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Drazin P. — Introduction to Hydrodynamic Stability
Drazin P. — Introduction to Hydrodynamic Stability



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Название: Introduction to Hydrodynamic Stability

Автор: Drazin P.

Аннотация:

Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment. They are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography, physics, and engineering. This is a graduate-level textbook to introduce these phenomena by modeling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized with many figures. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differntial equations, complex variable and the elements of fluid mechanics. The book is aimed at graduate students, but is very useful for specialists in other fields.


Язык: en

Рубрика: Физика/Классическая физика/Механика жидкости и газа/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 258

Добавлена в каталог: 19.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Buoyancy frequency      107 135 194
Burgers equation      85 90
Burgers equation, nonlinear modes for      90
Burgers equation, spatial mode for      86
Bypass transition      5 176 177 211 212
Calculus of variations      114
Capillary instability, of gas jet      66
Capillary instability, of plane jet      66
Cat's-eye pattern      147 190
Cat's-eye pattern, nonlinear solution for      190
Cells, hexagonal      112
Cells, rectangular      112
Cells, roll      100 112 115
Centre mode      170 181
Chaos      1 4 7 116 130 210 212
Chaos, Ruelle — Takens — Newhouse route to      213
Characteristics, stability      34
Clear-air turbulence      54
Closed flow      69
Clouds      54 105
Coanda effect      226
Coherent structure      221
Completeness of normal modes      30 31 38
Complex Landau equation      36
Condition for instability, Fjortoft's necessary      145 146
Condition for instability, Rayleigh's necessary      144—146
Condition for stability, Miles — Howard      194 195
Condition, solvability      80 87 199
Conditions, at a discontinuity of the basic flow      149 202
Conditions, jump      149 182 183 202
Constant, complex Landau      87
Constant, Landau      21 78
Convection cells, hexagonal      112
Convection cells, rectangular      112
Convection cells, roll      100 112 115
Convection driven by variation of surface tension with temperature      121
Convection in a porous medium      117
Convection of energy      82
Convection, double-diffusive      119 122
Convection, Lapwood      117
Convection, Marangoni      121
Convection, nonlinear thermal      116
Convection, Rayleigh — Benard      99
Convection, Rayleigh — Darcy      117
Convective instability      69 85 99
Couette flow      136
Couette flow, plane      14
Criterion for instability of swirling flow, Rayleigh's      124 135 137
Criterion, Schwarzchild's      60
Critical layer      143 147 148 150 157 164—168 170 171 183
Critical Rayleigh number      98 214
Critical Reynolds number      3 4 31 158 214
Critical Reynolds number, Poiseuille pipe flow      3
Cross-flow, instability of      192 205
Crossing, avoided      42
Crystal growth      105
Curve, marginal      98 200
Curve, neutral      200
Cycle, limit      26
Cylinder, instability of flow past a      220
Darcy'slaw      61 117
Dean equation      40 229
Dean problem      40 229
Deck, triple      166
Degree theory, Leray — Schauder      208
Diffusion equation      111
Diffusion equation, nonlinear      76
Diffusion, double      119 120
Discriminant, Rayleigh      135 136
dispersion relation      70 73 85 86 200
Dissipation of energy      82
Distinguished limit      78
Disturbance      4 22
Double diffusion      119 120
Double-diffusive convection      119 122
Double-diffusive instability      122
Double-diffusive nonlinear wave      120
Doubling, period      103 210 213
Effect, Coanda      226
Effect, Gibbs — Thomson      105
Effect, Marangoni      105 121
Effect, Soret      105
Elevation of a material surface      48 183
Elliptical flow, instability of      42
