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Shirer H.N. — Nonlinear Hydrodynamic Modeling: A Mathematical Introduction
Shirer H.N. — Nonlinear Hydrodynamic Modeling: A Mathematical Introduction

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Название: Nonlinear Hydrodynamic Modeling: A Mathematical Introduction

Автор: Shirer H.N.

Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 546

Добавлена в каталог: 08.01.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adjoint system      336 338
Alexander — Yorke Continuation      225 263
Alexander — Yorke Continuation, altering time-step in      243 246
Alexander — Yorke Continuation, and degenerate systems      256 257 263
Alexander — Yorke Continuation, complex variables in      237 238
Alexander — Yorke Continuation, correcting at each time-step      241 242
Alexander — Yorke Continuation, correcting failure of      243 246
Alexander — Yorke Continuation, differential equations for      236 239
Alexander — Yorke Continuation, examples of in two equations      246 255
Alexander — Yorke Continuation, flow chart for      247
Alexander — Yorke Continuation, in larger spectral models      255 263
Alexander — Yorke Continuation, multiple roots detected by      243 245 262
Alexander — Yorke Continuation, numerical integration in      240 246
Alexander — Yorke Continuation, theory and development of      226 239
Alexander — Yorke Continuation, track-jumping in      244 246
Alteration of an unfolding, minimal      187
Alteration of an unfolding, simple      186 187
Altering unfoldings      182 193
Altering unfoldings, steps in      186 187
Amplitude of waveform      49 54
Amplitude, polynomial equations for      271 277
Amplitude, vacillation of waveforms      51 53
Antipodal points      234 235
Antisymmetric property of Jacobian      27
Antisymmetry of interaction coefficients      460 465
Aperiodic flows      386
Aperiodic solutions      391 392 399 409 411
Aspect ratio, cell      (see Cell aspect ratio)
Aspect ratio, domain      (see Domain aspect ratio)
Asymptotic orbital stability, definition for      358
Asymptotic orbital stability, necessary condition for      365 367
Asymptotically stable solution      70 71 73 74 96
Atmosphere, finite-dimensional model of      444 445
Atmosphere, infinite-dimensional model of      445 (see also Canonical partial differential equations for the atmosphere)
Attracting direction      79 85 416 420 468 469
Attractor      80 84 412 443
Attractor and truncation dependency      408 411 441 442
Attractor and turbulence      386 392
Attractor as residing in limit set of unstable manifold      79 84 469 470 486
Attractor in infinite-dimensional case      80 85 224 425 484
Attractor, basin      81 82 417
Attractor, classifying      418 421 424 428
Attractor, definition of      412
Attractor, density of points on      423
Attractor, diagnosing structure of      412 443
Attractor, dimension of      412 426 457
Attractor, global      464
Attractor, Lorenz      (see Lorenz attractor)
Attractor, minimal      464
Attractor, model form and structure of      506 507
Attractor, restricted      438 439
Attractor, shape of      84
Attractor, strange      (see Strange attractor)
Available potential energy in partial differential system      32 108 109 281 299 449 450
Available potential energy in spectral model      40 284 303
Band splitting      393 395
Basic solution, definition of      87
Basic solution, exchanging stability with primary branch      94 99 110
Basic solution, nontrivial      114 115
Basic solution, stability properties of      102 111
Basic solution, uniqueness of      106 111
Basin of attraction      81 82 417
Basin of attraction for Newton's method      243 246
Basis functions and unstable manifolds      486 496
Basis functions for linear system with time-dependent coefficients      361 376 377
Basis functions for linear system with time-independent coefficients      73
Basis functions for rectangular domain      57 60
Basis functions, finding for spectral model      55 60 457 459 485 504
Basis functions, finding optimum for a flow regime      500 501
Basis functions, produced by Proper Orthogonal Decomposition Theorem      496 501
Bezout's theorem      227 228 233 234 256 257
Bifurcating two-torus      (see Two-torus)
Bifurcation analysis, stationary solutions      86 105
Bifurcation analysis, temporally periodic solutions      372 383
Bifurcation and stability exchange      92 105 269 466 469
Bifurcation diagram for convection      34 200 206 211 214 219 223 410
Bifurcation diagram for temporally periodic solutions      272 274 276 328 330
Bifurcation diagram, goal form for      209 218
Bifurcation diagram, hypothetical primary      113 123
Bifurcation diagram, hypothetical secondary      205 216 219 223 409 411
