Cohen I.M., Kundu P.K. Fluid Mechanics
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862 Index
Forces in fluid (continued)
origin of, 88–89
surface, 88
Form drag, 367, 705
Fourier’s law of heat conduction, 6
f -plane model, 612
Franca, L. P., 429, 439, 464
Frank, Otto, 791
Frequency, wave
circular or radian, 217
Doppler shifted, 219
intrinsic, 218
observed, 218
Frey S. L., 439, 464
Friction drag, 357–358, 684, 705
Friction, effects in constant-area ducts,
747–750
Friedrichs K. O., 410, 763
Froude number, 248, 282, 292
internal, 292–293
Fry R. N., 750, 763
Fully developed flow, 298
Fuselage, 680
Gad-el-Hak, M., 576, 577, 600
Galerkin least squares (GLS), 439
Galerkin’s approximation, 420–421
Gallo, W. F., 352, 409
Gas constant
defined, 16–18
universal, 16
Gas dynamics, 679
See also Compressible flow
Gases, 3–4
Gauge functions, 390–391
Gauge pressure, defined, 9
Gauss’ theorem, 44–47, 82
Geophysical fluid dynamics
approximate equations for thin layer on
rotating sphere, 610–612
background information, 603–605
baroclinic instability, 665–673
barotropic instability, 663–664
Ekman layer at free surface, 617–622
Ekman layer on rigid surface, 622–625
equations of motion, 607–610
geostrophic flow, 613–617
gravity waves with rotation, 636–639
Kelvin waves, 639–643
normal modes in continuous stratified
layer, 628–634
Rossby waves, 657–663
shallow-water equations, 625–627,
634–636
vertical variations of density, 605–607
vorticity conservation in shallow-water
theory, 644–647
George W. K., 576, 600–601
Geostrophic balance, 613
Geostrophic flow, 613–617
Geostrophic turbulence, 673–676
Ghia, U., 440, 464
Ghia, K. N., 464
Gill, A. E., 258, 270, 277, 637, 661, 662, 677
Glauert, M. B., 385, 409
Glowinski scheme, 437
Glowinski, R., 437, 439, 464
Gnos, A. V., 409
Goldstein, S., 409, 500
G
¨
ortler vortices, 493
Gower J. F. R., 372, 409
Grabowski, W. J., 521, 535
Gradient operator, 38–39
Gravity force, effective, 109
Gravity waves
deep water, 230–231
at density interface, 255–259
dispersion, 233, 242–246, 270–272
energy issues, 272–276
equation, 214–216
finite amplitude, 250–253
in finite layer, 259–261
group velocity and energy flux, 238–241
hydraulic jump, 248–250
internal, 267–270
motion equations, 263–266
nonlinear steepening, 246–248
parameters, 216–219
refraction, 233
with rotation, 636–639
shallow water, 231–233, 262–263,
246–248
standing, 237–238
Stokes’ drift, 253–255
in stratified fluid, 267–270
surface, 205–209, 209–215, 219–223,
223–229
surface tension, 234–237
Gresho, P. M., 427, 465
Group velocity
concept, 215, 224–231, 240, 238–246
of deep water wave, 230–231
energy flux and, 238–241
Rossby waves, 660–662
wave dispersion and, 242–246
Hagen-Poiseuille flow, 783–785
application, 807–809
effect of developing flow, 788–789
effect of vessel wall elasticity, 789–791
Fahraeus-Lindqvist effect and, 785–787
Half-body, flow past a, 175–178
Hardy, G. H., 2
Harlow, F. H., 433, 465
Harmonic function, 168
Index 863
Hatsopoulos, G. N., 24
Hawking, S. W., 701, 711
Hayes, W. D., xvii, 740, 763
Heart, pumping action, 769–771
Heat diffusion, 297
Heat equation, 115–116
Boussinesq equation and, 127–128
Heat flux, turbulent, 554
Heating, effects in constant-area ducts,
747–750
Heisenberg, W., 535, 539
Hele-Shaw, H. S., 337
Hele–Shaw flow, 332–334
Helmholtz vortex theorems, 149