Elliptical instability      42 176
Energy budget      82
Energy convection      82
Energy dissipation      82
energy equation      91 162 196
Energy equation, Reynolds — Orr      83 147 149
Energy method      83 113 162
Energy perturbation      82
Energy transfer      82
Energy, kinetic      43 82 83
Equation(s), adjoint      183
Equation(s), Boussinesq      95 114
Equation(s), Burgers      85 90
Equation(s), complex Landau      36
Equation(s), Dean      40 229
Equation(s), diffusion      111
Equation(s), energy      91 162 196
Equation(s), Euler — Lagrange      92 114
Equation(s), Euler's      44 138^ 184 192
Equation(s), Ginzburg — Landau      81
Equation(s), Helmholtz's      97 100 112
Equation(s), Landau      21 35 36 75 78 80 82 102 116 119
Equation(s), Liouville's      190
Equation(s), Navier 1 Stokes      7 10 11 28 41 42 198
Equation(s), nonlinear diffusion      76
Equation(s), nonlinear Poisson      191
Equation(s), nonlinear Schroedinger      87
Equation(s), Orr — Sommerfeld      157 198 201 202
Equation(s), parabolized stability      159
Equation(s), Poisson's      44
Equation(s), Rayleigh stability      142 182
Equation(s), Reynolds — Orr energy      83 91 147 149 196
Equation(s), Taylor — Goldstein      194 195
Equations of motion of a fluid, Euler's      44 123 134 138 179 184 192
Equations of motion of a fluid, Navier — Stokes      10 11 41 42
Equivalence, principle of      51
Euler — Lagrange equations      92 114
Euler's equations of motion      186
Euler's equations of motion of a fluid      44 123 134 138 179 184 192
Exchange of stabilities      27
Exchange of stabilities, principle of      97 107 121 126 134 209
First harmonic      76
Fjortoft's necessary condition for instability      145
Flat plate, instability of flow past a      216
Floquet theory      209 234
Flow past a cylinder, instability of      220
Flow past a flat plate, instability of      216
Flow past a sphere, instabilities of      225
Flow, basic      28
Flow, closed      69
Flow, Couette      136
Flow, Jeffery — Hamel      16 39—41 228 235
Flow, laminar      3
Flow, open      69
Flow, plane Couette      14
Flow, plane Poiseuille      5 14 40
Flow, Poiseuille pipe      5 34
Flow, primary      27 210
Flow, secondary      27 210
Flow, Stokes      41 84 208 219 221 225
Flow, uniform      91
Flow, uniformly rotating      91
Fluid, Boussinesq      95 117
Fold bifurcation      12
Form, normal      82
Fredholm alternative      80 89
Fredholm operator      89
Free shear layer      53 69 187
Free shear layer, instability of      187
Free-free boundary conditions      98 99 112
Free-rigid boundary conditions      99
Frequency, Brunt — Vaeisaela      194
Frequency, buoyancy      107 135 194
Function, Airy      137 165 201
Functional, Liapounov      84 162
Fundamental      76
Galilean transformation      53 69 73 87 147
Gas jet, capillary instability of      66
Gaster's transformation      200
Generation of waves by wind      46
Gibbs-Thomson effect      105
Ginzburg-Landau equation      81
Global asymptotic stability      35
Global mode      219
Globally asymptotic stability      84 91 92
Gortler instability      131
Gortler number      134
Gortler vortices      131
Gravity wave, internal      50 192
Gravity wave, surface      50
Group velocity      70 72 73 86 87 200
Harmonic      211
Harmonic, first      76
Harmonic, second      76
Heisenberg's solutions of Orr — Sommerfeld equation      164
Helmholtz's equation      97 100 112
Hexagonal cells      112
Hopf bifurcation      26 27 209 221 232
Howard's semicircle theorem      147
Identity, Lagrange's      88
Incompleteness of normal modes      31 38
Inflection-point condition for instability, Rayleigh's      144
Instabilities of flow past a sphere      225
Instability      1
Instability of $\mathrm{sech}^2$ jet      170 188
Instability of Bickley jet      170 188
Instability of Blasius's boundary layer      158 166 169 170
Instability of boundary layer      169 219
Instability of boundary layer on a plate      170
Instability of broken-line jet      187
