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Acceleration Comoving, 248 Gravitational, 40 Inertial, 248 Index acceleration angle of attack, 543, 551 comoving, 248 angle of incidence, 543 gravitational, 40 angular momentum, 306, 650 inertial, 248 anisotropy standard, 41 elastic, 174 adiabatic antigravity, see centrifugal force, 111 process, 72 apple adiabatic deformation, 213 Newton, 46 advection spin-up, 456 Archimedes aelotropic principle, 78 elastic, 174 Archimedes’ principle, 78 aerodynamic Archimedes, of Syracuse, 77 drag, 541 aspect ratio, 547, 552 forces, 541 atm, 58 lift, 541 atmosphere, 60 aerodynamic efficiency, 556 homentropic, 71 aerodynamics, 537 isothermal, 69 aircraft standard, 74 ailerons, 538 temperature lapse rate, 73 controls, 538 average elevator, 538 pressure, 146, 176 pitch, 538 Avogadro’s number, 5 roll, 538 Avogadro, Lorenzo, 4 rudder, 538 axial vector, 30 yaw, 538 aircraft takeoff, cruise, landing, 539 B´enard,Henri, 608 airfoil, 547 balance thin, 566 angular momentum, 306 analytic drill, 93 energy, 578 Copyright °c 1998{2004, Benny Lautrup Revision 7.7, January 22, 2004 724 INDEX kinetic energy, 316 Brownian motion, 5 laws, 10 bubbles mass, 296 sessile, 135 momentum, 296, 557 bucket balance, laws of, 291 rotating, 111 banked turn, 545 bulk modulus, 69, 176 bar, 58 buoyancy, 63, 78 barotropic fluid, 68 center of, 82 basis vectors, 21 Burger’s vortex, 454 bathtub vortex, 458 bathtub whirl, 534 capillary bearing, 477 surface, 134 Bernoulli’s theorem, 264 capillary constant, 127 Bernoulli, Daniel, 58 capillary effect, 130 black hole, 51 capillary length, 125 Blasius Cartesian boundary layer, 493 coordinate transformations, 24 Blasius, Paul Richard Heinrich, 493 Cartesian coordinates, 19 body, 10 Cauchy, 277 floating, 83 equation of motion, 249 submerged, 83 Cauchy, Augustin, 141 body force, 11, 40 center of buoyancy, 82 Boeing 747, 539, 544 center of gravity, 82 bound vortex, 550 center of mass, 41, 238 boundary conditions Moon-Earth, 118 fluids, 336 center of roll, 85 boundary layer, 483 centrifugal acceleration, 487 force, 111 Blasius’, 493 potential, 111 deceleration, 487 centrifugal force, 519 downwash, 487 on Earth, 520 Ekman, 526 CFD, 393 merging, 487 channel entrance flow, 402 separation, 487, 488, 504 circulating flow, 367 theory, 491 circulation, 284, 549, 561 thickness, 468, 484, 490, 494 Clapeyron, Benoit Paul Emile,´ 67 thickness estimate, 484 clock, 16 turbulence, 488 comoving turbulent, 496 acceleration, 248 universal growth, 489 comoving derivative, 246 upflow, 487 comoving volume, 239 varying slip-flow, 501 completeness, 22, 26 viscous growth, 485 compressibility, 69, 176 Boussinesq, Valentin Joseph, 597 compression braking a car, 332 uniform, 179 Copyright °c 1998{2004, Benny Lautrup Revision 7.7, January 22, 2004 INDEX 725 computational fluid dynamics, 393 cross product, 20 connected tubes, 292 curl, 29 conservation curling, 332 of mass, 244 current density of mass, 245 constant curvilinear gravity, 43 basis vectors, 656 constitutive equations, 148 curvilinear coordinates, 655 contact cylinder symmetry, 367 surface, 57 cylindrical contact angle, 129 Laplacian, 657 contact force, 11 cylindrical coordinates, 655 continuity cylindrical vortex, 450 equation, 245 precision, 6 