Hematocrit, 774
plasma skimming, 778
Herbert, T., 469, 515, 535
Herreshoff, H. C., 709, 711
Hinze, J. O., 601
Hodograph plot, 619
Holstein, H., 364, 409
Holton, J. R., 105, 137, 657, 678
Homogeneous turbulent flow, 525
Hooke’s law, blood vessels and, 790–791
Hou, S., 465
Houghton, J. T., 658, 664, 678
Howard, L. N., 500, 504, 506, 507, 512, 536
Howard’s semicircle theorem, 504–506
Hughes T. J. R., 426, 429, 459, 464, 465, 600
Hugoniot, Pierre Henry, 735
Human body, biotransport and distribution
processes, 765–766
Huppert, H. E., 482, 536
Hydraulic jump, 248–250
Hydrostatics, 11
Hydrostatic waves, 233
Hypersonic flow, 716
Images, method of, 158, 189–190
Incompressible aerodynamics. See
Aerodynamics
Incompressible fluids, 102
Incompressible viscous fluid flow, 426
convection-dominated problems,
427–429
Glowinski scheme, 437
incompressibility condition, 429
MAC scheme, 433–437
mixed finite element, 438–439
SIMPLE-type formulations, 410–413
Induced/vortex drag, 697, 700
coefficient, 703
Inertia forces, 321
Inertial circles, 639
Inertial motion, 639
Inertial period, 611, 639
Inertial sublayer, 574–576
Inertial subrange, 562–564
Inflection point criterion, Rayleigh, 511, 663
inf-sup condition, 438
Initial and boundary condition error, 412
Inlet (entrance) length, 788–789
Inner layer, law of the wall, 571–573
Input data error, 412
Instability
background information, 469
baroclinic, 665–673
barotropic, 663–664
boundary layer, 517–518, 520–522
centrifugal (Taylor), 486–493
of continuously stratified parallel flows,
500–507
destabilizing effect of viscosity, 519–520
double-diffusive, 482–486
inviscid stability of parallel flows,
510–514
Kelvin–Helmholtz instability, 493–500
marginal versus neutral state, 470
method of normal modes, 469–470
mixing layer, 515–516
nonlinear effects, 522–523
Orr–Sommerfeld equation, 509–510
oscillatory mode, 470
pipe flow, 516–517
plane Couette flow, 516
plane Poiseuille flow, 516
principle of exchange of stabilities, 470
results of parallel viscous flows,
514–520
salt finger, 482, 483, 485
sausage instability, 535
secondary, 524
sinuous mode, 535
Squire’s theorem, 492–493, 507, 509
thermal (B
´
enard), 470–482
Integral time scale, 546
Interface, conditions at, 130, 131
Intermittency, 565–566
Internal energy, 12, 115–117
Internal Froude number, 292–293
Internal gravity waves, 214
See also Gravity waves
energy flux, 272, 275
at interface, 255, 259
in stratified fluid, 267–270
in stratified fluid with rotation, 646–657
WKB solution, 650–652
Internal Rossby radius of deformation, 643
Intrinsic frequency, 218, 656
Inversion, atmospheric, 19
Inviscid stability of parallel flows, 510–514
Inviscid theory, blood flow, 793–796
long wave length approximation,
809–812
864 Index
Irrotational flow, 63
application of complex variables,
169–171
around body of revolution, 206–208
axisymmetric, 201–205
conformal mapping, 190–192
doublet/dipole, 174–175
forces on two-dimensional body,
184–189
images, method of, 158, 189–190
numerical solution of plane, 195–201
over elliptic cylinder, 192–194
past circular cylinder with circulation,
180–184
past circular cylinder without
circulation, 178–180
past half-body, 175–178
relevance of, 165–167
sources and sinks, 173
uniqueness of, 194–195
unsteady, 121–122
velocity potential and Laplace equation,
167–169
