Instabilities, chaos and turbulence:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Imperial College Press
2010
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | ICP fluid mechanics
1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 439 S. Ill., graph. Darst. |
| ISBN: | 9781848163928 1848163924 9781848163935 1848163932 |
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| 264 | 1 | |a London |b Imperial College Press |c 2010 | |
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Datensatz im Suchindex
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| adam_text | IMAGE 1
INSTABILITIES, CHAOS
AND TURBULENCE AN INTRODUCTION TO NONLINEAR DYNAMICS AND COMPLEX SYSTEMS
PAUL MANNEVILLE ECOLE POLYTECHNIQUE, FRANCE
^FFI
IMPERIAL COLLEGE PRESS
IMAGE 2
CONTENTS
PREFACE VII
1. INTRODUCTION AND OVERVIEW 1
1.1 DYNAMICAL SYSTEMS AS A CONTEXT 2
1.2 CONTINUOUS MEDIA AS A SUBJECT 5
1.3 FROM SIMPLE TO COMPLEX 9
1.3.1 THERMAL CONVECTION: THE INSTABILITY MECHANISM . .. 10
1.3.2 NONLINEAR CONVECTION AND DYNAMICAL SYSTEMS 12
1.3.3 STABILITY AND INSTABILITY OF OPEN FLOWS 15
1.3.4 BEYOND THE TRANSITION: FULLY DEVELOPED TURBULENCE . . 17 1.4
CONCLUSION 20
1.5 EXERCISES 20
2. FIRST STEPS IN NONLINEAR DYNAMICS 25
2.1 FROM OSCILLATORS TO DYNAMICAL SYSTEMS 25
2.1.1 FIRST DEFINITIONS 25
2.1.2 FORMALISM OF ANALYTICAL MECHANICS 32
2.1.3 GRADIENT SYSTEMS 33
2.2 STABILITY AND LINEAR DYNAMICS 35
2.2.1 FORMULATION OF THE LINEAR STABILITY PROBLEM 36
2.2.2 TWO-DIMENSIONAL LINEAR SYSTEMS 37
2.2.3 STABILITY OF A TIME-INDEPENDENT REGIME 41
2.3 TWO-DIMENSIONAL NONLINEAR SYSTEMS 43
2.3.1 TWO EXAMPLES OF OSCILLATORS 44
2.3.2 AMPLITUDE AND PHASE OF NONLINEAR OSCILLATORS 50
2.4 WHAT NEXT? 60
2.5 EXERCISES 61
XI
IMAGE 3
XII INSTABILITIES, CHAOS AND TURBULENCE
3. LIFE AND DEATH OF DISSIPATIVE STRUCTURES 71
3.1 EMERGENCE OF DISSIPATIVE STRUCTURES 71
3.1.1 QUALITATIVE ANALYSIS OF THE INSTABILITY MECHANISM . . 71 3.1.2
SIMPLIFIED MODEL 73
3.1.3 NORMAL MODE ANALYSIS, GENERAL PERSPECTIVE 75
3.1.4 BACK TO THE MODEL 78
3.1.5 VICINITY OF THE THRESHOLD: LINEAR STAGE 82
3.1.6 CLASSIFICATION OF UNSTABLE MODES 84
3.2 DISINTEGRATION OF DISSIPATIVE STRUCTURES 86
3.2.1 SIMPLIFIED MODEL OF NONLINEAR CONVECTION 86
3.2.2 TRANSITION TO TURBULENCE OF CONVECTION CELLS 90
3.2.3 TRANSITION TOWARD CHAOS IN CONFINED SYSTEMS 94
3.2.4 DYNAMICS OF TEXTURES IN EXTENDED SYSTEMS 97
3.2.5 TURBULENT CONVECTION 101
3.3 EXERCISES 103
4. NONLINEAR DYNAMICS: FROM SIMPLE TO COMPLEX 115
4.1 REDUCTION OF THE NUMBER OF DEGREES OF BVEEDOM 116
4.1.1 ROLE OF ASPECT RATIOS 116
4.1.2 LOW DIMENSIONAL EFFECTIVE DYNAMICS 118
4.1.3 CENTER MANIFOLDS AND NORMAL FORMS 121
4.2 TRANSITION TO CHAOS 125
4.2.1 FIRST STEPS: TIME-INDEPENDENT AND PERIODIC REGIMES . 126 4.2.2
QUASI-PERIODICITY AND RESONANCES 130
4.2.3 QUASI-PERIODICITY AND LOCKINGS 136
4.3 CHARACTERIZATION OF CHAOTIC REGIMES 147
4.3.1 INSTABILITY OF TRAJECTORIES AND LYAPUNOV EXPONENTS . 148 4.3.2
FRACTAL ASPECTS 150
4.4 EMPIRICAL APPROACH OF CHAOTIC SYSTEMS 154
4.4.1 STANDARD ANALYSIS BY MEANS OF FOURIER TRANSFORM . . 156 4.4.2
RECONSTRUCTION BY THE METHOD OF DELAYS 157
4.4.3 SAMPLING FREQUENCY AND EMBEDDING DIMENSION . . .. 160 4.4.4
