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Acheson D.J. — Elementary Fluid Dynamics
Acheson D.J. — Elementary Fluid Dynamics

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Название: Elementary Fluid Dynamics

Автор: Acheson D.J.

Аннотация:

The study of fluid dynamics is a central theme in modern applied mathematics. It is used to model a vast range of physical phenomena and plays a vital role in science and engineering. This textbook provides a clear introduction to both the theory and application of fluid dynamics that is suitable for all undergraduates coming to the subject for the first time. Students need only a basic knowledge of vector calculus, complex analysis, and simple methods of solving differential equations. Numerous exercises (with hints and answers) illustrate the main ideas and serve to organize the reader's understanding. The wide range of topics discussed include inviscid and viscous flows, waves in fluids, boundary layer flow, and instability in flows, along with historical information and many references to important experiments. This is a comprehensive and absorbing introduction to the mathematical study of fluid behavior.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 408

Добавлена в каталог: 16.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Acceleration of fluid particle      4
Aerofoil, drag      59 143 151
Aerofoil, flow round      20 60 139
Aerofoil, generation of circulation round      23 158
Aerofoil, lift      21 59 120 143
Aerofoil, stall      30
Attached vortices      180 194
Axisymmetric flow, irrotational      174 199
Axisymmetric flow, stream function      173
Axisymmetric flow, viscous      223 253
Baroclinic instability      335
Barotropic flow      192
Bernoulli equation for compressible flow      118
Bernoulli equation for steady irrotational flow      10
Bernoulli equation for unsteady irrotational flow      66 193
Bernoulli streamline theorem      9
Biharmonic equation      230 254
Blasius’s theorem      140
Bluff-body flows      28 150 180 262 264 290
Body force      8
Bore      97 100
Boundary conditions at free surface      65 67
Boundary conditions for in viscid fluid      199
Boundary conditions for viscous fluid      26 30 265
Boundary layer      26
Boundary layer, adverse pressure gradient      29 261 263
Boundary layer, approximation      260 266
Boundary layer, converging channel      275
Boundary layer, equations      260 266 268
Boundary layer, flat plate      271
Boundary layer, instability      275 290 340
Boundary layer, Prandtl’s paper      260
Boundary layer, reversed flow      179 262 287 293
Boundary layer, rotating fluid      278
Boundary layer, separation      28 122 150 160 169 180 261 287
Boundary layer, similarity solutions      271 275 292
Boundary layer, thickness      32 50 268
Boundary layer, triple-deck      288
Bubble, slow flow past      253
Buoyancy (or Brunt — Vaisala) frequency      87 115 344
Buoyancy force, internal gravity waves      86
Buoyancy force, thermal instability      305
Buoyancy force, vorticity generation      86 305
Burgers vortex      187
Burgers’ equation      107
Capillary waves      76
Catastrophe theory      332
Cauchy — Lagrange theorem      161
Cauchy — Riemann equations      124
Cauchy’s vorticity formula      198
Cavitation      265
Centrifugal instability      313
Channel flow      51 324
Chaos      334
Characteristics, method of      91
Circle theorem      129
Circular cylinder, flow due to rotation of      53
Circular cylinder, flow past, development from rest      178 262
Circular cylinder, flow past, high Reynolds number      28 150 178 190 289
Circular cylinder, flow past, irrotational      28 130
Circular cylinder, flow past, low Reynolds number      226 253
Circular cylinder, spin-down within      45 165
Circular flow      12 43
Circulation, definition      19
Circulation, generated by vortex shedding      158
Circulation, Kelvin’s theorem      157
Circulation, Kutta — Joukowski condition      20 140
Circulation, related to lift      21 120 143 147
Circulation, related to velocity potential      122
Circulation, related to vorticity      19
Circulation, round a line vortex      126
Circulation, round an aerofoil      19 121 139
Clap-and-fling lift mechanism      159
Coefficient of viscosity      26
Complex potential for 2D flow, defined      125