d’Alembert’s paradox, 283, 560 continuous matter, 3 d’Alembert, Jean le Rond, 244 continuum, 13 Darcy, 359 approximation, 6, 238 friction factor, 361 dynamics, 248 Darcy, Henri-Philibert-Gaspard, 362 hypothesis, 239 deformation, 6, 156 continuum physics, 10 adiabatic, 213 contraction energy, 180 uniform, 156 isentropic, 213 control volume, 63 local, 158 coordinate non-linear, 165 axes, 21 rate of, 335 system, 17 uniform static, 178 transformations, 18, 24 degrees of freedom, 661 coordinate transformations, 18 delta coordinates, 17 Kronecker, 23 Cartesian, 19 density curvilinear, 655 angular momentum, 306 cylindrical, 655 critical, 254 spherical, 658 Earth, 39 Copernican principle, 252 mass, 38 Copernicus, Nicolaus, 252 density of force, 40 Coriolis force, 517, 519 derivative on Earth, 520 comoving, 246 cosmic ‘democracy’, 252 material, 239, 246, 248 cosmology derivatives, 21 Newtonian, 252 Descartes, Ren´e,19 Couette flow, 369 descent Couette, Maurice Fr´ed´eric Alfred, unpowered, 544 369 differences Coulomb, Charles, 143 finite, 225 creeping flow, 379, 380 differential equations, 11 Copyright °c 1998{2004, Benny Lautrup Revision 7.7, January 22, 2004 726 INDEX diffusion, 9, 333 Earth diffusive vortex spin-down, 451 gravity diffusivity, 333 plot, 45 dilatation mass density of, 39 uniform, 156 potential, 47 direct product, 20 spherical, 48 discharge surface gravity, 41 mass, 245 tides, 113 discharge rate, 352 Earth’s density, 39 discretization effective spatial, 397 incompressibility, 240 temporal, 396 effective force, 64 displacement, 156, 238 effective incompressibility, 269 field, 156 effective mass, 284 gradient, 159 effective viscosity, 361 linear, 157 Ekman layer, 526 dissipation suction, 529 Couette flow, 370 upwelling, 529 Poiseuille flow, 360 valve, 532 distance, 19 Ekman number, 523 invariance of, 19 Ekman spiral, 528 divergence, 29, 95 Ekman, Vagn Walfrid, 523 dot product, 20 elastic drag, 332, 541, 557 energy, 180 coefficient, 386 energy density, 181 crisis, 387 materials, 155 flat wing, 474 elastic fluid, 270 form, 554 elastic tube, 198 induced, 555 elasticity, 171 pipe, 359 elastostatic drag estimates, 552 uniqueness, 183 drain flow, 318, 365 elastostatics, 187 laminar, 365 numeric, 223 turbulent, 366 energy draught of ship, 84 elastic, 180 droplets external field, 104 hanging, 136 graviational, 106 sessile, 135 internal, 661 dry fluid, 259 of deformation, 180 dust cloud, 250 potential, 49 dyadic product, 20 energy balance, 578 dynamic energy density, 106 friction, 142 engine thrust, 539 dynamic pressure, 265 entrance length, 402 dynamics, 248, 648 entropy, 72 Copyright °c 1998{2004, Benny Lautrup Revision 7.7, January 22, 2004 INDEX 727 equation of continuity, 245 velocity, 238 equation of state, 67 vorticity, 276 equations of motion field energy density, 106 creeping flow, 380 fields, 11, 29 equilibrium mechanic, 11 mechanical, 148 physical reality, 12 global, 63 thermodynamic, 11 homentropic, 68 finite differences, 225 hydrostatic, 63, 96 flat Earth isothermal, 68 approximation, 521 local, 148 flat wing, 474 hydrostatic, 65 flight mechanical, 63 subsonic, 537 Navier’s equation, 188 floating block, 88 equipartition theorem, 661 floating body, 83 equipotential flow, 6, 238 surface, 47, 110 stationary, 263 