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Ting L., Klein R. — Viscous Vortical Flows (Lecture Notes in Physics)
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Название: Viscous Vortical Flows (Lecture Notes in Physics)Авторы: Ting L., Klein R. Аннотация: From the reviews:
Язык: Рубрика: Физика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1991Количество страниц: 227Добавлена в каталог: 14.11.2008Операции: Положить на полку |
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Accuracy Acoustic, monopole 3 27 34 102 Acoustic, potential 34 Acoustic, quadrupole 3 27 34 42 102 Approximate, boundary data 8 124 126 Approximate, N.-S.-solution 8 118 133 150 153 155 Asymmetric/symmetric parts of solutions 65ff Atmosphere 189 also Axial mass flux in a vortex core 109 Axial, core dynamics 181 Axisymmetric (coaxial) vortex rings 162 Axisymmetric problems 2 6 9 16 103 Background, rotational flow Background, velocity potential 11 38/39 Bessel vortex 175 189 190 Biot-Savart integral 5 38/39 52 79 177 Biot-Savart integral, finite part of 55 82 90 Body forces 175 also Boundary data for farfield acoustics 33 Boundary data, proximate 8 117 121 126 Boundary layer 29 176 187 Cancellation of vorticity 112 133 157 168 169 172 Center of vorticity 18 19 136 143 Center of vorticity, of positive sign (2-D) 137 Circulation (vortex strength) 4 42 78 86 Circulation (vortex strength) for axisymmetric flow 17 162 Classical inviscid theory 5 8 42 70 Classification of mergings Coaxial moment 13 22 Coaxial vortex rings Compatibility conditions for 2-D vortices 63 Compatibility conditions for filaments 6 84 85 Complex potential 44 51 Composite numerical schemes 129 131 132 Composite solutions 100 Compressibility effects 3 26 Consistency conditions 2 9 13 20 22 Convection of background vorticity 186 coordinates Core size Core structure 5 6 Core structure for 2-D vortices 55 66 76 Core structure for filaments 86 94ff 181 Core structure for vortex rings 103 Cross flow behind wings 142 Curvilinear coordinates 52 79 Cutting of a filament Decay length 4 118 Decay, farfield of vorticity 2 12 19 20 134 150 Decay, time of polar moment 19 Delta wing 181 Density, fluctuation Dilatation 3 30 31 Dissipation function 29 16 Dissipation, rate of energy 3 9 16 28 36 102 Doublet as long time limit 138 Doublet farfield in 2-D flows 44 76 Doublet in farfield acoustics 34 Doublet in general farfield expansions 3 9 16 18 25 Doublet optimum 136 Doublet, long time motion 159 Doublet, vector 16 Effective height Efficient numerical scheme 7 Efficient numerical scheme, meaning of 123 126 Energy dissipation Errors, sources of numerical 121 125 Euler background solution 187 Euler equations 5 Expansion parameter for 2-D vortices 45 57 Expansion parameter for farfield acoustics 26 Expansion parameter for slender filaments 3 Expansion scheme for 2-D flows 49 59 61/62 Expansion scheme for filaments 81 Extended asymptotic solution 133 139 149 168 Extended asymptotic solution, comparison with approx. solution 153 38ff Farfield condition 2 9 11 85 89 Farfield expansion 2 9 11 15 117 122 164 Farfield, potential 20 Filament Function 177 Filament(s) 78ff Filament(s) in rotational background 175 185ff Filament(s) velocity 88—90 Filament(s), cut by a surface 194ff Filament(s), head-on collision of 126 Filament(s), interacting 129ff Filament(s), intersecting 118 129 Filament(s), long 175 also Filament(s), multiple axial scales on 176ff 181ff Filament(s), near surfaces/boundaries 16 176 185ff 193ff Filament(s), perturbed 175 176ff Filament(s), reconnection of 132 Finite part also Finite part of filament vector potential 53 55 Fluctuation 27 36 Fourier decomposition 69 71 88 Geostrophic 175 189 Geostrophic, inner solution for vortex 191 Global merging Half span Hasimoto transform 177 Induced velocity 5 53 153 Induced, vector potentials 52 131 Integral invariants Interaction of 2-D vortices 133ff Interaction of filaments 103 108 Interaction of vortices and boundaries 193 Interaction terms for merging filaments 130 Interaction, Biot-Savart Interaction, Poisson Interface (of a 2-D vortex) 47 Intersection of filaments Invariants 128 Invariants for filaments 93 