Instability of cross flow      205
Instability of elliptical flow      42
Instability of flow past a cylinder      220
Instability of flow past a flat plate      216
Instability of jet      169 182
Instability of Landau — Squire jet      182
Instability of parallel flow of stratified fluid      193—195
Instability of plane Couette flow      169
Instability of plane Poiseuille flow      5 169 170
Instability of sech jet      189
Instability of self-gravitating gas      44
Instability of shear layer      53 152 169
Instability of tanh shear layer      170
Instability of top-hat jet      187
Instability of triangular jet      153
Instability of unbounded shear layer      170
Instability of vortex sheet      47 53 151
Instability of wake      169 219
Instability, absolute      69 85
Instability, convective      69 85 99
Instability, cross-flow      192 205
Instability, double-diffusive      122
Instability, elliptical      42 176
Instability, Fjortoft's necessary condition for      145 146
Instability, Gortler      131
Instability, Jeans      44
Instability, Kelvin — Helmholtz      46 57 58 60 125 151 224
Instability, parametric      210
Instability, primary      27 36 210
Instability, Rayleigh — Benard      99
Instability, Rayleigh — Taylor      51 59—61 193
Instability, Rayleigh's necessary condition for      144—146
Instability, Saffman — Taylor      61
Instability, secondary      27 36 210
Instability, subcritical      22 212
Instability, thermohaline      122
Interaction of modes, nonlinear      76 86
Intermittent transition      213
Internal gravity wave      50 192 193
Inviscid solution of Orr — Sommerfeld equation      163
Irrotational flow, stability of      43
Jeans instability      44
Jeffery — Hamel flow      16 39—41 228 235
Jet of gas, capillary instability of      66
Jet, $\matrhm{sech}^2$      170 188
Jet, Bickley      170 188
Jet, capillary instability of plane      66
Jet, instability of      169 170 187 188
Jet, Landau — Squire      182
Jet, marginal curve for      170
Jet, sech      189
Jump conditions      149 182 183 202
Karman's vortex street      233
Kelvin's cat's-eye pattern      147 190
Kelvin's minimum energy principle      43
Kelvin-Helmholtz instability      46 57 58 60 125 151 224
kinetic energy      43 82 83
Lagrange's identity      88
Lambda vortices      174
Laminar flow      3
Landau constant      21 78 87
Landau equation      21 35 36 75 78 80 82 102 116 119
Landau equation, complex      36
Landau — Squire jet, instability of      182
Lap wood convection      117
Laplace's law of surface tension      57 59 62
Lapse rate      60
Law, Darcy's      117
Layer, critical      143 147 148 150 157 164—168 170 171 183
Leray — Schauder degree theory      208
Liapounov functional      84 162
Liapounov's direct method      8 84 162
Liapounov's sense of stability      29
Lift-up mechanism of instability, Orr's      184
Limit cycle      26
Limit, distinguished      78
Linear resonance, instability due to      41
Linearized problem      30
Liouville's equation      190
Local mode      160 219
Lorenz system      114 115
Lower branch of marginal curve      166 170
Mackerel sky      54
Marangoni convection      121
Marangoni effect      105 121
Marangoni number      121
Marginal curve      98 200
Marginal curve, Bickley jet      170
Marginal curve, Blasius's boundary layer      170
Marginal curve, jet      170
Marginal curve, lower branch of      166 170
Marginal curve, plane jet      170
Marginal curve, plane Poiseuille flow      170
Marginal curve, unbounded shear layer      170
Marginal curve, upper branch of      166 170
Marginal curve, wake      170
Marginal stability      27 31
Material surface, elevation of      48 183
Mean, stability in the      29 84 91
Mechanism of instability, Orr's lift-up      184
Mechanism of instability, Venetian-blind      184
Method of normal modes      5 24 27 32
Method, $e^N$      111
Method, energy      83 113
Method, Liapounov's direct      8 84 162
Method, numerical      171 172 204
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