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Van Dyke M. Ч Perturbation methods in fluid mechanics
Van Dyke M. Ч Perturbation methods in fluid mechanics

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Ќазвание: Perturbation methods in fluid mechanics

јвтор: Van Dyke M.

јннотаци€:

Techniques for treating regular and singular perturbations are illustrated by application to problems of fluid motion. In particular, the method of matched asymptotic expansions is applied to the aerodynamics of airfoils and wings, and to viscous flow at high and low Reynolds numbers. Other topics include the methods of strained coordinates and of multiple scales, and the improvement of series.


язык: en

–убрика: ‘изика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1964

 оличество страниц: 229

ƒобавлена в каталог: 07.12.2009

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
"Impossible" inner problem      85 101 173
$M^{2}$Чexpansion method      see "Janzen Ч Rayleigh approximation"
Accuracy of asymptotic series      30Ч32
Accuracy, effect of logarithmic terms      202
Accuracy, improvement of      202Ч210
Additive composition      94 190
Airfoil integral      49 172
Airfoil theory, singular perturbation problems      45Ч76
Airfoil, supersonic      106Ч117
Analytic continuation      31Ч32 210
Angle of attack, effective      172 173
Angles, ratio of      83
Approximations, irrational      2
Approximations, rational      2
Approximations, role of in fluid mechanics      1Ч8
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      29Ч30 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 200Ч202 207
Asymptotic series, accuracy of      30Ч32
Asymptotic series, convergence of      27 30Ч32
Asymptotic series, definition      26
Asymptotic series, error in      31
Asymptotic series, power series      27
Asymptotic series, properties of      32Ч34
Asymptotic series, uniqueness of      33Ч34
Asymptotic solution      3
Axisymmetric      see "Body of revolution" "Blunt-body "Paraboloid
Backward influence      38 39 42
Basic solution      4 93
Biconvex airfoil      56Ч59 68 74 97
Blasius series for boundary layer, inverse for parabola      41 211
Blasius series for boundary layer, on circle      18Ч19
Blasius series for boundary layer, on parabola      6 39 204 208
Blasius solution for flat plate      129Ч131
Blasius solution for flat plate, uniqueness      131Ч132
Block matching      74
Blunt-body problem      6 39 40 203 206 207 208Ч209
Blunted wedge in hypersonic flow      182Ч192
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      36Ч37 43 47
Boundary layer in Oseen approximation      156
Boundary layer, change of coordinates      140Ч145
Boundary layer, coordinates      17
Boundary layer, first-order equation      128
Boundary layer, higher approximations      121
Boundary layer, on circle      17Ч19
Boundary layer, on flat plate      129Ч140 142Ч145 196Ч197
Boundary layer, on parabola      6 204 208 211Ч212
Boundary layer, theory      17 121Ч147
Boundary layer, thickness      127
Boundary layer, unsteady growth      38Ч39
Change of characteristics      42 43Ч44
Change of type      42 129
Characteristics, change of      42 43Ч44
Circular cylinder      9Ч20
Circular cylinder in parabolic shear      19 98
Circular cylinder in uniform shear flow      11Ч13
Circular cylinder, at low Reynolds number      161Ч164
Circular cylinder, boundary layer on      17Ч19
Circular cylinder, compressible flow      4 15Ч16 214
Circular cylinder, corrugated      19
Circular cylinder, distorted      13Ч14
Circular cylinder, drag at low Reynolds number      164
Circular cylinder, inviscid irrotational flow      10Ч11
Circular cylinder, Janzen Ч Rayleigh approximation      4 15Ч16
Circular cylinder, porous      19
Circular cylinder, pulsating      19
Circular cylinder, separation      19 121Ч122 150 214
Circular cylinder, skin friction      18
Circular cylinder, Stokes approximation      152Ч153
Circular cylinder, viscous flow      16Ч19
Complementary solution      12
Composite expansion      83Ч85 98 163 197Ч198 199
Composite expansion for blunted wedge      190Ч192
Composite expansion, construction of      94Ч97
Composite expansions, method of      197Ч198 213
Composition, additive      94 190
Composition, multiplicative      96 190
Compressible flow      see "Hypersonic flow" "Subsonic "Supersonic "Transonic
Cone in slightly supersonic flow      176Ч182
Cone, circular perturbation of solution for supersonic flow      9
Conservation principle, global      53
Convergence of asymptotic series      27 30Ч32
Convergence of Janzen Ч Rayleigh expansion      4
Convergence, improvement of      202Ч210
Convergence, radius of      32 206 207Ч208
Convergence, value of      30
Coordinate perturbation      3
Coordinate perturbation for elliptic equations      39Ч40
Coordinate perturbation, boundary layer on flat plate      123
Coordinate perturbation, convergence of      31
Coordinate perturbation, direct expansion      37Ч40
Coordinate perturbation, inverse expansion      41Ч42
Coordinate perturbation, joining of      210Ч212
Coordinate perturbation, nonuniformity of      81
Coordinate perturbation, replacement by parameter perturbation      82Ч83
Coordinate perturbation, singular      82
Coordinates, alternative for flat plate      142Ч144
Coordinates, change of in boundary layer      140Ч145
Coordinates, natural      203Ч204
Coordinates, optimal      141 144Ч146 200
Coordinates, parabolic      142 203 206 209 211
Coordinates, semicharacteristic      108
Coordinates, semioptimal      144 146
Coordinates, shrinking rectangular      143Ч144
Corner on supersonic airfoil      112Ч115
Correlation theorem      142 147
Corrugated quasi cylinder      19
Critical Mach number      4 214
Cumulative effect      106 107
Direct coordinate expansion      37Ч40
Disparate lengths      81 82 168 189 198