at wall angle, 171–173
Irrotational vector, 40
Irrotational vortex, 70, 142–143, 174
Isentropic flow, one-dimensional, 729–732
Isentropic process, 17
Isotropic tensors, 37, 100
Isotropic turbulence, 551
Iteration method, 195–201
Jets, two-dimensional laminar, 381–385
Kaplun, S., 329, 337
Karamcheti, K., 711
Karman. See under von Karman
Karman number, 576
Karman, T., 24, 409, 539–540, 701, 711, 763,
853
Keenan, J. H., 24
Keller, H. B., 465
Kelvin–Helmholtz instability, 493–500
Kelvin’s circulation theorem, 144–149
Kelvin waves
external, 639–643
internal, 618–619, 643
Kim, John, 585, 600
Kinematics
defined, 53
Lagrangian and Eulerian specifications,
54–55
linear strain rate, 60–61
material derivative, 55–57
one-, two-, and three-dimensional flows,
71–73
parallel shear flows and, 67–68
path lines, 57–59
polar coordinates, 75–77
reference frames and streamline pattern,
59–60
relative motion near a point, 64–67
shear strain rate, 61–62
streak lines, 59
stream function, 73–75
streamlines, 57–59
viscosity, 7
vortex flows and, 67–71
vorticity and circulation, 62–64
Kinetic energy
of mean flow, 554–556
of turbulent flow, 556–559
Kinsman, B., 234, 277
Klebanoff, P. S., 524, 536
Kline, S. J., 584, 585, 586, 600
Kolmogorov, A. N., 521
microscale, 522
spectral law, 290, 562–564
Korotkoff sounds, 818–819
Korteweg–deVries equation, 252
Kronecker delta, 36–37
Krylov V. S., 137
Kuethe, A. M., 688, 711
Kundu, P. K., 621, 678
Kuo, H. L., 664, 678
Kutta condition, 684–686
Kutta, Wilhelm, 183
Kutta–Zhukhovsky lift theorem, 183, 185–189,
684
Lagerstrom, P. A., 410
Lagrangian description, 54
Lagrangian specifications, 54–55
Lam, S. H., 584, 600
Lamb, H., 120, 131, 137
Lamb, Horace, 120
Lamb surfaces, 120
Laminar boundary layer equations,
Falkner–Skan solution, 358–360
Laminar flow
creeping flow, around a sphere, 322–327
defined, 296
diffusion of vortex sheet, 313–315
Hele–Shaw, 332–334
high and low Reynolds number flows,
320–322
oscillating plate, 317–320
pressure change, 297–298
similarity solutions, 306–313
steady flow between concentric
cylinders, 303–306
steady flow between parallel plates,
298–302
steady flow in a pipe, 302–303
Index 865
Laminar flow, of a Casson fluid in a rigid
walled tube, 826–829
Laminar jet, 381–388
Laminar shear layer, decay of, 401–407
Laminar solution, breakdown of, 360–361
Lanchester, Frederick, 686
lifting line theory, 697–701
Landahl, M., 562, 584, 600, 701, 711
Lanford, O. E., 526, 536
Laplace equation, 167
numerical solution, 195–201
Laplace transform, 312
Law of the wall, 571–573
LeBlond, P. H., 251, 271, 633, 673
Lee wave, 656–657
Leibniz theorem, 82, 83
Leighton, R. B., 600
Lesieur, M., 538, 600
Levich, V. G., 131, 137
Liepmann, H. W., 246, 277, 686, 713, 732
Lift force, airfoil, 683–684
characteristics for airfoils, 704–705
Zhukhovsky, 692–694
Lifting line theory
Prandtl and Lanchester, 697–701
results for elliptic circulation, 701–703
Lift theorem, Kutta–Zhukhovsky, 183,
185–188, 684
Lighthill, M. J., 159, 163, 245–246, 246, 251,
277, 298, 337, 701, 706, 711
Limit cycle, 527
Lin C. Y., 371, 409, 465, 536
Lin, C. C., 448, 500, 518
Linear strain rate, 60–61
Line forces, 89
Line vortex, 140, 315–317
Liquids, 3–4
Logarithmic law, 573–578
Long-wave approximation. See Shallow-water
approximation
Lorenz, E., 467, 528, 529, 530, 532, 536
Lorenz, E.
