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Schmid P.J., Henningson D.S. — Stability and Transition in Shear Flows
Schmid P.J., Henningson D.S. — Stability and Transition in Shear Flows

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Название: Stability and Transition in Shear Flows

Авторы: Schmid P.J., Henningson D.S.

Аннотация:

This book is a detailed look at some of the more modern issues of hydrodynamic stability, including transient growth, eigenvalue spectra, secondary instability. Analytical results and numerical simulations, linear and (selected) nonlinear stability methods will be presented. By including classical results as well as recent developments in the field of hydrodynamic stability and transition, the book can be used as a textbook for an introductory, graduate-level course in stability theory or for a special-topics fluids course. It will also be of value as a reference for researchers in the field of hydrodynamic stability theory or with an interest in recent developments in fluid dynamics. Since the appearance of "Drazin & Reid", no book on hydrodynamic stability theory has been published. However, stability theory has seen a rapid development over the past decade. Direct numerical simulations of transition to turbulence and linear analysis based on the initial-value problem are two of many such developments that will be included in the book.


Язык: en

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

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 556

Добавлена в каталог: 30.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\beta$-cascade      188 461
Absolute instability      270
Absolute instability, branch points      275
Absolute instability, Briggs’ method      273
Absolute instability, cusp map      278
Absolute instability, global instability      337
Absolute instability, pinch points      275
Absolute instability, rotating disk flow      284
Absolute instability, steepest descent method      278
Absolute instability, two-dimensional wake      281
Adjoint equation      86 304 332 363
Adjoint operator      85 111 231
Algebraic growth      100 105
Algebraic instability      47
Amplitude expansion      162 185
Asymptotic results      78
Asymptotic results, Blasius flow      82
Asymptotic results, localized disturbances      149
Asymptotic results, nonparallel effects      301
Asymptotic results, plane Poiseuille flow      81
Asymptotic results, triple-deck theory      82
Bi-orthogonality      87 509
Bifurcation from infinity      185
Bifurcation, Hopf      214
Bifurcation, subcritical      165
Bifurcation, supercritical      165
Blasius boundary layer flow, asymptotic results      82
Blasius boundary layer flow, linear stability      66
Blasius boundary layer flow, neutral curve      71
Blasius boundary layer flow, optimal growth      118
Bounds on eigenvalues      94
Bounds on matrix exponential      139
Bounds on maximum response      128
Bounds, Kreiss matrix theorem      140
Branch, A,P,S-branch      64
Branch, lower branch      73 414
Branch, upper branch      73 414
Briggs’ method      273
Briggs’ method, cusp map      278
Busse balloon      397
Bypass transition      402
Case solution      49
Center manifold expansion      160 179
Compressibility      237
Compressible boundary layer, linear stability      246
Compressible boundary layer, neutral curve      246
Compressible boundary layer, transient growth      249
Continuous spectrum, inviscid      43 48
Continuous spectrum, Laplace transform      77
Continuous spectrum, viscous      74 107
Convective instability      270
Couette flow, Case solution      49
Couette flow, linear stability      66
Craik’s resonance      168
Critical layer      19 78
Critical Reynolds number definition      5
Critical Reynolds number table      6
Crossflow vortices      205 450
Crossflow vortices, breakdown      155
Crossflow vortices, secondary instability      394 452
Curved channel flow      446
Curved channel flow, linear stability      207
Curved channel flow, optimal growth      210
Curved channel flow, small curvature approximation      208
Curved rotating channel flow, linear stability      213
Curved rotating channel flow, neutral curve      214
Cusp map      278
Dean vortices      446
Dean vortices, Eckhaus instability      398
Dispersion relation, spatial branch      271
Dispersion relation, temporal branch      271
Disturbance environment      351
Disturbance equations, linear inviscid      15
Disturbance equations, linear viscous      55 102
Disturbance equations, nonlinear      2
Disturbance group velocity      34 97