Displacement thickness flow due to      132Ч135 137 138 139
Displacement thickness for wake of finite flat plate      136Ч137
Displacement thickness of entropy layer      1 89
Distorted circle      13Ч14
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 209Ч210
Drag, leading-edge      54Ч56 138
Eddy, behind circle and sphere      150 156 159Ч160
Effective angle of attack      1 72 173
Eigensolutions in flat-plate boundary layer      131Ч132
Eigensolutions in inverse coordinate expansions      41 42
Eigensolutions in thin-airfoil theory      52Ч54 58 62Ч67 73 89
Ellipsoid of revolution      74 192
Elliptic airfoil, block matching      74
Elliptic airfoil, composite solution      96Ч97
Elliptic airfoil, incompressible thin-airfoil solution      50Ч52 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      72Ч73
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 118Ч119 167
Elliptic wing      6 168 174Ч176 207 213
Entropy layer      182 186Ч189
Entropy layer, displacement effect      189
Euler transformation      32 33Ч34 207Ч210
Exponential decay of vorticity      131 139Ч140 201
Exponential terms in asymptotic sequence      29
Extension theorem      92
Finite flat plate, first-order boundary layer      123Ч124 129 130
Finite flat plate, inclined in potential flow      169Ч170
Finite flat plate, second-order boundary layer      136Ч137
Finite flat plate, skin friction      137 139
First approximation      4
First-order solution      4
Flat plate in viscous flow, alternative coordinates      142Ч144
Flat plate in viscous flow, alternative interpretations of Blasius solution      122Ч124
Flat plate in viscous flow, boundary-layer solution      129Ч140 142Ч145 196Ч197
Flat plate in viscous flow, finite      123Ч124 129 130 136Ч137
Flat plate in viscous flow, flow due to displacement thickness      132Ч134
Flat plate in viscous flow, leading edge      39 138Ч139
Flat plate in viscous flow, method of composite equations      196Ч197
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      134Ч136
Flat plate in viscous flow, skin friction      137Ч139 140
Flat plate in viscous flow, third-order boundary layer      139Ч140
Flow due to displacement thickness      132Ч135 137 138 139
Free-streamline flow      42
Gauge Functions      23Ч28
Gauge functions, choice of      24Ч25
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 208Ч209
Hypersonic flow, blunted wedge      182Ч192
Hypersonic flow, similarity rule      22 43
Hypersonic small-disturbance theory      22 35 185
Improvement of series      202Ч210
Impulsive motion, blunt body at hypersonic speed      40 206Ч207
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      187Ч189
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      85Ч88
Inner variables, definition      85
Intermediate limit      91 161
Intermediate matching      91Ч93
Intermediate matching principle      92Ч93 161
Intermediate problem      91
Intermediate solution      92
Intermediate variable      91
Inverse Blasius series      41 211
Inverse coordinate expansion      41Ч42
Irrational approximation      2Ч4
Iteration      15 34Ч35
Janzen Ч Rayleigh approximation      4
Janzen Ч Rayleigh approximation for circle      4 15Ч16 35 36
Janzen Ч Rayleigh approximation for parabola      212
Joining of coordinate expansions      210Ч212
Joining of parameter expansions      212Ч213
Joukowski airfoil      54Ч56
Kutta Ч joukowski condition      42 169
Leading edge, round-nosed airfoil      52 53 54Ч56 59Ч68 71Ч73
Leading edge, sharp-nosed airfoil      56Ч57 68Ч70 74
Leading edge, square-nosed airfoil      57Ч59 73
Leading edge, viscous flow over flat plate      39 138Ч139
Leading-edge drag      54Ч56 138
Leading-edge thrust      56
Least degeneracy, principle of      86 127
Lifting-line theory      6 167Ч176 192
Lighthill's rule      61
Lighthill's technique      see "Strained coordinates method
Limit matching principle      90 161
Limit process      21Ч23
Limit process, double      21 189
Limit process, multiple      21 82
Log log      25 29 201
Logarithms      5 200Ч202
Logarithms as gauge functions      25
Logarithms in asymptotic expansions      5 29 30 33 35 47 57 59 68 69 73 140 160Ч161 162 200Ч202 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 160Ч161 162
Logarithms, log log      25 29 201
Logarithms, relation to algebraic companion      201Ч202
Logarithms, source of      68 201
Mach lines, revised      110Ч111
Mach number, critical      4 214
Mass on spring      98
Matched asymptotic expansions, blunted wedge in hypersonic flow      183Ч192
Matched asymptotic expansions, circle at low Reynolds number      161Ч164
Matched asymptotic expansions, failure      213
Matched asymptotic expansions, lifting wing of high aspect ratio      167Ч176
Matched asymptotic expansions, method of      7 77Ч98
Matched asymptotic expansions, sphere at low Reynolds number      156Ч161
Matching      88Ч89 89Ч90 210
Matching and principle of minimum singularity      73 88
Matching condition for boundary layer      128 129
Matching in thin-airfoil theory      64Ч70
Matching of circulation in lifting-line theory      171
Matching order      93Ч94
Matching principle      89Ч90
Matching principle, asymptotic      64 90 128 161 186
Matching principle, intermediate      92Ч93 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 186Ч191 see method
Middle expansion      82 97 183 186Ч191
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      198Ч200 213
Multiplicative composition      96 190
Multiplicative correction, round edges      59Ч61 74
Multiplicative correction, sharp edges      74
Natural coordinates      203Ч204
Navier Ч Stokes equations      124 153 165
Newton Ч Busemann theory      6 22 23
Newtonian approximation      43 208
Nonequilibrium flow over wavy wall      192Ч193
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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