model of thermal convection, 528–529
strange attractor, 530–531
Lumley J. L., 559, 564, 568, 574, 583, 586, 600
MacCormack, R. W., 411, 430, 432, 440, 444,
449, 450
McCreary, J. P., 662, 678
Mach, Ernst, 715
angle, 751
cone, 750–752
line, 751
number, 248–293, 686–687
MAC (marker-and-cell) scheme, 433
Magnus effect, 183
Marchuk, G. I., 433, 465
Marginal state, 470
Marvin, J. G., 409
Mass, conservation of, 84–86
Mass transport velocity, 255
Material derivative, 53–54
Material volume, 84
Mathematical order, physical order of
magnitude versus, 391
Matrices
dimensional, 284–285
multiplication of, 29–30
rank of, 285–286
transpose of, 26
Matrix equations, 421–424
Mean continuity equation, 548–549
Mean heat equation, 553–554
Mean momentum equation, 549–550
Measurement, units of SI, 2–3
conversion factors, 841
Mechanical energy equation, 111–115
Mehta, R., 377, 378, 409
Miles, J. W., 500, 536
Millikan, R. A., 325, 326, 337, 539
Milne-Thompson, L. M., 212
Mixed finite element, 438–439
Mixing layer, 515–516
Mixing length, 580–584
Modeling error, 412
Model testing, 290–291
Moens-Kortewag wave speed, 794–795
Moilliet, A., 600
Mollo-Christensen, E., 600
Momentum
conservation of, 92–93
diffusivity, 297
thickness, 347–348
Momentum equation, Boussinesq equation
and, 126–127
Momentum integral, von Karman, 362–364
Momentum principle, for control volume, 723
Momentum principle, for fixed volume, 93–97
angular, 98–100
Monin, A. S., 539, 600
Monin–Obukhov length, 588–589
Moore, D. W., 110, 137
Moraff, C. A., 741, 763
Morton K. W., 418, 465
Munk, W., 657, 678
Murray’s Law, 808
application, 808–809
Mysak L. A., 251, 277, 633, 679
Narrow-gap approximation, 490
National Committee for Fluid Mechanics
Films (NCFMF), 855
866 Index
Navier–Stokes equation, 104–105, 281
convection-dominated problems,
427–429
incompressibility condition, 429–430
Nayfeh, A. H., 389, 391, 408–409, 521, 536
Neumann problem, 195
Neutral state, 470
Newman J. N., 709, 711
Newtonian fluid, 100–103
non-, 103–104
Newton’s law
of friction, 7
of motion, 92
Nondimensional parameters
determined from differential equations,
280–284
dynamic similarity and, 287–290
significance of, 292–294
Non-Newtonian fluid, 103–104
Nonrotating frame, vorticity equation in,
146–150
Nonuniform expansion, 393–394
at low Reynolds number, 394
Nonuniformity
See also Boundary layers
high and low Reynolds number flows,
320–322
Oseen’s equation, 329–331
region of, 393–394
of Stokes’ solution, 327–331
Normal modes
in continuous stratified layer, 628–634
instability, 469–470
for uniform N, 631–634
Normal shock waves, 733–741
Normal strain rate, 60–61
Normalized autocorrelation function, 545
No-slip condition, 296
Noye, J., 419, 464
Nozzle flow, compressible, 729–733
Numerical solution
Laplace equation, 195–201
of plane flow, 195–201
Oblique shock waves, 752–756
Observed frequency, 656
Oden, J. T., 438, 464
One-dimensional approximation, 71
One-dimensional flow
area/velocity relations, 729–733
equations for, 721–724
One-dimensional flow, in a collapsible tube,
820–826
Order, mathematical versus physical order of
magnitude, 391
Ordinary differential equations (ODEs),
422–423
Orifice flow, 123–124
Orr–Sommerfeld equation, 509–510
Orszag S. A., 389, 391, 409, 469, 515, 535,
584, 600
Oscillating plate, flow due to, 317–320
Oscillatory mode, 470, 485–486
Oseen, C. W., 327, 328, 329, 331, 337, 369
Oseen’s approximation, 329–331
Oseen’s equation, 329
Oswatitsch, K., 853
Outer layer, velocity defect law, 573
Overlap layer, logarithmic law, 573–579
Panofsky, H. A., 581, 586, 587, 600
Panton, R. L., 410
Parallel flows
instability of continuously stratified,
500–506
inviscid stability of, 510–514
results of viscous, 514–520
Parallel plates, steady flow between, 298–302