Invariants in two dimensions 19 133ff Inviscid 86 94 also Inviscid theory for vortex lines in 3-D 52ff Inviscid theory for vortices in 2-D 42ff 139 Joukowski (theorem/force) 43 76 kinetic energy 16 32 40 Laguerre polynomials 67 Lamb vortex 2 5 src='/math_tex/e5d134f35dc4949fab12ec64d186248a82.gif' Lamb vortex as approximate core structure 67 118 Lamb vortex as initial data 139 Lamb vortex in merging problems 147 Lamb vortex, 3-D generalization of 99 Lamb vortex, age of a 147 Lamb vortices, superposition of 133 149 153 Legendre polynomials 12 Length scales for merging problems, 117ff Length scales, characteristic for filaments 38 175 176 182/183 Load/lift distribution 142 Local induction approximation 177 Long filaments Mach number 3 9 27 Matching conditions Maxwell's representation 21 Merging of type 1(a) 124 135 162 170 Merging of type 1(b) 124 126 135 145 164 171 Merging of type II 124 129 131 Merging of vortex filaments 170 Merging of vortices 117 133 138 156 Merging, (three) stages of 141 150 170 Merging, classification of problems 117 Merging, global 8 117 132 133 145 162 Merging, local 8 117 129 133 Merging, rules of 8 133 147 148 Milne — Thomson 39 43 44 Minimum principle 8 118 133 Moments of vorticity 9 12 28 36 125 127 Momentum equation monopole Multiple scales Navier — Stokes (N-S) Equations 6 10 29 56 80 Nonlocal self induction 180 Nonuniform outer (shear) flow 77 188 Normal length 38 46 76 Normal plane 79 Normal time 6 40 46 69 76 Numerical accuracy 121 139 One-domain method 123 124 One-time solution 6 8 40 79 80 One-time solution vs. averaged two-time solution 64ff 74 Optimum, doublet 136 138 Optimum, filament core structure 106 Optimum, Lamb vortex 6 133 141 Optimum, similarity solution 6 8 66 98 99 also Optimum, time shift 67ff Orthogonal coordinates Oscillation of a disc/2-D vortex 39 43 47 71ff 76 Oscillation of a vortex interface 51 Overlap (of vortex rings) 113 Poincare relations 118 134 147 Point vortex 42 136 Poisson integral 12 126 139 163 164 Poisson solver 123 126 Polar moment 6 15 118 134 148 Potential, acoustic 3 34 Potential, scalar 2 9 10 20 25 Potential, vector 2 9 23 100 also Practical region of validity 7 42 103 139 Prandtl 81 Pressure fluctuation Quadrupoles 2 9 also Quadrupoles for rolling up shear layers 136 Quadrupoles in 2-D flows 45 76 Quadrupoles in general farfield expansions 25 27 31 Rankine vortex 6 39 45 47 Rate of (energy) dissipation Reconnection Retarded 9 27 102 Reynolds' number 5 118/119 Reynolds' number for 2-D flow 57 Reynolds' number for vortex filaments 40 109 Roll-up of a vortex layer Rotational background flow 8 175 185 Rules of merging Scalar potential Schrodinger equation (cubic) 177 Semispan 144 Serret — Frenet formulae 52 80 178 Similarity solution for 2-D vortices 66 74 148 also Similarity solution for vortex filaments 98 99 Slender vortex approximation 185 Slenderness 3 175 Sound generation 3 26 36 41 102 Sphere & vortex ring 104 Spherical harmonics 21 Spinning disc 5 43 Stream function for 2-D flow 19 42 46 134 135 139 Stream function for axisymmetric flow 18 162 165 Stream function for filaments 85 88 Stretching subdomains 127 135 Superposition Swirling flow 38 79 Symbols & terminology 1 Symmetric/asymmetric Tangent plane approximation 189 175 Terminology Time invariants 2 9 12 Torsion 80 177 Trailing vortex layer 138 141 Trajectory of a 2-D vortex 51 69 74 Trajectory of a spinning disc 44 Turbulence 28 36 Turbulence in geostrophic vortex 191 Two-dimensional problems 2 5 9 18 56ff Two-domain method 124 164 Two-time analysis/solution 5 6 40 46 60 71 also Validity Vector potential also Vector potential, composite solution 100 Vector potential, curl free 23 24 Vortex/vortices line 52ff Vortex/vortices merging Vortex/vortices rings 17 162 164 Vortex/vortices, (axial) core dynamics 181 Vortex/vortices, (self-) stretching 168 178 180 Vortex/vortices, breakdown 181 Vortex/vortices, center (velocity) 58 70 Vortex/vortices, core size 5 78 139 Vortex/vortices, geostrophic Vortex/vortices, layers/sheets 133 135 138 142 51 Vorticity, antisymmetric distribution (2-D) 137 Vorticity, evolution equation 10 14 162
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