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Chorin A., Marsden J. — A Mathematical Introduction to Fluid Mechanics
Chorin A., Marsden J. — A Mathematical Introduction to Fluid Mechanics

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Название: A Mathematical Introduction to Fluid Mechanics

Авторы: Chorin A., Marsden J.

Аннотация:

The goal of this text is to present some of the basic ideas of fluid mechanics in a mathematically attractive manner, to present the physical background and motivation for some constructions that have been used in recent mathematical and numerical work on the Navier-Stokes equations and on hyperbolic systems, and to interest some of the students in this beautiful and difficult subject. The third edition has incorporated a number of updates and revisions, but the spirit and scope of the original book are unaltered.


Язык: en

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

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: third edition

Год издания: 1993

Количество страниц: 169

Добавлена в каталог: 19.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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