Wave turbulence:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2011
|
| Schriftenreihe: | Lecture notes in physics
825 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XVI, 279 S. graph. Darst. |
| ISBN: | 9783642159411 |
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| 100 | 1 | |a Nazarenko, Sergey |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Wave turbulence |c Sergey Nazarenko |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2011 | |
| 300 | |a XVI, 279 S. |b graph. Darst. | ||
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Datensatz im Suchindex
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IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 WHAT IS WAVE TURBULENCE? 1
1.2 HISTORIC REMARKS 1
1.3 RECENT DEVELOPMENTS 2
1.3.1 RAPID EXPANSION OF WT APPLICATIONS 3
1.3.2 HIGHLY IMPROVED QUALITY OF EXPERIMENTAL DATA AND NUMERICAL
SIMULATIONS OF WT SYSTEMS 4 1.3.3 DISCOVERY OF IMPORTANCE OF COHERENT
STRUCTURES IN WT EVOLUTION 5
1.3.4 THEORY EXTENSION BEYOND SPECTRA 6
1.3.5 STUDY OF THE FINITE-BOX EFFECTS 6
1.4 WHAT IS THIS BOOK ABOUT? 7
REFERENCES 9
PART I PRIMER ON WAVE TURBULENCE
2 WAVE TURBULENCE AS A PART OF GENERAL TURBULENCE THEORY 17 2.1 BASIC
FACTS ABOUT HYDRODYNAMIC TURBULENCE 17
2.1.1 RICHARDSON CASCADE 18
2.1.2 KOLMOGOROV-OBUKHOV THEORY 19
2.1.3 2D TURBULENCE 20
2.2 PLACING WAVE TURBULENCE IN THE CONTEXT OF GENERAL TURBULENCE 25
2.2.1 COMMON TURBULENCE PROPERTIES 25
2.2.2 DISTINCT PROPERTIES OF WT 26
REFERENCES . . 27
3 FOR THE IMPATIENT: A WT CHEATSHEET 29
3.1 WEAK WAVE TURBULENCE 30
VLL
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/100564652X
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
3.1.1 THREE-WAVE? FOUR-WAVE? N-WAVE? 30
3.1.2 DIMENSIONAL DERIVATION OF KZ SPECTRA 32
3.1.3 EXAMPLES 34
3.2 STRONG WAVE TURBULENCE AND CRITICAL BALANCE 40
3.2.1 MHD TURBULENCE 40
3.2.2 GRAVITY WATER WAVES 41
3.2.3 STRATIFIED TURBULENCE 42
3.2.4 ROTATING TURBULENCE 43
3.2.5 QUASI-GEOSTROPHIC TURBULENCE 44
3.2.6 KELVIN WAVES 45
3.2.7 BURGERS? KDV? 46
REFERENCES 47
SOLUTIONS TO EXERCISES 49
4.1 FJ0RTOFT ARGUMENT IN TERMS OF CENTROIDS: EXERCISE 2.1 49 4.2
FC-CENTROIDS VERSUS /-CENTROIDS: EXERCISE 2.2 50
4.3 FOUR-WAVE RESONANCES IN ID SYSTEMS: EXERCISE 3.1 50 4.4 FOUR-WAVE 3
-» 1 RESONANCES IN 2D SYSTEMS: EXERCISE 3.2. . 51 REFERENCES 52
PART II WAVE TURBULENCE CLOSURES
5 STATISTICAL OBJECTS IN WAVE TURBULENCE 55
5.1 STATISTICAL VARIABLES 55
5.2 PROBABILITY DENSITY FUNCTIONS 57
5.3 RANDOM PHASE AND AMPLITUDE FIELDS 58