Bifurcation equation      90 92
Bifurcation point as butterfly point      194
Bifurcation point as cusp point      194
Bifurcation point as singular point      128 172 194
Bifurcation point, definition of      34 87 269
Bifurcation point, double-valued and secondary branching      200 206 211 214 215 401
Bifurcation point, exchange of stability at      34 37 77 92 100 128 130 269 325 373—383
Bifurcation point, found by Hurwitz Theorem      78 145 508 509
Bifurcation point, Hopf      (see Hopf bifurcation point)
Bifurcation point, identifying with Lyapunov exponents      425 426 428 432 435—436
Bifurcation point, locating on stationary solution      34 37 42 90 92 269
Bifurcation point, locating on temporally periodic solution      373 383
Bifurcation point, minimum values of      111 131 138 143 163 218 222 305—307 312 314 402 403
Bifurcation point, ordering and hierarchy of transitions      146 154 218 222 402 403
Bifurcation point, preferred values of      (see Bifurcation point minimum
Bifurcation point, primary (defined)      87
Bifurcation point, secondary (defined)      87
Bifurcation point, secondary and double primary bifurcation point      204 206 211 214 215 401
Bifurcation point, single (defined)      93
Bifurcation point, well diagram for      133 138 151
Bifurcation, expected      (see Bifurcation points minimum and
Bifurcation, from periodic solution      372 383
Bifurcation, harmonic      375 376 430
Bifurcation, Hopf      (see Hopf bifurcation)
Bifurcation, period-doubling      375 376 390 395 402 403 429 432
Bifurcation, periodic      326 341 355 357 367—372
Bifurcation, simple examples of stationary      92 100
Bifurcation, snap-through      96 97 100 117 330 331
Bifurcation, subcritical      (see Subcritically branching solutions)
Bifurcation, subharmonic      (see Bifurcation period-doubling)
Bifurcation, supercritical      (see Supercritically branching solutions)
Bifurcation, three types from periodic solutions      375 382
Bifurcation, three types from stationary solutions      92 100
Bifurcation, transcritical      (see Transcritically branching solutions)
Boundary conditions for atmosphere      448 449
Boundary conditions for convection      30 31 281
Boundary conditions for orthogonal functions      56 57
Boundary conditions for rotating convection      142
Boundary conditions, free      31
Boundary dissipation terms in partial differential equations      449 451
Boundary value problem      55 60 106 111
Boundary value problem for the atmosphere      447 450
Boundary values, incorporating spatially or temporally varying      449 459
Boundary, conducting      30 281
Boundary, cyclically continuous      31 108 281 299
Boundary, energy loss at      449
Boundary, nonconducting      30
Boundary, rigid      30 281
Boundary, stress-free      30 281
Boussinesq system, dimensionless      28 119 185 190 192
Boussinesq system, global      448
Boussinesq system, linearized form      35
Boussinesq system, Lorenz form      29
Boussinesq system, Shirer and Dutton form      28
Boussinesq system, two-dimensional      25 26
Boussinesq system, with background wind      278 282 298 300 308 309
Branching      (see Bifurcation)
Branching behavior, generic      112 130 204 215 270 277
Branching behavior, in partial differential equations as implied by spectral'model      222 223
Branching behavior, qualitative changes in      119 130
Branching behavior, under model enlargement      409 411
Branching stationary solutions, allowable forms for      112 118
Branching stationary solutions, expected stabilities of      92 100 103 105 202 206 214—218
Branching stationary solutions, expected wavelengths for      131 163
Branching stationary solutions, power series expansions for      326 334 336
Branching stationary solutions, simple examples of      92 100
Branching temporally periodic solutions, allowable forms for      270 277 328 330
Branching temporally periodic solutions, asymptotic orbital stability of      358
Branching temporally periodic solutions, computing branching direction of      325 341
Branching temporally periodic solutions, creation from stationary point      266 268 325 326
Branching temporally periodic solutions, deduced from stability analysis of stationary solutions      144 154 264 277 288 291 325—354
Branching temporally periodic solutions, expected stability of      325 355 357
Branching temporally periodic solutions, expected wavelengths and orientations for      292 324
Branching temporally periodic solutions, limiting frequency of      146 148 269 270 287 305 307 308 312 322 327 333 373 383
Branching temporally periodic solutions, limiting period of      373 374
Branching temporally periodic solutions, polynomial equation for amplitude      271 277 290 327 329
