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| Авторизация |
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| Поиск по указателям |
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| Chorin A., Marsden J. — A Mathematical Introduction to Fluid Mechanics |
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| Предметный указатель |
Acceleration of a fluid particle 4
Algorithm 94
Almost potential flow 59
Asymptotically stable 97
Autonomous 97
Back 124
Balance of momentum 4 6 12
Balance of momentum, differential form 6
Balance of momentum, integral form 7
Bernoulli's theorem 16 48 55 71
Bifurcation 99 100
Blasius' theorem 52
Body force 6
Body, force on 52
Boundary condition 34 41
Boundary layer 67 68
Boundary layer separation 71
Boundary layer, approximation 76
Boundary layer, equation 75
Boundary layer, separation 79
Boundary layer, thickness 71
Boundary layer, vorticity in 76
burning 152
Cauchy's theorem 32
Centered rarefaction wave 114
Centered wave 137 138 158
Central limit theorem 84
Channel flow 17
Chapman — Jouguet points 154
Characteristic 103 105 108
Characteristic, intersecting 106 108
Characteristic, length 35
Characteristic, linearly degenerate 150
Characteristic, velocity 35
Chemical energy 151
Circulation 21 48 57
Coefficients of viscosity 33
Combustion 103 152
Combustion, front 152
Combustion, wave 145
Complex potential 51
Complex variables methods 51
Complex velocity 51 53
Compressible flow 14 33 103
Compressive shock 131 134
Concave up 146
Conformal transformation 65
Connected state 115
Connected wave 115
Conservation law 122 129 145
Conservation of energy 12
Conservation of mass 2 12
Conservation of vorticity 28
Consistency of an algorithm 94
Constant state 111
Contact discontinuity 124
Continuity equation 3
Continuum assumption 2
Convective term 40
Convergence of an algorithm 94
Convex characterisitics 151
Couette flow 31
Courant — Friedrichs — Lewy condition 141
Cylindrical coordinates 45
D'Alembert's paradox 54
d'Alembert's paradox, in 3d 58
Decompostion theorem 37
Deflagration branch 154
Deformation 18
Deformation tensor 19 31
Degenerate linearly 151
density 1 14
Derivative, material 5
Detonation branch 154
Differential form 120
Differential form of mass conservation 3
Diffusion 39
Discontinuity 121 146 148
Discontinuity, separating 148
Disjoint 82
Disjoint event 82
Dissipation term 39
Divergence, free part 38
Divergence, space-time 119
Downstream 93
Drag 54 57 60 66
Drag, form 80
Drag, skin 80
Dynamics 96
Endothermic 152
Energy 12
Energy, equation 118
Energy, flux 18
Energy, internal 12 117
Energy, kinetic 12
Energy, per unit volume 117
Enthalpy 14
entropy 14 118 158
Entropy, condition 127 130 133 157
Equation, continuity 3
Equation, differential form 120
Equation, Euler 13 15
Equation, heat 84
Equation, Hugoniot 125
Equation, Navier — Stokes 34
Equation, of state 44
Equation, Prandtl 75
Equation, Stokes' 40
Equation, vorticity 24
Equation, weak form 120
Error function 70
Euler equation 13 15 49 78 94 96
Event 82
Event, disjoint 82
Exothermic 152
Expectation 82 143
Field velocity 1
Field vorticity 18
Filament 65
Filon's paradox 67
First coefficient of viscosity 33
First law of thermodynamics 14 118
Fixed point 97
Flat plate 69
Flow 14
Flow, almost potential 59
Flow, around a disk 55
Flow, around a half circle 51
Flow, around an obstacle 52
Flow, between plates 41
Flow, between two plates 42
Flow, compressible 14 33
Flow, Couette 31
Flow, gas 103
Flow, homogeneous 11 48
Flow, ideal 48
Flow, in a channel 17
Flow, in a pipe 45
Flow, in the half-plane 69
Flow, in the upper half-plane 51
Flow, incompressible 10
Flow, induced by a vortex filament 65