5.4 GENERATING FUNCTIONS 59
5.5 WAVE SPECTRUM, HIGHER MOMENTS AND STRUCTURE FUNCTIONS. 60 5.6 RPA
AVERAGING 63
REFERENCES 66
6 WAVE TURBULENCE FORMALISM 67
6.1 DHARMACHAKRA OF WAVE TURBULENCE: MAIN STEPS, IDEAS AND BUILDING
BLOCKS 67
6.1.1 MAHAYANA (COMPREHENSIVE SCHEME) 68
6.1.2 HINAYANA (REDUCED SCHEME) 71
6.2 MASTER EXAMPLE: PETVIASHVILLI EQUATION 71
6.2.1 CONSERVATION LAWS 72
6.2.2 FOURIER SPACE 73
6.2.3 INTERACTION REPRESENTATION 74
6.3 WEAK NONLINEARITY EXPANSION 75
6.3.1 SOLUTION FOR THE WAVE AMPLITUDES AT INTERMEDIATE TIMES 75
IMAGE 3
CONTENTS
6.3.2 WEAK NONLINEARITY EXPANSION FOR THE GENERATING FUNCTION 76
6.4 STATISTICAL AVERAGING 77
6.5 LARGE-BOX AND WEAK-NONLINEARITY LIMITS 80
6.5.1 TAKING L - OO 81
6.5.2 TAKING E - 0 81
6.6 THE PDF 83
6.7 KINETIC EQUATION 84
6.7.1 SYMMETRICAL FORM OF THE KINETIC EQUATION 85 6.8 GENERALIZATION TO
COMPLEX WAVEFIELDS 86
6.8.1 HAMILTONIAN WAVE EQUATIONS 86
6.9 FOUR-WAVE AND HIGHER-ORDER SYSTEMS 88
6.9.1 FOUR-WAVE SYSTEMS 88
6.9.2 SYSTEMS WITH HIGHER-ORDER WAVE RESONANCES . . . 91 6.10 EVOLUTION
OF MULTI-MODE STATISTICS 94
6.10.1 WEAK NONLINEARITY EXPANSION OF THE GENERATING FUNCTION 95
6.10.2 STATISTICAL AVERAGING AND GRAPHS 96
6.10.3 EQUATION FOR 2 {N) 100
6.10.4 EQUATION FOR THE PDF 101
6.11 GENERALIZATION TO THE FOUR-WAVE AND THE HIGHER-ORDER SYSTEMS 103
REFERENCES 104
SOLUTIONS TO EXERCISES 107
7.1 ONE-MODE GENERATING FUNCTION FOR GAUSSIAN FIELDS: EXERCISE 5.1 107
7.2 ONE-MODE MOMENTS FOR GAUSSIAN FIELDS: EXERCISE 5.2 107 7.3 SIX-ORDER
MULTI-POINT MOMENT: EXERCISE 5.3 108
7.4 FOURTH-ORDER STRUCTURE FUNCTION: EXERCISE 5.4 109
7.5 INVARIANTS OF THE PETVIASHVILLI EQUATION: EXERCISE 6.1 109 7.6
CHARNEY-HASSEGAWA-MIMA MODEL: EXERCISE 6.2 110 7.7 T -» OO LIMIT:
EXERCISE 6.4 I LL
7.8 SLOW AND FAST TIMESCALES IN THE WAVE AMPLITUDE EVOLUTION: EXERCISE
6.7 112
7.9 ELIMINATING / 123 : EXERCISE 6.9 113
7.10 NONLINEAR PHASE EVOLUTION: EXERCISE 6.11 113
7.11 INCONSISTENCY OF WT EXPANSIONS WITHOUT FREQUENCY RE-NORMALIZATION:
EXERCISE 6.12 114
7.12 FINDING G 3 -G 5 : EXERCISE 6.16 115
7.13 APPENDIX: INTERACTION COEFFICIENT FOR THE DEEP WATER SURFACE WAVES
115
REFERENCES 116
IMAGE 4
X CONTENTS
PART III WAVE TURBULENCE PREDICTIONS
8 CONSERVED QUANTITIES IN WAVE TURBULENCE AND THEIR CASCADES . . 119
8.1 CONSERVED QUANTITIES IN WAVE TURBULENCE 119
8.1.1 ENERGY AND MOMENTUM 119
8.1.2 THREE-WAVE SYSTEMS 120
8.1.3 FOUR-WAVE SYSTEMS 122
8.1.4 CONSERVATION LAWS IN THE MULTI-PARTICLE STATISTICS 123
