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