equivalence principle, 40, 521 steady, 263 escape velocity, 50 between plates, 351 Euclidean geometry, 19 circulating, 367 Euler Couette, 369 equation, 260 creeping, 379, 380 Euler, Leonhard, 260 geostrophic, 523 Eulerian irrotational, 277, 278 displacement, 166 isobaric, 524 exactly solvable flows, 349 laminar, 328 explosion, 250 nearly ideal, 487 extensive quantity, 291 planar, 331 external forces, 652 potential, 278 external stress, 143 pressure driven, 351 extreme flying, 540 rotating, 521 visualization, 242 f¨ohn,74 flow potential, 279 falling sphere, 383 fluid falling sphere viscometer, 384 elastic, 270 fictitious at rest, 57 forces, 111 barotropic, 68 fictitious forces, 518 dry, 259 field ideal, 259, 260 equations, 249 incompressible, 241 displacement, 156 interface, 110 energy, 104 isotropy, 334 equations, 11 macroscopic definition, 58 lines, 41, 277 Newtonian, 327 pressure, 59 particle, 9 Copyright °c 1998{2004, Benny Lautrup Revision 7.7, January 22, 2004 728 INDEX rotating, 111, 517 planar, 351 fluid matter, 6 planar curves, 131 flux tubular, 355 velocity, 239 geostrophic flow, 523 gravity, 94 two-dimensionality, 525 flux of mass, 245 glide angle, 544 force, 648 glide ratio, 544 body, 11 global centrifugal, 519 mass balance, 296 contact, 11 global quantities, 10 Coriolis, 519 global quantity, 38 effective, 64 Goldstein singularity, 504, 506 fictitious, 518 gradient, 29 moment, 40 field, 46 shear, 141 forces, 67 total, 40 gradient descent, 225, 394 forces Grashof, Franz, 598 aerodynamic, 541 gravitational form drag, 554 flux, 94 Fourier, Jean Baptiste Joseph, 581 work, 49 friction, 142 gravitational constant, 43 dynamic, 142 gravitational potential, 46 factor, 385 gravity, 37, 40 pipe, 359 additivity, 43 skin, 553 asymptotic, 44, 48 static, 142 center of, 82 viscous, 332 closed loops, 50 friction coefficient, 495 constant, 41, 48, 79 friction factor, 361 flux of, 94 Darcy, 359 Newton’s law, 43 Froude, William, 622 non-locality, 46 source of, 95 galaxies, 250 sources, 43 Galilei, Galileo, 40 spherical, 44 Galileo, 113 gravity-driven flow, 354 gas ideal, 67 Hagen, Gotthilf Heinrich Ludwig, gas constant, 67 356 Gauss Hagen-Poiseuille law, 357 theorem, 95 heat, 316 Gauss, Johann Karl Friedrich, 66 heat capacity, 662 geodesic, 19 heat equation, 68 geometry Helmholtz, Hermann von, 448 axially invariant, 133 hierarchies of interactions, 653 Euclidean, 19 homentropic Copyright °c 1998{2004, Benny Lautrup Revision 7.7, January 22, 2004 INDEX 729 atmosphere, 71 internal forces, 652 star, 99 internal stress, 143 homentropic equilibrium, 68 internal waves, 433 homentropic state, 72 interpolation Hooke’s law, 172 Rankine vortex, 451 inverted, 176 invariance of distance, 19 Hooke, Robert, 171 irrotational flow, 277, 278 horseshoe vortex system, 550 isentropic Hubble’s process, 72 constant, 251 isentropic deformation, 213 law, 251 isobar, 110 Hugoniot, Pierre Henri, 627 isobaric flow, 524 hydrodynamic similarity, 340 isothermal hydrostatic atmosphere, 69 equilibrium, 63, 65, 96 isothermal equilibrium, 68 paradox, 60 isotropic fluids, 334 pressure, 146 isotropy hydrostatic equilibrium, 57 elastic, 174 hydrostatic shapes, 109 hydrostatics, 63 Jesus number, 129 Joukowsky, Nikolai
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