8.1.5 RELATION BETWEEN THE DYNAMICAL AND THE STATISTICAL INVARIANTS 125
8.2 DIRECTIONS OF TURBULENT CASCADES 126
8.2.1 DUAL CASCADE IN THE NLS AND OTHER EVEN-WAVE SYSTEMS 126
8.2.2 CASCADE OF MOMENTUM AND OTHER NON-POSITIVE INVARIANTS 128
8.2.3 TRIPLE CASCADE IN THE PETVIASHVILLI AND OTHER ROSSBY/DRIFT WAVE
SYSTEMS 129
REFERENCES 132
9 STEADY STATE AND EVOLVING SOLUTIONS FOR THE WAVE SPECTRUM . . . 133
9.1 THERMODYNAMIC EQUILIBRIUM STATES: RAYLEIGH-JEANS SPECTRA 133
9.2 CASCADE STATES: KOLMOGOROV-ZAKHAROV SPECTRA 134
9.2.1 THREE-WAVE SYSTEMS 135
9.2.2 FOUR-WAVE SYSTEMS 140
9.2.3 TEMPORAL EVOLUTION LEADING TO KZ SPECTRA: FINITE AND INFINITE
CAPACITY SYSTEMS 143
9.2.4 KZ SPECTRA IN ANISOTROPIE MEDIA 146
9.2.5 OTHER POWER-LAW SPECTRA IN ANISOTROPIE MEDIA. 148 9.2.6 LOCALITY
AND STABILITY 150
REFERENCES 161
10 FINITE-SIZE EFFECTS IN WAVE TURBULENCE 163
10.1 SMALL-BOX REGIME: DISCRETE TURBULENCE 164
10.2 INFINITE-BOX REGIME: KINETIC WAVE TURBULENCE 166 10.3 MESOSCOPIC
TURBULENCE: SANDPILE BEHAVIOR 167
10.4 COEXISTENCE OF DIFFERENT REGIMES IN THE K-SPACE 169 10.5 CASCADE
TREE IN THE DISCRETE K-SPACE 169
REFERENCES 171
IMAGE 5
CONTENTS XI
11 PROPERTIES OF THE HIGHER-ORDER STATISTICS. INTERMITTENCY AND WT LIFE
CYCLE 173
11.1 SOLUTIONS FOR THE ONE-MODE PDFS AND THE MOMENTS 173 11.2 WAVE
TURBULENCE LIFE CYCLE 177
11.3 SOLUTIONS FOR THE //-MODE JOINT PDF'S 180
11.4 VALIDITY OF RPA 182
REFERENCES 184
12 SOLUTIONS TO EXERCISES 185
12.1 ZONOSTROPHY INVARIANT: EXERCISE 8.1 185
12.2 WAVEACTION CONSERVATION FOR THE FOUR-WAVE SYSTEMS: EXERCISE 8.3 186
12.3 RAYLEIGH-JEANS SOLUTIONS: EXERCISE 9.1 186
12.4 ENERGY FLUX DIRECTION IN SYSTEMS WITH A SINGLE RELEVANT DIMENSIONAL
PARAMETER: EXERCISE 9.2 187 12.5 ZAKHAROV TRANSFORM FOR THE FOUR-WAVE
SYSTEMS: EXERCISE 9.3 187
12.6 GEOMETRICAL CONDITION OF STABILITY: EXERCISE 9.9 187 REFERENCE 188
PART IV SELECTED APPLICATIONS
13 NONLOCAL DRIFT/ROSSBYWAVE TURBULENCE 191
13.1 WHEN IS TURBULENCE NONLOCAL? 191
13.2 NONLOCAL WEAK DRIFT/ROSSBY TURBULENCE 192
13.2.1 NONLOCAL INTERACTION WITH LARGE SCALES 192
13.2.2 EVOLUTION OF NONLOCAL ROSSBY/DRIFT TURBULENCE: A FEEDBACK LOOP
194
13.2.3 NONLOCAL INTERACTION WITH SMALL-SCALE ZONAL FLOWS 197 13.3 BEYOND
WEAK TURBULENCE: TWO REGIMES OF ZONAL-FLOW GROWTH 199
13.3.1 WEAK ZF: DIFFUSIVE REGIME 202
13.3.2 STRONG ZF: RAPID DISTORTION REGIME 203
13.3.3 TRANSITION BETWEEN THE TWO REGIMES OF THE ZONAL FLOW GENERATION
204
13.4 NUMERICAL MODELING OF THE FORCED-DISSIPATED CHM EQUATION 204
13.5 SOLUTION TO EXERCISE 207
