Porous circle 19
Pressure coefficient, cone in slightly supersonic flow 178 182
Pressure coefficient, subsonic thin-airfoil theory 75
Primary reference length 80 168
Principle of least degeneracy 86 127
Principle of minimum singularity 53 64 65 73 88 132 158 163
Propeller, linearized supersonic theory 36
Pseudo-transonic flow 78 107
Pulsating circle 19
Radius of convergence 32 206 207—208
Rational approximation 2—4
Rational fraction 205—207
Rectangular airfoil 56—59 73
Reference length, primary 80 168
Reference length, secondary 81 82 83 168
Region of nonuniformity 104
Region of nonuniformity in boundary layer 126
Region of nonuniformity in thin-airfoil theory 51 57 58
Region of nonuniformity, at low Reynolds number 153—154
Region of nonuniformity, exponentially small 57 87—88
Regular perturbation problem 6—8 9—20 81 82
Reynolds number 16
Reynolds Number, high 121—147
Reynolds number, infinite, limiting flow for 121—122
Reynolds number, low 149—166
Round edge, local solution 62—68
Round edge, multiplicative correction 59—61 74
Round edge, nonuniformity in thin-airfoil theory 52 53 54—56
Round edge, shifting correction 71—73
Secondary reference length 81 82 83 168
Self-similar solution 1—2 4 129
| Semicharacteristic coordinates 108
Separation of flow 121—122 150 159—160 214
Series expansion 34—35
Series expansion, improvement of convergence 202—210
Series expansion, successive approximations by 34
Sharp edge 56—57 68—70 74
Shear flow past circle 11—13 19—20 98
Shear flow past flat plate 146—147
Shifting correction for round edges 71—73
Shock wave on supersonic airfoil 115—116
Shrinking rectangular coordinates 143—144
Similarity parameter 21—22
Similarity parameter for hypersonic flow 22
Similarity parameter for transonic flow 21 182
Similarity rule, hypersonic 22 43
Similarity rule, second-order subsonic 76 212
Similarity rule, transonic 21 182
Singular perturbation problem 6—8 33 45
Singular perturbation problem at high and low Reynolds number 153
Singular perturbation problem in airfoil theory 45—76
Singular perturbation problem in coordinate perturbation 82
Singular perturbation problem in parameter perturbation 81—82
Singular perturbation problem, inviscid 167—193
Singular perturbation problem, prediction of 78
Singular perturbation problem, slight bluntness 182
Skin friction on circle 18
Skin friction on circle on finite flat plate 137 139
Skin friction on circle on parabola 6 204 208 211—212 213
Skin friction on circle on semi-infinite flat plate 137—139 140
Slender-body theory 5 37 74 75
Slight shear flow past circle 11—13 19—20 98
Slightly distorted circle 13—14
SLIP 147
Source distribution for airfoil 49 59 71
Source plane 49
Sphere drag 5 149 161 206 209—210
Spindle, body of revolution 74
Square edge 57—59 73
Standoff distance for blunt body 6 40 208—209
Stokes approximation 5
Stokes approximation for circle 151—152
Stokes approximation for parabola 166
Stokes approximation for paraboloid 165
Stokes approximation for sphere 151—152
Stokes expansion 156 159—161 161—164
Stokes' paradox 152
Stokeslet 152 158
Strained coordinates for blunted bodies in hypersonic flow 192
Strained coordinates for elliptic and parabolic equations 100 118—119 167
Strained coordinates for slightly supersonic How past cone 177—182
Strained coordinates for supersonic airfoil theory 109—112
Strained coordinates inapplicability of 118 192
Strained coordinates utility of 118—119
Strained coordinates, comparison with method of matchedasymptotic expansions 100—101 104—106 118—119
Strained coordinates, method of 7 99—120
Strained coordinates, relation to optimal coordinates 146
Strained coordinates, resemblance to method of multiple scales 199
Stream function for blunt body in supersonic flow 39—40 203—204 206
Stream function for circle in plane potential flow 10
Stream function for circle in shear flow 12
Stream function for plane compressible flow 183
Stream function for plane incompressible flow 10
Stream function for slightly distorted circle 14
Stream function for thin-airfoil theory 73
Stream function for viscous flow near leading edge of flat plate 39
Subsonic flow past body of revolution, particular integral 36
Subsonic flow past circle 15—16
Subsonic flow past parabola 212—213
Subsonic flow past thin airfoil 75—76
Subsonic flow second-order similarity rule 76 212
Subsonic flow, potential equation for 15
Successive approximations 34—36
Supersonic flow airfoil theory 106—117
Supersonic flow past blunt body 6 39—40 203 206 207 208—209
Supersonic flow past slender body of revolution, particular integral 36
Supersonic flow past slender cone 176—182
Tangency condition see "Boundary conditions"
Thin-airfoil theory 5 29 33 35 45—76 213
Transcendentally small term 34 163 166
Transfer of boundary conditions 36—37 43 47
Transonic flow 35
Transonic flow, pseudo-transonic 78 107
Transonic flow, similarity rule 21 182
Transonic flow, slender cone 176—182
Transonic flow, small-disturbance theory 177
Type, change of 42 129
Uniformity, physical criterion for 80—83 168
Uniformly valid expansion see "Composite expansion"
Uniqueness of Blasius solution for flat plate 131—132
Uniqueness of thin-airfoil solution 52—54
Upstream influence 129
Velocity potential for circle in incompressible flow 11
Velocity potential for circle in subsonic flow 15—16
Velocity potential for plane source 49
Velocity potential in subsonic flow, equation for 15
Viscous flow at high Reynolds number 121—147 see
Viscous flow at low Reynolds number 149—166 see "Oseen
Viscous flow near leading edge of flat plate 39 138—139
Viscous flow past circle and sphere 150
Viscous flow past paraboloid 165
Vorticity, exponential decay in boundary layer 131 139—140 201
Vorticity, external, effect of 146
Wake of finite flat plate 136—137
Wake plane 165
Wake, axisymmetric 166
Wedge, blunted in hypersonic flow 182—192
Wedge, boundary layer on 146
Wedge, potential flow past 69
Whitehead's paradox 152—153
Wing of high aspect ratio 6 167—176
Wing, elliptic 6 168 174—176 207 213
Wing, thickness effects 192
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