Disturbance kinetic energy, definition      3
Disturbance measure      102 218 250 346
Eckhaus instability      394 446 448
Eckhaus instability, Busse balloon      397
Eckhaus instability, Dean vortices      398
Eckhaus instability, rotating channel flow      396
Eckhaus instability, sideband instability      396
Elliptical instability      381 423
Energy inner product      110
Energy norm      89 110
Energy Reynolds number      189
Energy theory      188
Energy theory, constraints      191
Equilibrium states      180
Falkner — Skan boundary layer, linear stability      198
Falkner — Skan boundary layer, optimal growth      200
Falkner — Skan — Cooke boundary layer, linear stability      203
Falkner — Skan — Cooke boundary layer, optimal growth      205
Fjortoft’s criterion      21
Floquet theory      227 373
Fredholm alternative      163 170 304
Freestream turbulence      429
Gaster’s transformation      264
Ginzburg — Landau equation      167
Ginzburg — Landau equation, global instability      341
Global instability      337
Global instability, frequency selection criterion      340
Global instability, Ginzburg — Landau equation      341
Global instability, nonnormality      342
Goertler flow      313
Goertler flow, transition      448
Goertler vortices      448
Goertler vortices, linear stability      313
Goertler vortices, receptivity      370
Goertler vortices, saturation      349
Goertler vortices, secondary instability      389
Green’s theorem, generalized      363
Green’s theorem, group velocity      97
Group velocity      34
Gulf Stream      234
Hagen — Poiseuille flow, linear stability      66
Hagen — Poiseuille flow, optimal growth      114
Harmonic point source      266
Hartree parameter      199 204
Howard’s semicircle theorem      22
Inflection point criterion      21
Inflection point criterion, compressible      241
Initial value problem, compressible      237
Initial value problem, inviscid      38
Initial value problem, inviscid, Laplace transform      42
Initial value problem, nonlinear      155
Initial value problem, spatial      290
Initial value problem, viscous      99
Initial value problem, viscous, continuous formulation      106
Initial value problem, viscous, discrete formulation      108
Kelvin — Helmholtz instability, inviscid      29
Klebanoff mode      429 436
Lagrange identity      363
Landau coefficients      163
Landau equation, derivation      162
Landau equation, stability      165
Landau equation, steady states      164
Lift-up effect      46 144
Localized disturbance, asymptotic results      149
Localized disturbance, breakdown      456
Localized disturbance, inviscid      50
Localized disturbance, linear evolution      144
Localized disturbance, nonlinear evolution      185
Localized disturbance, transition      456
Localized disturbance, viscous      144
Lyapunov equation      137
Lyapunov exponent      235
Mathieu’s equation, Lyapunov exponent      236
Mathieu’s equation, stability      223
Mathieu’s equation, transient growth      228
Matrix exponential      111
Maximum energy growth, bounds      139
Maximum energy growth, temporal      112
Maximum growth rate      132
Maximum response      126
Maximum response, bounds      128
Maximum response, stochastic forcing      133
Mixing layer, damped inviscid solutions      45
Mixing layer, inviscid stability      32
Mixing layer, piecewise linear approximation      26
Mixing layer, rib vortices      423
Mixing layer, roll-up and pairing      421
Mixing layer, transition      420
Neutral curve, Blasius boundary layer flow      71
Neutral curve, compressible boundary layer      246
Neutral curve, curved channel flow      210
Neutral curve, curved rotating channel flow      214
Neutral curve, Falkner — Skan boundary layer      200
Neutral curve, Falkner — Skan — Cooke boundary layer      205
Neutral curve, nonparallel effects      326
Neutral curve, oscillating channel flow      226
Neutral curve, parallel flow      71
Neutral curve, plane Poiseuille flow      71
Neutral curve, rotating channel flow      212
Neutral curve, water table flow      221
Nonlinear effects      344
Nonlinear equilibrium states      180
Nonlinear stability      153
Nonnormality      93
Nonparallel effects      300
Nonparallel effects, multiple-scale analysis      302
Nonparallel effects, neutral curve      326
Nonparallel effects, triple-deck theory      306
Numerical range      132
Oblique transition      436 444 445
Optimal disturbance, general      230
Optimal disturbance, spatial      329
Optimal disturbance, temporal      119