Branching temporally periodic solutions, represented as a power series      325 341
Branching temporally periodic solutions, simple examples of      326 341 355 357 367 372
Branching temporally periodic solutions, stability analysis for      (see Stability analysis for branching temporally periodic solutions)
Branching temporally periodic solutions, structural stability of      269
Branching temporally periodic solutions, uniqueness of      269
Broad-band spectrum      387 388
Butterfly point      178 194 196
Canonical partial differential equations for the atmopshere, condition for stability in      455
Canonical partial differential equations for the atmopshere, dimensionless equations      448
Canonical partial differential equations for the atmopshere, energetics of      449 450
Canonical partial differential equations for the atmopshere, Jeffreys' Theorem for      451
Canonical partial differential equations for the atmopshere, limits on predictability for      454
Canonical partial differential equations for the atmopshere, origin of instability in      453 454
Canonical partial differential equations for the atmopshere, Trapping Theorem for      451 452
Canonical partial differential equations for the atmopshere, uniqueness of solutions to      454 455
Canonical ratio      359 396
Canonical spectral model for the global atmosphere, energy equations for      462 463
Canonical spectral model for the global atmosphere, equations for      460
Canonical spectral model for the global atmosphere, existence of solutions to truncated versions of      462 463
Canonical spectral model for the global atmosphere, Jeffreys' Theorem for      464
Canonical spectral model for the global atmosphere, limit and recurrent points in      464
Canonical spectral model for the global atmosphere, Trapping Theorem for      463 464
Canonical spectral model for the global atmosphere, truncated versions of      460 464
Cantor set      398 405 413
Cantor set, fractal dimension of      413
Cantor set, structure and stange attractor      414 421
Catalytic terms and secondary branching      207 208 211
Catastrophe theory      (see Contact catastrophe theory)
Catastrophic behavior in stationary, solutions      129 130
Cell aspect ratio, definition of      133
Cell aspect ratio, effects on critical Rayleigh number      37 133 138 143 157 292 295 305 308 314 324
Cell aspect ratio, effects on critical Reynolds number      312 324
Cell aspect ratio, preferred values of      136 143 144 148 157 292 295 305 307 314 324
Cell aspect ratio, solution dependence on      290
Cell broadening      197 198 211 223
Cell frequency      146 290
Cell period      146
Cell wavelength, preferred      136 138 144 153 314
Cell wavelength, variations in      197 198 222 223
Center manifold and Hopf bifurcation      267
Center subspace      468
Chang and Shirer model      206 224 435 439
Chang and Shirer model and modeling principles      208 210
Chang and Shirer model as a family of models      219 224
Chang and Shirer model as solution to      11
Chang and Shirer model as suitable extension of Lorenz model      197 198 210
Chang and Shirer model, bifurcation points in      208 214
Chang and Shirer model, branching in      209 218 435 439
Chang and Shirer model, chaotic solutions in      435 439
Chang and Shirer model, coefficient model      435 439 440 442
Chang and Shirer model, conductive solution stability      208
Chang and Shirer model, dimensions of attractors in      435 439
Chang and Shirer model, expansions for      206
Chang and Shirer model, goal form in      211 218 408 410
Chang and Shirer model, Hopf bifurcation points in      435 436
Chang and Shirer model, Lyapunov exponent spectrum in      438
Chang and Shirer model, multiple applications of      219 223
Chang and Shirer model, primary branches in      208 435
Chang and Shirer model, secondary branching in      211 218
Chang and Shirer model, stream function diagram for      201
Chang and Shirer model, sudden transition to chaos in      400 435 439
Chang and Shirer model, summary of solution regimes in      429
Chaos, abrupt transition to      400 408 411 427
Chaos, and M-frequency quasi-periodic motion on an M-torus      424 425
Chaos, deterministic      423 438
Chaos, intermittent      395 429 432
Chaos, necessary conditions for      418 425
Chaos, routes to      (see Routes to chaos)
Chaos, smooth transition to      400 404 427
Chaos, well versus weakly developed      423 424 436 442
Chaotic attractor as modeling turbulence      392 401 404
Chaotic attractor in specific low-order models      428 432 435 439 441—442
Chaotic attractor, dimensions of      421 424
Chaotic attractor, spurious      410 411 442
Chaotic solutions      386 390 411