Parallel shear flows, 67–68
Particle derivative, 55
Particle orbit, 638–639, 652–654
Pascal’s law, 10
Patankar, S. V., 410, 411, 412, 432, 450
Path functions, 13
Path lines, 57–59
Pearson J. R. A., 329, 337
Pedlosky, J., 105, 136, 163, 609, 622, 666,
673, 675, 678
Peletier, L. A., 352, 409
Perfect differential, 195
Perfect gas, 16–17
Peripheral resistance unit (PRU), 780–781
Permutation symbol, 37
Perturbation pressure, 224
Perturbation techniques, 389
asymptotic expansion, 391–393
nonuniform expansion, 393–394
order symbols/gauge functions, 390–391
regular, 394–396
singular, 396–401
Perturbation vorticity equation, 666–668
Petrov–Galerkin methods, 421
Peyret, R., 436, 465
Phase propagation, 662
Phase space, 526–527
Phenomenological laws, 6
Phillips, O. M., 240, 253, 277, 586, 592, 600,
658, 678
Phloem, 835–836
flow, 836–837
Physical order of magnitude, mathematical
versus, 391
Pipe flow, instability and, 516
Pipe, steady laminar flow in a, 302–303
Index 867
Pitch axis of aircraft, 681
Pi theorem, Buckingham’s, 285–287
Pitot tube, 122–123
Plane Couette flow, 300, 516
Plane irrotational flow, 195–201
Plane jet
self-preservation, 567–568
turbulent kinetic energy, 568–570
Plane Poiseuille flow, 301–302
instability of, 516
Planetary vorticity, 155, 156–157, 611
Planetary waves. See Rossby waves
Plants
fluid mechanics, 831–837
physiology, 831–832
Plasma, blood, 774–776
skimming, 778
viscosity, 775, 776
Plastic state, 4
Platelets (thrombocytes), 774
Pohlhausen, K., 350, 362, 364, 409
Poincar
´
e, Pitot, Henri, 533
Poincar
´
e waves, 637
Point of inflection criterion, 366
Poiseuille flow
circular, 302–303
instability of, 516
plane laminar, 300–301
Polar coordinates, 75–77
cylindrical, 845–846
plane, 847
spherical, 847–849
Pomeau, Y., 526, 531, 532, 535
Potential, complex, 170
Potential density gradient, 22, 587
Potential energy
baroclinic instability, 671–673
mechanical energy equation and,
113–115
of surface gravity wave, 228
Potential flow. See Irrotational flow
Potential temperature and density, 20–22
Potential vorticity, 646
Prager, W., 51
Prandtl, L., 2, 24, 79, 163, 183, 209, 212, 294,
340, 353, 389, 405, 409, 474, 477,
500, 529, 531, 539, 540, 574, 581,
582, 588, 591, 604, 678, 697, 700,
701, 711, 741, 756, 757, 763, 851,
852, 853
Prandtl, Ludwig, 2, 340, 851, 853
biographical information, 851–852
mixing length, 580–584
Prandtl and Lanchester lifting line
theory, 697–701
Prandtl–Meyer expansion fan, 756–758
Prandtl number, 294
turbulent, 588
Pressure
absolute, 9
coefficient, 177, 283
defined, 5, 9
drag, 684, 705
dynamic, 123, 297–298
gauge, 9
stagnation, 123
waves, 214, 717
Pressure-drop limitation, 820
Pressure gradient
boundary layer and effect of, 364–366,
517–518
constant, 299
Pressure pulse, 771
Principal axes, 42, 64–67
Principle of exchange of stabilities, 470
Probstein, R. F., 131, 137
Profile drag, 705
Proudman theorem, Taylor-, 615–616
Proudman, I., 329, 337
Pulmonary circulation, 766, 767–768, 829–831
Pulsatile flow, 791
aorta elasticity and Windkessel theory,
791–792
inviscid theory, 793–796
in rigid cylindrical tube, 796–800
tube material viscoelasticity, 806–807
wall viscoelasticity, 800–806
Quasi-geostrophic motion, 658–660
Quasi-periodic regime, 531
Raithby, G. D., 411, 413, 450
Random walk, 595–596
Rankine, W.J.M., 735
vortex, 71
Rankine–Hugoniot relations, 735
Rayleigh
equation, 510
inflection point criterion, 511, 663
inviscid criterion, 486–487
number, 471
Rayleigh, Lord (J. W. Strutt), 133, 137
Red blood cells, 774
Reduced gravity, 262
Reducible circuit, 194
Refraction, shallow-water wave, 233
Regular perturbation, 394–396
Reid W. H., 469, 471, 481, 491, 513, 498, 513,
515, 535, 678
Relative vorticity, 645
Relaxation time, molecular, 12
Renormalization group theories, 558