Complex potential for 2D flow, examples      125
Complex potential for 2D flow, flow past aerofoil      139
Complex potential for 2D flow, flow past circular cylinder      141
Complex potential for 2D flow, line vortices      126 178 183 193
Complex potential for 2D flow, relation to flow speed      125
Compressible flow, Bernoulli equation for      118
Compressible flow, equations      79
Compressible flow, past thin aerofoil      59
Compressible flow, shock waves      62 103
Compressible flow, sound waves      58 79
Compressible flow, unsteady 1D      102
Compressible flow, viscous      107
Conformal mapping      134
Conservation of mass      23
Conservative force      9
Constitutive equations      202 207
Continuity equation      see Conservation of mass
Continuum hypothesis, breakdown of      63
Convective derivative      see D/Dt
Converging channel, flow in, at high Reynolds number      275
Converging channel, flow in, at low Reynolds number      255
Coriolis force      279
Corner eddies      229
Couette flow, between rotating cylinders      44 313
Couette flow, in channel      52
Creeping flow      see Slow flow
D/Dt      4
Dam break problem      92
Deformation of fluid element      13 212
density      6
Density variations, conservation of mass      23 79
Density variations, effect of gravity on      86 111 115 306
Differentiation ‘following the fluid’      see D/Dt
Diffusion of heat      36 307 345
Diffusion of salt      345
Diffusion of vorticity      33 37 46 48 179 187
Diffusivity, thermal      307
Dimensionless parameters      31 51 59 101 305 311 317 331
dispersion      56 64 69 108
Dissipation of energy due to viscosity      54 216 341
Divergence theorem      349
Diverging channel, flow in      278 296
Double diffusive convection      345
Doubly-connected region      19 122
Drag at high Reynolds number      150 261 274
Drag at low Reynolds number      226 253
Drag coefficient      150
Drag crisis      290
Drag due to waves      61
Drag in ideal flow      59 149
Drag in supersonic flow      61
Drag on streamlined bodies      151 274
Draining plate      256
Dyed’ fluid      6
D’Alembert’s paradox      147
Ekman layer      280
Elliptic cylinder, flow round      136 142
Energy and group velocity      70 74 114
Energy cascade      341
Energy dissipation      54 216 341
energy equation      24 306
Energy Kelvin’s theorem on minimum      199
Energy loss in hydraulic jump      100
Entropy change across a shock      104
entropy, defined      79
Equation of state      307
Equations of motion, Cauchy      205
Equations of motion, Euler (inviscid)      8
Equations of motion, Navier — Stokes (viscous)      30 207
Equations of motion, Navier — Stokes (viscous), in cylindrical polar coordinates      42 353
Equations of motion, Navier — Stokes (viscous), in spherical polar coordinates      355
Equations of motion, Navier — Stokes (viscous), relative to a rotating frame      279
Ertel’s theorem      196
Euler’s equations      8
Euler’s principle of linear momentum      202
Euler’s principle of moment of momentum      202
Falkner — Skan equation      292
Feigenbaum number      337
Fish, mechanical      235
Flat plate, boundary layer      49 261 271 340
Flat plate, drag      274
Flat plate, irrotational flow round      137
Force, buoyancy      86 115 305
Force, calculated by Blasius’s theorem      140
Force, centrifugal      164 318
Force, Coriolis      279
Force, on an accelerating body      149 200
Force, pressure      6 208 219
Force, viscous      26 35 209 219 lift)
Free streamline theory      289
Free surface, conditions at      39 65 67 245
Froude number      101
Gas, perfect      79
Gravity waves      see Water waves
Group velocity      56 69
Hagen — Poiseuille flow      see Poiseuille flow
Heat conduction      36 307
Hele — Shaw cell      241
Helicity      196
Helium, superfluid properties of      185
Helmholtz’s vortex theorems      162
Hexagonal convection cells      312
Hill’s spherical vortex      175
Homentropic flow      102 118
Hydraulic jump      63 100
Hydrostatic pressure distribution      9
Hysteresis      332 345
Ideal fluid      6
Images, method of      128 171
Incompressible fluid, conditions for behaviour as      7 58
Incompressible fluid, equation      7
Induced drag on a lifting body      23
Inertia term      31
Inertial waves (in rotating fluid)      116
Inner and outer solutions      270 (see also Matched asymptotic expansions)