Chaotic solutions and insufficient degrees of freedom      409 411
Chaotic solutions as representing turbulence      386 391 400 408 411
Chaotic solutions, physical interpretation of      411
Characteristic equation for Chang and Shirer model      208 210
Characteristic equation for Lorenz model      41 77
Characteristic equation for model      285 287
Characteristic equation for Shirer (      1980
Characteristic equation for stationary solutions      74 92
Characteristic equation for temporally periodic solutions      371
Characteristic equation for Veronis model      143 145
Characteristic exponents and fastest growing wave      138 140
Characteristic exponents and Lyapunov exponents      433
Characteristic exponents and stability of conductive solution      41 113 199 206 285 288 322 325
Characteristic exponents and stability of convective solution      77 79 202 206 211—224
Characteristic exponents and stability of stationary solution      74 75 264 269 270 332
Characteristic exponents as temporal eigenvalues      74 466 468
Characteristic exponents behavior when both Hopf and stationary bifurcation points occur on trivial solution      160 163
Characteristic exponents for temporally periodic solution      367
Characteristic exponents, definition of      41 74 466
Characteristic exponents, double zero-valued      200 206 211 214 215 287 288
Characteristic exponents, imaginary part of and expected bifurcating solution      373 382
Characteristic exponents, pair crossing the imaginary axis with nonzero speed      269 270 325
Characteristic exponents, tracking signs of      101 105 156 157 212 222
Characteristic multipliers      359 372
Characteristic multipliers and necessary condition for orbital stability      365 367
Characteristic multipliers and perturbation behavior      364 367
Characteristic multipliers as eigenvalues of a matrix      363
Characteristic multipliers, checking accuracy of      369 372 417
Characteristic multipliers, numerically determining      366 367
Characteristic multipliers, product of      369 372
Circulation patterns for convection      24 43 45 46 201 293
Circulation sense, expected      122
Classical Rayleigh-Benard convection as Boussinesq system      23 37 119
Classical Rayleigh-Benard convection, bifurcation diagram for      34 200 206 211 214 219 223 409—411
Classical Rayleigh-Benard convection, bifurcation in      34 37 198 206
Classical Rayleigh-Benard convection, changes of wavenumber in      198 218 223
Classical Rayleigh-Benard convection, energetics for      32 33 108 111
Classical Rayleigh-Benard convection, laboratory experiments for      7 8 384 390
Classical Rayleigh-Benard convection, observed characteristics of      7 8 23 197 292
Classical Rayleigh-Benard convection, partial differential equations for      28 31 61 107
Classical Rayleigh-Benard convection, physical interpretation of onset of convection in      110 111
Classical Rayleigh-Benard convection, preferred wavelengths in      131 140 222 223 292 293
Classical Rayleigh-Benard convection, secondary branching in      198 206 218 224
Classical Rayleigh-Benard convection, spectral models for      (see Chang and Shirer model Curry Elevencoefficient Lorenz Marcus Saltzman and
Classical Rayleigh-Benard convection, transition to turbulence in      384 390 400
Classical Rayleigh-Benard convection, trivial solution in      70
Classical Rayleigh-Benard convection, unfoldings in      194 195
Classifying attractors      418 421 424 428
Closed orbits      266 273 356 357 373 382 425 427 464
Cloud streets      278 290 292 324
Cloud streets, comparison of pure modes for      314 321
Cloud streets, coordinate system for      279 280 293 294
Cloud streets, energetics of      297 300 303 304 310 311
Cloud streets, inflection point instability for      (see Inflection point instability)
Cloud streets, linking of parallel and thermal, mechanisms for      308 322 324
Cloud streets, parallel instability for      (see Parallel instability)
Cloud streets, preferred alignment for      293 294 297 318 324
Cloud streets, Rayleigh-Benard instability for      (see Thermal instability)
Cloud streets, three mechanisms for formation of      296 297 314 321
Codimension of a singularity      178 196
Codimension of a subset of a space      237
Computational methods for finding optimum spectral models      485 504
Conductive basic state      24 25 108 278
Conductive solution, stability properties of      (see Conductive solution Stability
Contact catastrophe theory      164 196
Contact equivalence      169
Contact transformation, definition of      169
Contact transformation, need for      168 169 177
Contact transformation, steps in      169 171
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