Reshotko, E., 522, 536
Reversible processes, 13
868 Index
Reynolds analogy, 588
decomposition, 547–548
experiment on flows, 278
similarity, 568
stress, 550–553
transport theorem, 84
Reynolds W. C., 296, 539, 584, 600
Reynolds, O., 514
Reynolds number, 166, 282, 292, 369
high and low flows, 320–322, 369,
373–375
Rhines, P. B., 675, 678
Rhines length, 675, 679
Richardson, L. F., 540
Richardson number, 293, 587, 588
criterion, 503, 504
flux, 587
gradient, 293, 504
Richtmyer, R. D., 465
Rigid lid approximation, 633–634
Ripples, 236
Roll axis of aircraft, 680
Root-mean-square (rms), 543
Rosenhead, L., 352, 364, 409
Roshko A., 246, 277, 714, 741, 762
Rossby number, 613
Rossby radius of deformation, 642
Rossby waves, 658–663
Rotating cylinder
flow inside, 305–306
flow outside, 304–305
Rotating frame, 105–111
vorticity equation in, 121–125
Rotation, gravity waves with, 637–639
Rotation tensor, 65
Rough surface turbulence, 576–578
Ruelle, D., 533, 536
Runge–Kutta technique, 355, 423
Saad, Y., 440, 469
Sailing, 707–709
Salinity, 21
Salt finger instability, 482–485
Sands, M., 599
Sargent, L. H., 525, 535
Saric W. S., 521, 535
Scalars, defined, 25
Scale height, atmosphere, 22
Schlichting, H., 337, 341, 364, 409, 469, 516,
520
Schlieren method, 715
Schraub, F. A., 600
Schwartz inequality, 545
Scotti, R. S., 536
Secondary flows, 388–389, 492
Secondary instability, 524
Second law of thermodynamics, 15
entropy production and, 116–118
Second-order tensors, 30–32
Seiche, 237
Self-preservation, turbulence and, 566–568
Separation, 366–368
Serrin, J., 352, 409
Shallow-water approximation, 262–263
Shallow-water equations, 625–627
high and low frequencies, 634–636
Shallow-water theory, vorticity conservation
in, 644–647
Shames, I. H., 212
Shapiro, A. H., 714, 763
Shapiro, Ascher H., 855
Shaw, H. S., 295, 332, 334, 337
Shear flow
wall-bounded, 570–580
wall-free, 564–570
Shear production of turbulence, 556, 559–562
Shear strain rate, 61
Shen, S. F., 516, 521–522, 536
Sherman, F. S., 364, 409
Shin, C. T., 464
Shock angle, 752
Shock structure, 720, 734
Shock waves
normal, 733–741
oblique, 752–756
structure of, 736–741
SI (syst
`
eme international d’unit
´
es), units of
measurement, 2–3
conversion factors, 841
Similarity
See also Dynamic similarity
geometric, 281
kinematic, 281
Similarity solution, 280
for boundary layer, 352–361
decay of line vortex, 315–317
diffusion of vortex sheet, 313–315
for impulsively started plate, 306–313
for laminar jet, 381–388
Singly connected region, 194
Singularities, 170
Singular perturbation, 396–401, 516
Sink, boundary layer, 348–352
Skan, S. W., 358, 409
Skin friction coefficient, 357–358
Sloping convection, 674
Smith, L. M., 584, 600
Smits A. J., 575, 601
Solenoidal vector, 40
Solid-body rotation, 68–69, 141
Solids, 3–4
Solitons, 252–253
Sommerfeld, A., 32, 51, 149, 159, 163, 539,
715
Sonic conditions, 726
Sonic properties, compressible flow, 724–729
Index 869
Sound
speed of, 16, 17, 717–720
waves, 717–720
Source-sink
axisymmetric, 206
near a wall, 189–190
plane, 173
Spalding D. B., 410, 450
Spatial distribution, 10
Specific heats, 14
Spectrum
energy, 546
as function of frequency, 546
as function of wavenumber, 547
in inertial subrange, 562–564
temperature fluctuations, 589–591
Speziale, C. G., 583, 600
Sphere
creeping flow around, 322–327
flow around, 206
flow at various Re, 375–376
Oseen’s approximation, 329
Stokes’ creeping flow around, 322–327
Spiegel, E. A., 124, 137
Sports balls, dynamics of, 376–381
Squire’s theorem, 500, 507, 509
Stability, 415–418
See also Instability
Stagnation density, 725
Stagnation flow, 172
Stagnation points, 167
Stagnation pressure, 123, 725
Stagnation properties, compressible flow,
724–729
Stagnation temperature, 725