13.5.1 RELATION BETWEEN THE SPECTRUM AND THE VELOCITY OF THE LARGE
SCALES: EXERCISE 13.1 207
REFERENCES 207
IMAGE 6
XII CONTENTS
14 MAGNETO-HYDRODYNAMIC TURBULENCE 209
14.1 INTRODUCTION 209
14.2 REDUCED MHD MODEL 210
14.3 VERY WEAK WT: DISCRETE REGIME AND 2D ENSLAVING 213 14.4 LARGE-BOX
LIMIT: KINETIC REGIME 215
14.4.1 WEAK NONLINEARITY EXPANSION 215
14.4.2 STATISTICAL AVERAGING 216
14.4.3 CONDITIONS OF REALIZABILITY OF THE KINETIC REGIME 220
14.4.4 SPECTRA IN THE KINETIC REGIME: ENERGY CASCADES-BALANCED AND
IMBALANCED TURBULENCE. . . 221 14.4.5 CROSS-HELICITY 223
14.4.6 TRANSIENT EVOLUTION LEADING TO FORMATION OF THE KZ SPECTRUM 224
14.4.7 PDF'S IN THE KINETIC REGIME: TURBULENCE INTERMITTENCY 224
14.5 MESOSCOPIC MHD WAVE TURBULENCE 226
14.6 SUMMARY 227
14.7 FURTHER READING 227
REFERENCES 229
15 BOSE-EINSTEIN CONDENSATION 231
15.1 INTRODUCTION 231
15.2 KINETIC EQUATION FOR THE WAVE SPECTRUM 231
15.3 ROLE OF THERMODYNAMIC SOLUTIONS 232
15.4 NON-EQUILIBRIUM CONDENSATION AND KZ SPECTRA 236 15.5 DIFFERENTIAL
APPROXIMATION MODEL 238
15.5.1 DAM FOR NLS WAVE TURBULENCE 238
15.5.2 WHAT HAPPENS WHEN A PURE KZ SPECTRUM CORRESPONDS TO "WRONG" FLUX
DIRECTION? 240 15.5.3 EXTENDING BEC DESCRIPTION TO INCLUDE THERMAL
CLOUDS 242
15.5.4 WAVE-PARTICLE CROSSOVER IN TURBULENT BEC CASCADES 244
15.6 TRANSIENT EVOLUTION, SELF-SIMILAR SPECTRA 245
15.7 BREAKDOWN OF THE WEAK FOUR-WAVE TURBULENCE AND TRANSITION TO A
THREE-WAVE REGIME 246
15.7.1 WT ON BACKGROUND OF STRONG CONDENSATE 246 15.7.2 STRONGLY
NONLINEAR TRANSITION BETWEEN THE TWO WEAKLY NONLINEAR REGIMES 248
15.8 DIRECT CASCADE IN 3D NLS 254
15.9 INHOMOGENEOUS WT IN A TRAPPING POTENTIAL 256
15.10 CONDENSATION IN ID SYSTEMS: OPTICAL TURBULENCE 259 15.11 SUMMARY
262
IMAGE 7
CONTENTS XIII
15.12 SOLUTIONS TO EXERCISES 263
15.12.1 DIRECT CASCADE IN 2D NLS: EXERCISE 15.2 263 15.12.2 FRONT
SOLUTION FOR INVERSE CASCADE IN 2D NLS: EXERCISE 15.3 263
15.12.3 KZ SOLUTIONS AND FLUX DIRECTIONS FOR BOLTZMANN GAS: EXERCISE
15.4 264
15.12.4 FRONT SOLUTIONS FOR BOLTZMANN: EXERCISE 15.5 265 15.12.5
MADELUNG TRANSFORMATION: EXERCISE 15.6 265 15.12.6 KZ SPECTRA FOR ID
OPTICAL TURBULENCE: EXERCISE 15.7 265
15.12.7 DAM FOR ID OPTICAL TURBULENCE: EXERCISE 15.8 . . 267 REFERENCES
267
16 LIST OF PROJECTS 269
16.1 DIFFERENTIAL APPROXIMATION MODELS FOR WT AND FOR STRONG TURBULENCE
269
16.2 COLLAPSES AND THEIR ROLE IN WT CYCLE 271
16.3 MODULATIONAL INSTABILITY AND ITS ROLE IN WT 271
16.4 INTERACTING PARTICLE SYSTEMS 272
16.5 SUPERFLUID TURBULENCE 273