Flow, irrotational 47
Flow, isentropic 14 15
Flow, map 7 95
Flow, over a plate 66
Flow, past a sphere 59
Flow, Poiseuille 45
Flow, potential 47 48
Flow, potential around a disk 55
| Flow, potential vortex 56
Flow, stationary 29 49
Flow, supplementary region half-plane 51
Fluid, flow map 7
Fluid, ideal 5
Fluid, particle 4
Fluid, velocity 1
Fluid, viscous 33
Flux 7
Flux of vorticity 22
force 5 53
Force on a body 52
Form drag 80
Fourth power law 46
Front 124
Function, error 70
Function, Green's 61 86
Gamma, law gas 114 118 125 131 139
Gamma, simple wave 111
Gas dynamics 103 111
Gas flow 103
Gas, ideal 118 125 131 139
Gaussian 84
Generation of vorticity 43
Geometric entropy condition 135
Glimm's existence proof 145
Global stability 97
Gradient part 38
Green's function 61 63 64 86
Half-plane flow 69
Hamiltonian system 62
Heat equation 84 86
Helmholtz decomposition theorem 37
Helmholtz theorem 26 37
Hodge theorem 37
Hodograph transformation 110
Homogeneous 11
Homogeneous flow 48
Hopf bifurcation theorem 99
Hugoniot curve 126 153
Hugoniot equation 125 139
Hugoniot function 125 153
Hugoniot hyperbolic 104
Ideal flow 48
Ideal fluid 5 31
Ideal gas 44 118 125 131 139
Ignition temperature 152
Incompressible 11
Incompressible flow 10 13 34
Incompressible, approximately 44
Independent 82
Independent random variables 83
Integral form 120
Integral form of balance of momentum 7
Integral form of mass conservation 3
Intensity of a vortex sheet 88
Internal energy 12 40 117
Invariant, Riemann 109
Irrotational 47
Isentropic, flow 14 15
Isentropic, fluids 14
Isentropic, gas flow 122
Jacobian 8
Jacobian matrix 24
Jump 122
Jump relations 124
Jump, discontinuity 121 122
Kelvin's circulation theorem 21
Kinematic viscosity 34
kinetic energy 12 40 49
Kutta — Joukowski theorem 53
Law of Large Numbers 83
Law, conservation 129 145
Layer, boundary 67 71
Leading edge 93
Left state 115
Left-centered wave 138
Length, characteristic 35
Liapunov stability theorem 97
Lie derivative 43
Lie — Trotter product formula 95
Line, vortex 22
Linearly degenerate 150 151
Mach number 44
Mass conservation 11
mass density 1
Mass flow rate 46
Matching solutions 78
Material derivative 5 18
Mean 82
Mechanical jump relations 124
Momentum, balance of 6
Momentum, flux 7
Moving with the fluid 7
Navier — Stokes equation 31 33 38 67 77 94 95
Neumann problem 37 49 63
Newton's second law 2 6
No-slip condition 34 43
Noncompressive shock 133
Nonconvex 151
Nonlinear dynamics 96
Obstacle 58
Obstacle, flow around 52
Oleinik's condition 149 154
Orthogonal projection 38
oscillations 100
Oseen's equation 66
Paradox, d'Alembert 54 58
Paradox, Filon 67
Paradox, Stokes 67
Pipe flow 45
Piston 111
Plate 80
Plate, flow between 41
Plate, flow over 66 69
Plate, flow past 87
Point vortices 60
Poiseuille flow 45
Potential, complex 51
Potential, flow 47 48 51 56 58
Potential, flow around a disk 55
Potential, flow, almost 59
Potential, velocity 48
Potential, vortex 56
Potential, vortex flow 56
Prandtl, boundary layer equation 73 75
Prandtl, equation 78 94
Prandtl, relation 132 151
Pressure 5 14
probability 82
Probability, density function 83
Probability, theory 82
Product formula 95
Projection operator 38
Quasilinear 104
Random choice method 144 159
Random variable 82 141
Random variable, Gaussian 84
Random walk 85 88 96
Rankine — Hugoniot relations 124
Rarefaction fan 148
Rarefaction shock 127 129
Rarefaction wave 114
Rayleigh lines 154
Reaction, endothermic 152
Reaction, exothermic 152
Reaction, front 152
Reversibility 136
Reynolds number 36 96
Riemann invariant 109 110 113
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