Standard deviation, 543
Standing waves, 237–238
Starling resistor, flow in a collapsible tube,
819–820
Starting vortex, 661–662, 687
State functions 13, 15
surface tension, 8–9
Stationary turbulent flow, 543
Statistics of a variable, 543
Steady flow
Bernoulli equation and, 119–120
between concentric cylinders, 303–306
between parallel plates, 298–302
in a pipe, 302–303
Steady flow, in a collapsible tube, 820–826
Stern, M. E., 482, 536
Stewart, R. W., 600
Stokes’ assumption, 102
Stokes’ creeping flow around spheres, 315–322
Stokes’ drift, 253–255
Stokes’ first problem, 306
Stokes’ law of resistance, 288, 325
Stokes’ second problem, 317
Stokes’ stream function, 203
Stokes’ theorem, 47–49, 63
Stokes’ waves, 251
Stommel, H. M., 110, 137, 482, 536, 625
Strain rate
linear/normal, 60–61
shear, 61–62
tensor, 61
Strange attractors, 530–531
Stratified layer, normal modes in continuous,
628–634
Stratified turbulence, 540
Stratopause, 506
Stratosphere, 605
Streak lines, 59
Streamfunction
generalized, 87–88
in axisymmetric flow, 203–205
in plane flow, 73–75
Stokes, 203
Streamlines, 57–59
Stress, at a point, 90–91
Stress tensor
deviatoric, 100
normal or shear, 89
Reynolds, 551
symmetric, 90–91
Strouhal number, 371
Sturm–Liouville form, 629
Subcritical gravity flow, 248
Subharmonic cascade, 531–532
Sublayer
inertial, 547–576
streaks, 584
viscous, 572
Subrange
inertial, 562–564
viscous convective, 591
Subsonic flow, 294, 715
Substantial derivative, 56
Sucker, D., 436, 465
Supercritical gravity flow, 248
Supersonic flow, 294, 716
airfoil theory, 758–761
expansion and compression, 756–758
Surface forces, 89, 93
Surface gravity waves, 214, 219–223
See also Gravity waves
in deep water, 230–231
features of, 223–229
in shallow water, 231–233
Surface tension, 8–9
Surface tension, generalized, 130
Sverdrup waves, 637
Sweepback angle, 681, 705
Symmetric tensors, 40–41
eigenvalues and eigenvectors of, 41–44
870 Index
Systemic circulation, 766-767
pressure throughout, 771
Systole, 770–771
systolic blood pressure, measurement,
818–819
Takami, H., 465
Takens F., 531, 536
Taneda, S., 370, 409
Tannehill, J. C., 432, 465
Taylor T. D., 2, 24, 436, 465, 486, 539, 582,
591, 596–597, 600, 624, 678,
852–853
Taylor, G. I., 2, 24, 600, 678, 852–853
biographical information, 852–853
centrifugal instability, 486–493
column, 616
hypothesis, 547
number, 490, 491
theory of turbulent dispersion, 591–598
vortices, 491
Taylor–Goldstein equation, 500–503
Taylor–Proudman theorem, 615–617
TdS relations, 15
Temam, R., 436, 465
Temperature
adiabatic temperature gradient, 19, 605
fluctuations, spectrum, 589–591
potential, 20–22
stagnation, 725
Tennekes, H., 559, 564, 568, 574, 600, 656
Tennis ball dynamics, 379–380
Tensors, Cartesian
boldface versus indicial notation, 49–50
comma notation, 49
contraction and multiplication, 32–33
cross product, 38
dot product, 37
eigenvalues and eigenvectors of
symmetric, 41–44
force on a surface, 33–36
Gauss’ theorem, 44–47
invariants of, 33
isotropic, 37, 100
Kronecker delta and alternating, 36–37
multiplication of matrices, 29–30
operator del, 38–40
rotation of axes, 26–29
scalars and vectors, 25–26
second-order, 30–32
Stokes’ theorem, 47–49
strain rate, 60–61
symmetric and antisymmetric, 40–41
vector or dyadic notation, 49–51
Tezduyar, T. E., 439, 465
Theodorsen’s method, 689
Thermal conductivity, 6
Thermal convection, Lorenz model of, 528–530
Thermal diffusivity, 116, 128
Thermal energy equation, 115–116
Boussinesq equation and, 124–128
Thermal energy, 13
Thermal expansion coefficient, 16
Thermal instability (B
´
enard), 470–482
Thermal wind, 614–615
Thermocline, 606
Thermodynamic pressure, 100
Thermodynamics
entropy relations, 15
equations of state, 13, 16
first law of, 12–14, 115–116
review of, 688–689