Optimal growth      111
Optimal growth rate      126
Optimal growth, Reynolds number dependence      120
Optimal growth, spatial      472
Optimal response      126 128
Optimal response, Reynolds number dependence      129
Optimal response, stochastic forcing      133
Orr mechanism      120
Orr — Sommerfeld equation      56
Orr — Sommerfeld equation, adjoint      85
Oscillating channel flow, linear stability      224
Oscillating channel flow, neutral curve      226
Oscillatory flow, linear stability      223
Oscillatory flow, transient growth      226
Parabolized stability equations, linear      318
Parabolized stability equations, nonlinear      346 474
Parabolized stability equations, step-size restriction      327
Peak position      379
Permanent scar      50
Piecewise linear velocity      24
Piecewise linear velocity, boundary layer      29
Piecewise linear velocity, jump conditions      25
Piecewise linear velocity, mixing layer      26
Pipe flow      61
Pipe flow, linear stability      66
Pipe flow, optimal growth      114
Plane Poiseuille flow, asymptotic results      81
Plane Poiseuille flow, linear stability      64
Plane Poiseuille flow, neutral curve      71
Plane Poiseuille flow, optimal growth      113
Pressure equation      17 55
PSE, linear      318
PSE, nonlinear      346 474
PSE, step-size restriction      327
Pseudo-eigenvalues      93
Rayleigh equation      17
Rayleigh equation, compressible      241
Rayleigh equation, logarithmic singularity      20 45
Rayleigh’s criterion      21
Rayleigh’s criterion, compressible      241
Receptivity      351
Receptivity, adjoint approach      363 368
Receptivity, asymptotic theory      351
Receptivity, localized      361
Receptivity, nonlocalized      356
Relative Mach number      240
Resolvent      126
Resonant triad interaction      167
Reynolds number dependence, optimal growth      120
Reynolds number dependence, optimal response      129
Reynolds — Orr equation      7 189
Reynolds — Orr equation, consequences      9
Reynolds — Orr equation, derivation      7
Reynolds — Orr equation, energy theory      189
Rotating channel flow, Eckhaus instability      396
Rotating channel flow, linear stability      211
Rotating channel flow, neutral curve      212
Rotating channel flow, optimal growth      212
Rotating curved channel flow, linear stability      213
Rotating disk flow, absolute instability      284
Secondary instability      373
Secondary instability, channel flow streaks      392
Secondary instability, crossflow vortices      394 452
Secondary instability, Dean vortices      398
Secondary instability, detuned mode      375
Secondary instability, Eckhaus instability      394 446 448
Secondary instability, elliptical instability      381 423
Secondary instability, fundamental mode      375
Secondary instability, Goertler vortices      389
Secondary instability, mixing layer      420
Secondary instability, peak position      379
Secondary instability, rotating channel flow      396
Secondary instability, shape assumption      377
Secondary instability, streaks      383 392 407 427
Secondary instability, streaks, inviscid      385
Secondary instability, subharmonic mode      375
Secondary instability, Tollmien — Schlichting waves      374 404
Secondary instability, Tollmien — Schlichting waves, fundamental      379
Secondary instability, Tollmien — Schlichting waves, subharmonic      378
Secondary instability, two-dimensional waves      374
Secondary instability, valley position      379
Secondary instability, vortices      383
Separation bubble      202 441
Shape assumption      377
Sideband instability      396
Spatial analysis      253
Spatial evolution concept      6
Spectrum, Blasius boundary layer flow      66
Spectrum, bounds on eigenvalues      94
Spectrum, continuous operator      69
Spectrum, continuous, spatial      262
Spectrum, continuous, temporal      74
Spectrum, Couette flow      66
Spectrum, pipe flow      66
Spectrum, plane Poiseuille flow      64
Spectrum, pseudo-eigenvalues      93
Spectrum, sensitivity      89
Spectrum, spatial      255
Spectrum, unresolved      92
Squire equation      56
Squire equation, adjoint      88
Squire equation, forced      103
Squire’s theorem      59
Squire’s transformation      58
Stability problem, compressible      238
Stability problem, compressible, higher modes      244
Stability problem, spatial      253
Stability problem, temporal      17 57
Stability problem, weakly nonlinear      160
Stability, complex flows      197
Stability, compressible      237
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