Insect flight, clap-and-fling mechanism      159
Instability, and chaos      334
Instability, and turbulence      334
Instability, B$\acute{e}$nard      313
Instability, baroclinic      335
Instability, boundary layer      290 340
Instability, centrifugal      313
Instability, double diffusive      345
Instability, due to surface tension variations      313
Instability, instability, Rayleigh’s inflection point theorem      323
Instability, jet      295
Instability, Kelvin — Helmholtz      113 303
Instability, line vortex arrays      184
Instability, low Reynolds number      341
Instability, pipe flow      300
Instability, Rayleigh — Taylor      112
Instability, Rayleigh’s criterion for circular flow      318
Instability, Saffman — Taylor      342
Instability, shear flow      320
Instability, stratified shear flow      344
Instability, subcritical      301 325 345
Instability, thermal      305
Instability, thermohaline      345
Instability, vortex arrays      184
Instability, vortex rings      172
Interface waves      111
Internal gravity waves      86
Irrotational flow, axisymmetric      174 199
Irrotational flow, defined      10
Irrotational flow, kinetic energy      199
Irrotational flow, minimum energy of      199
Irrotational flow, past a aerofoil      138
Irrotational flow, past a circular cylinder      130
Irrotational flow, past a elliptical cylinder      136
Irrotational flow, past a flat plate      137
Irrotational flow, past a sphere      174
Irrotational flow, persistence of      161
Irrotational flow, pressure in      10 66 193
Irrotational flow, produced impulsively      179 199
Irrotational flow, uniqueness of      199
Irrotational flow, unsteady      66 149 193
Irrotational flow, velocity potential of      122
Isentropic flow      79
Isotropic medium      209
Jeffrey — Hamel flow      297
jet      293
Joukowski, condition at trailing edge      20 140
Joukowski, journal bearing      249
Joukowski, theorem      143
Joukowski, transformation      136
K$\acute{a}$rm$\acute{a}$n vortex street      180
Kelvin circulation theorem      157
Kelvin letter to Helmholtz      168
Kelvin minimum energy theorem      199
Kinematic condition at free surface      65
Kinematic viscosity      26 28
Kinetic energy of irrotational flow      199
Korteweg-de — Vries equation      108
Kutta — Joukowski hypothesis      20 140
Kutta — Joukowski lift theorem      21 143
Lagrangian description of flow      25 191 197 198
Lanchester, F. W.      22 120 265
Landau equation      346
Laplace’s equation      125 162
Leading edge suction      153
Length scale, characteristic      31
Lift on aerofoil      21 120 145 153
Lift, defined      20
Lift, on a cylinder with circulation      133
Line source      151
Line vortex      see Vortex
Linear stability theory      303
Local motion analysed      13 209 212
Lorenz equations      335
Lubrication theory      248
Mach lines      59 85
Mach number      59
Mach number and Froude number      101
Marginal stability      304 316 324
Mass-conservation equation      23 79
Matched asymptotic expansions      227 (see also Inner and outer solutions)
Material derivative      see D/Dt
Mean free path      63
Micro-organisms, swimming      33 235
Milne — Thomson circle theorem      129
Minimum energy theorem      199
Moment of forces and moment of momentum      202
Moment of forces on an aerofoil      141 154
Momentum equation in integral form      145
Momentum equation, inviscid      8
Momentum equation, viscous      30 208
Navier — Stokes equations      30 208
Navier — Stokes equations, derivation      34 207
Navier — Stokes equations, in cylindrical polar coordinates      42 353
Navier — Stokes equations, in spherical polar coordinates      355
Navier — Stokes equations, simple solutions of      33
Newtonian viscous fluid      26 207
No-slip condition      30 265
Non — NEWTONian fluids      26
Non-uniqueness of irrotational flow in multiply-connected regions      19 130
Non-uniqueness of steady viscous flow      278 297 330
Normal stresses      208
Of finite amplitude      61 102 107
Orr — Sommerfeld equation      323
Oscillating plate      52
Particle paths and streamlines      4 25
Particle paths in water waves      69
Pendulum, chaotic motion of      338
Perfect gas      79
Period doubling      336
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