16.6 GRAVITY WATER WAVE TURBULENCE 275
16.7 METAL-PLATE WAVE TURBULENCE 275
REFERENCES 276 |
| any_adam_object | 1 |
| author | Nazarenko, Sergey |
| author_facet | Nazarenko, Sergey |
| author_role | aut |
| author_sort | Nazarenko, Sergey |
| author_variant | s n sn |
| building | Verbundindex |
| bvnumber | BV036972278 |
| classification_rvk | UD 8220 |
| classification_tum | PHY 223f |
| ctrlnum | (OCoLC)729985479 (DE-599)DNB100564652X |
| dewey-full | 530.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.13 |
| dewey-search | 530.13 |
| dewey-sort | 3530.13 |
| dewey-tens | 530 - Physics |
| discipline | Physik Geographie |
| format | Book |
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| id | DE-604.BV036972278 |
| illustrated | Illustrated |
| indexdate | 2024-09-06T00:18:30Z |
| institution | BVB |
| isbn | 9783642159411 |
| language | English |
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| series | Lecture notes in physics |
| series2 | Lecture notes in physics |
| spelling | Nazarenko, Sergey Verfasser aut Wave turbulence Sergey Nazarenko Berlin [u.a.] Springer 2011 XVI, 279 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 825 Nichtlineare Welle (DE-588)4042102-8 gnd rswk-swf Turbulenztheorie (DE-588)4186472-4 gnd rswk-swf Turbulenztheorie (DE-588)4186472-4 s Nichtlineare Welle (DE-588)4042102-8 s DE-604 Lecture notes in physics 825 (DE-604)BV000003166 825 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3523433&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020887001&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nazarenko, Sergey Wave turbulence Lecture notes in physics Nichtlineare Welle (DE-588)4042102-8 gnd Turbulenztheorie (DE-588)4186472-4 gnd |
| subject_GND | (DE-588)4042102-8 (DE-588)4186472-4 |
| title | Wave turbulence |
| title_auth | Wave turbulence |
| title_exact_search | Wave turbulence |
| title_full | Wave turbulence Sergey Nazarenko |
| title_fullStr | Wave turbulence Sergey Nazarenko |
| title_full_unstemmed | Wave turbulence Sergey Nazarenko |
| title_short | Wave turbulence |
| title_sort | wave turbulence |
| topic | Nichtlineare Welle (DE-588)4042102-8 gnd Turbulenztheorie (DE-588)4186472-4 gnd |
| topic_facet | Nichtlineare Welle Turbulenztheorie |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3523433&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020887001&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003166 |
| work_keys_str_mv | AT nazarenkosergey waveturbulence |