second law of, 15–16, 116–118
specific heats, 14
speed of sound, 16
thermal expansion coefficient, 16
Thin airfoil theory, 689, 759–761
Thompson, L. M., 212
Thomson, R. E., 409
Thorpe, S. A., 497, 536
Three-dimensional flows, 71–73
Thwaites, B., 364, 409
Tidstrom, K. D., 524, 536
Tietjens, O. C., 24, 79, 163, 712
Time derivatives of volume integrals
general case, 82–83
fixed volume, 83
material volume, 84
Time lag, 544
Tip vortices, 695
Tollmien–Schlichting wave, 469, 516
Total peripheral resistance, 780–781, 785
Townsend, A. A., 564, 567, 568, 569, 600
Trailing vortices, 696, 698–699
Transition to turbulence, 366–367, 523–525
Translocation, 835
Transonic flow, 716
Transpiration, 833–834
Transport phenomena, 5–8
Transport terms, 112
Transpose, 26
Tropopause, 606
Troposphere, 606
Truesdell, C. A., 102, 137
Tube collapse, 818
Turbulent flow/turbulence
averaged equations of motion, 547–554
averages, 541–543
buoyant production, 558–559, 565
cascade of energy, 587
characteristics of, 538–539
coherent structures, 584–586
commutation rules, 542–543
correlations and spectra, 543–547
Index 871
Turbulent flow/turbulence (continued)
defined, 272
dispersion of particles, 591–595
dissipating scales, 561
dissipation of mean kinetic energy, 555
dissipation of turbulent kinetic energy,
559
eddy diffusivity, 581–583
eddy viscosity, 580–584
entrainment, 566
geostrophic, 673–676
heat flux, 554
homogeneous, 543
inertial sublayer, 574–576
inertial subrange, 562–564
integral time scale, 546
intensity variations, 580
intermittency, 565–566
isotropic, 551
in a jet, 567–570
kinetic energy of, 556–559
kinetic energy of mean flow, 554–556
law of the wall, 571–573
logarithmic law, 573–579
mean continuity equation, 548–549
mean heat equation, 553–554
mean momentum equation, 549–550
mixing length, 580–584
Monin–Obukhov length, 588–589
research on, 539–540
Reynolds analogy, 588
Reynolds stress, 550–553
rough surface, 579
self-preservation, 566–567
shear production, 556, 558–561
stationary, 543
stratified, 586–591
Taylor theory of, 591–598
temperature fluctuations, 589–591
transition to, 367, 523–525
velocity defect law, 573
viscous convective subrange, 591
viscous sublayer, 572
wall-bounded, 570–580
wall-free, 564–570
Turner J. S., 250, 253, 270, 277, 482–483, 499,
536, 588–589, 600
Two-dimensional flows, 71–73, 184–189
Two-dimensional jets. See Jets,
two-dimensional, 381–388
Unbounded ocean, 639
Uniform flow, axisymmetric flow, 205
Uniformity, 116
Unsteady irrotational flow, 121
Upwelling, 643
Vallentine, H. R., 212
Van Dyke, M., 389, 391, 392, 409
Vapor trails, 695
Variables, random, 541–543
Variance, 543
Vascular system, plant, 833
phloem, 835–837
xylem, 833–835
Vector(s)
cross product, 38
curl of, 40
defined, 25, 26, 29
divergence of, 39
dot product, 37
operator del, 38
Velocity defect law, 573
Velocity gradient tensor, 65
Velocity potential, 121, 161–169
Ventricles, work done on blood, 772–773
Veronis G., 124, 137
Vertical shear, 614
Vidal, C., 526, 529, 531, 532, 535
Viscoelastic, 4
Viscosity
coefficient of bulk, 102
destabilizing, 507
dynamic, 7
eddy, 580–584
irrotational vortices and, 141–144
kinematic, 7
net force, 142, 143
rotational vortices and, 139–140
viscosity, blood, 774–776
Viscous convective subrange, 591
Viscous dissipation, 112–113
Viscous fluid flow, incompressible, 426–439
Viscous sublayer, 572
Vogel, W. M., 600
Volumetric strain rate, 60
von Karman, 686
constant, 574
momentum integral, 362–364
vortex streets, 270, 369–373
Vortex
bound, 701
decay, 315–317
drag, 697–700
G
¨
ortler, 493
Helmholtz theorems, 149
interactions, 157–160
irrotational, 174
lines, 140, 315–317
sheet, 149–150, 295–296, 480, 670
starting, 661–662
stretching, 145, 621
Taylor, 491
tilting, 156, 622, 646
tip, 695