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Drazin P. — Introduction to Hydrodynamic Stability
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Название: Introduction to Hydrodynamic StabilityАвтор: 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: Рубрика: Физика /Классическая физика /Механика жидкости и газа /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2002Количество страниц: 258Добавлена в каталог: 19.06.2005Операции: Положить на полку |
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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 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, 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, 111 Method, energy 83 113 Method, Liapounov's direct 8 84 162 Method, numerical 171 172 204
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