APPLICATION 165
4.5 CONCLUSION 168
4.6 EXERCISES 168
IMAGE 4
CONTENTS XIII
5. NONLINEAR DYNAMICS OF PATTERNS 181
5.1 QUASI-ONE-DIMENSIONAL CELLULAR STRUCTURES 182
5.1.1 STEADY STATES 182
5.1.2 AMPLITUDE EQUATION 185
5.2 DISSIPATIVE CRYSTALS 187
5.3 SHORT TERM SELECTION OF PATTERNS 190
5.4 MODULATIONS AND ENVELOPE EQUATIONS 191
5.4.1 QUASI-ONE-DIMENSIONAL CELLULAR PATTERNS 191
5.4.2 2D MODULATIONS OF QUASI-* CELLULAR PATTERNS . . .. 193
5.4.3 QUASI-TWO-DIMENSIONAL CELLULAR PATTERNS 195
5.4.4 OSCILLATORY PATTERNS AND DISSIPATIVE WAVES 197
5.4.5 UNIVERSAL LONG-WAVELENGTH INSTABILITIES 199
5.5 WHAT LIES BEYOND? 204
5.6 EXERCISES 205
6. OPEN FLOWS: INSTABILITY AND TRANSITION 211
6.1 BASE FLOW PROFILES 213
6.1.1 STRICTLY ONE-DIMENSIONAL FLOWS 213
6.1.2 MORE GENERAL VELOCITY PROFILES 215
6.1.3 EXTENSION TO ARBITRARY PROFILES 218
6.2 LINEAR STABILITY 219
6.2.1 GENERAL FRAMEWORK 219
6.2.2 INVISCID FLOWS 223
6.2.3 VISCOUS FLOWS 231
6.2.4 INSTABILITY AND DOWNSTREAM TRANSPORT 234
6.3 TRANSITION TO TURBULENCE 241
6.3.1 NONLINEAR DEVELOPMENT OF INSTABILITIES 241
6.3.2 INVISCIDLY UNSTABLE FLOWS 244
6.3.3 INVISCIDLY STABLE FLOWS 249
6.3.4 TURBULENT SPOTS AND INTERMITTENCY 253
6.4 EXERCISES 265
7. DEVELOPED TURBULENCE 271
7.1 SCALES IN DEVELOPED TURBULENCE 272
7.1.1 PRODUCTION SCALE 272
7.1.2 INERTIAL SCALES AND KOLMOGOROV SPECTRUM 274
7.1.3 DISSIPATION SCALES 276
7.1.4 REMARKS 278
IMAGE 5
XIV INSTABILITIES, CHAOS AND TURBULENCE
7.2 MEAN FLOW AND FLUCTUATIONS 279
7.2.1 STATISTICAL APPROACH 279
7.2.2 REYNOLDS AVERAGED NAVIER-STOKES (RANS) EQUATIONS 280 7.2.3 ENERGY
EXCHANGES IN A TURBULENT FLOW 283
7.3 MEAN FLOW AND EFFECTIVE DIFFUSION 284
7.3.1 MIXING LENGTH AND EDDY VISCOSITY 284
7.3.2 APPLICATION TO THE DETERMINATION OF THE MEAN FLOW . 286 7.4 BEYOND
THE ELEMENTARY APPROACH 290
7.4.1 TURBULENCE MODELING 292
7.4.2 LARGE EDDY SIMULATIONS 294
7.5 EXERCISES 299
8. SUMMARY AND PERSPECTIVES 303
8.1 DYNAMICS, STABILITY, AND CHAOS 304
8.2 CONTINUOUS MEDIA, INSTABILITIES, AND TURBULENCE 308
8.3 APPROACH TO A COMPLEX SYSTEM: THE EARTH S CLIMATE . . .. 312
8.4 EXERCISE: ICE AGES AS CATASTROPHES 328
APPENDIX A LINEAR ALGEBRA 331
A.L VECTOR SPACES, BASES, AND LINEAR OPERATORS 331
A. 2 STRUCTURE OF A LINEAR OPERATOR 334
A.3 METRIC PROPERTIES OF LINEAR OPERATORS 343
A.4 EXERCISES 348
APPENDIX * NUMERICAL APPROACH 351
B.L TREATMENT OF THE TIME DEPENDENCE 352
B.2 TREATMENT OF SPACE DEPENDENCE IN PDES 358
B.2.1 FINITE DIFFERENCE METHODS 358
B.2.2 SPECTRAL METHODS 363
B.3 EXERCISES 369
B.4 CASE STUDIES 371
B.4.1 ODES 1: FORCED PENDULUM 371
B.4.2 ODES 2: LORENZ MODEL 373
B.4.3 ODES 3: ROESSLER AND CHUA MODELS 376
B.4.4 PDES 1: SH MODEL, FINITE DIFFERENCES 378
B.4.5 PDES 2: SH MODEL, PSEUDO-SPECTRAL METHOD 380
BIBLIOGRAPHY 383
INDEX 387
|
| any_adam_object | 1 |
| author | Manneville, Paul 1946- |
| author_GND | (DE-588)1102806889 |
| author_facet | Manneville, Paul 1946- |
| author_role | aut |
| author_sort | Manneville, Paul 1946- |
| author_variant | p m pm |
| building | Verbundindex |
| bvnumber | BV036856256 |
| classification_rvk | UG 3900 |
| classification_tum | MAT 344f PHY 066f MAT 587f |
| ctrlnum | (OCoLC)57486539 (DE-599)BSZ114681155 |
| dewey-full | 515.39 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.39 |
| dewey-search | 515.39 |
| dewey-sort | 3515.39 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV036856256 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:49:29Z |
| institution | BVB |
| isbn | 9781848163928 1848163924 9781848163935 1848163932 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020772124 |
| oclc_num | 57486539 |
| open_access_boolean | |
| owner | DE-11 DE-91G DE-BY-TUM DE-29T |
| owner_facet | DE-11 DE-91G DE-BY-TUM DE-29T |
| physical | XV, 439 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Imperial College Press |
| record_format | marc |
| series | ICP fluid mechanics |
| series2 | ICP fluid mechanics |
| spelling | Manneville, Paul 1946- Verfasser (DE-588)1102806889 aut Instabilities, chaos and turbulence Paul Manneville 2. ed. London Imperial College Press 2010 XV, 439 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier ICP fluid mechanics 1 Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Instabilität (DE-588)4139195-0 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Turbulente Strömung (DE-588)4117265-6 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 s DE-604 Strömungsmechanik (DE-588)4077970-1 s Chaostheorie (DE-588)4009754-7 s Turbulente Strömung (DE-588)4117265-6 s Chaotisches System (DE-588)4316104-2 s Instabilität (DE-588)4139195-0 s ICP fluid mechanics 1 (DE-604)BV039688948 1 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020772124&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Manneville, Paul 1946- Instabilities, chaos and turbulence ICP fluid mechanics Strömungsmechanik (DE-588)4077970-1 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd Chaostheorie (DE-588)4009754-7 gnd Instabilität (DE-588)4139195-0 gnd Chaotisches System (DE-588)4316104-2 gnd Turbulente Strömung (DE-588)4117265-6 gnd |
| subject_GND | (DE-588)4077970-1 (DE-588)4126141-0 (DE-588)4009754-7 (DE-588)4139195-0 (DE-588)4316104-2 (DE-588)4117265-6 |
| title | Instabilities, chaos and turbulence |
| title_auth | Instabilities, chaos and turbulence |
| title_exact_search | Instabilities, chaos and turbulence |
| title_full | Instabilities, chaos and turbulence Paul Manneville |
| title_fullStr | Instabilities, chaos and turbulence Paul Manneville |
| title_full_unstemmed | Instabilities, chaos and turbulence Paul Manneville |
| title_short | Instabilities, chaos and turbulence |
| title_sort | instabilities chaos and turbulence |
| topic | Strömungsmechanik (DE-588)4077970-1 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd Chaostheorie (DE-588)4009754-7 gnd Instabilität (DE-588)4139195-0 gnd Chaotisches System (DE-588)4316104-2 gnd Turbulente Strömung (DE-588)4117265-6 gnd |
| topic_facet | Strömungsmechanik Nichtlineare Dynamik Chaostheorie Instabilität Chaotisches System Turbulente Strömung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020772124&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV039688948 |
| work_keys_str_mv | AT mannevillepaul instabilitieschaosandturbulence |