Chaotic flows: correlation effects, transport, and structures
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
|
| Series: | Springer series in synergetics
Springer complexity |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIII, 351 S. Ill., graph. Darst. |
| ISBN: | 9783642203503 9783642203497 3642203493 |
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Record in the Search Index
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IMAGE 1
CONTENTS
PART I DIFFUSION AND CORRELATIONS 1 INTRODUCTION 3
1.1 DIFFUSION PHENOMENON 3
1.2 SELF-SIMILAR SOLUTIONS 7
1.3 INHOMOGENEOUS MEDIA AND NONLINEAR EFFECTS 11
1.4 PERIODIC MEDIA AND DIFFUSION AT LARGE SCALES 14
FURTHER READING 18
2 ADVECTION AND TRANSPORT 21
2.1 ADVECTION-DIFFUSION EQUATION 21
2.2 TRANSPORT AND ONE-DIMENSIONAL HYDRODYNAMICS 23
2.3 ADVECTION IN TWO-DIMENSIONAL SHEAR FLOW 25
2.4 EFFECTIVE DIFFUSIVITY AND ADVECTION 27
2.5 FLUCTUATION EFFECTS IN SCALAR TRANSPORT 30
2.6 THE ZELDOVICH SCALING FOR EFFECTIVE DIFFUSIVITY 33
FURTHER READING 34
3 THE LANGEVIN EQUATION AND TRANSPORT 37
3.1 BROWNIAN MOTION AND DIFFUSION 37
3.2 MEAN SQUARE VELOCITY AND EQUIPARTITION 41
3.3 AUTOCORRELATION FUNCTION 43
3.4 VELOCITY DISTRIBUTION FUNCTION 44
3.5 KINETICS AND DIFFUSION EQUATION 46
FURTHER READING 49
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1010479210
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
PART II LAGRANGIAN DESCRIPTION
4 LAGRANGIAN DESCRIPTION OF CHAOTIC FLOWS 53
4.1 THE TAYLOR DIFFUSION AND CORRELATION CONCEPT 53
4.2 THE BOLTZMANN LAW RENORMALIZATION 56
4.3 TURBULENT TRANSPORT AND SCALING 58
4.4 ANOMALOUS DIFFUSION IN TURBULENT SHEAR FLOWS 59
4.5 SEED DIFFUSIVITY AND TURBULENT TRANSPORT 62
FURTHER READING 67
5 LAGRANGIAN CHAOS 69
5.1 THE ARNOLD-BELTRAMI-CHILDRESS CHAOTIC FLOW 69
5.2 HAMILTONIAN SYSTEMS AND SEPARATRIX SPLITTING 73
5.3 STOCHASTIC INSTABILITY AND SINGLE-SCALE APPROXIMATION 76 5.4 CHAOTIC
MIXING IN MICROCHANNELS 80
5.5 MULTISCALE APPROXIMATION 83
FURTHER READING 85
PART III PHENOMENOLOGICAL MODELS
6 CORRELATION EFFECTS AND TRANSPORT EQUATIONS 89
6. 1 AVERAGING AND LINEAR-RESPONSE 89
6.2 CORRELATIONS AND PHENOMENOLOGICAL TRANSPORT EQUATION 93 6.3 HEAVY
PARTICLES IN CHAOTIC FLOW 95
6.4 THE QUASILINEAR APPROACH AND PHASE-SPACE 99
6.5 THE DUPREE APPROXIMATION 100
6.6 RENORMALIZATION THEORY REVISITED 102
FURTHER READING 105
7 THE TAYLOR SHEAR DISPERSION 107
7. 1 DISPERSION IN LAMINAR FLOW 107
7.2 SCALAR DISTRIBUTION FUNCTION I LL
7.3 TRANSPORT IN COASTAL BASINS 114
7.4 THE TAYLOR APPROACH TO CHAOTIC FLOWS 116
7.5 THE LAGRANGIAN MIXING IN TURBULENT FLOW IN A PIPE 119 7.6 THE TAYLOR
DISPERSION AND MEMORY EFFECTS 121
7.7 DISPERSION IN RANDOM SHEAR FLOWS 122
FURTHER READING 124
IMAGE 3
CONTENTS XI
PART IV FRACTALS AND ANOMALOUS TRANSPORT
8 FRACTAL OBJECTS AND SCALING 129
8.1 FRACTAL DIMENSIONALITY 129
8.2 SEACOAST LENGTH AND THE MANDELBROT SCALING 131
8.3 FRACTAL TOPOLOGY AND INTERSECTIONS 134
8.4 SELF-AVOIDING RANDOM WALKS 137
8.5 TWO-DIMENSIONAL RANDOM FLOWS AND TOPOGRAPHY 139 FURTHER READING 143
9 RANDOM SHEAR FLOWS AND CORRELATIONS 145
9.1 AUTOCORRELATION FUNCTION FOR FLUIDS 145
9.2 SUPERDIFFUSION AND RETURN EFFECTS 147
9.3 LONGITUDINAL DIFFUSION AND QUASILINEAR EQUATIONS 150 9.4 RANDOM
SHEAR FLOWS AND GENERALIZED SCALING 151
9.5 ISOTROPIZATION AND MANHATTAN FLOW 153
9.6 DIFFUSION IN POWER-LAW SHEAR FLOWS 157
9.7 THE FISHER RELATION 160
FURTHER READING 161
PART V STRUCTURES AND NONLOCAL EFFECTS
10 TRANSPORT AND COMPLEX STRUCTURES 165
10.1 BOND PERCOLATION PROBLEM 165
10.2 FRACTAL DIMENSIONALITY AND PERCOLATION 167
10.3 FINITE SIZE SCALING 169
10.4 COMB STRUCTURES AND PERCOLATION TRANSPORT 170
10.5 HILLY LANDSCAPE AND PERCOLATION 171
10.6 PHENOMENOLOGICAL ARGUMENTS FOR PERCOLATION PARAMETER 174 10.7
SUBDIFFUSION AND PERCOLATION 176
FURTHER READING 178
11 FRACTIONAL MODELS OF ANOMALOUS TRANSPORT 181
11.1 RANDOM WALKS GENERALIZATION 181
11.2 FUNCTIONAL EQUATION FOR RETURN PROBABILITY 184
11.3 ENSEMBLE OF POINT VORTICES AND THE HOLTSMARK DISTRIBUTION 186 11.4
FRACTAL TIME AND SCALING 189
11.5 FRACTIONAL DERIVATIVES AND ANOMALOUS DIFFUSION 192 11.6 COMB
STRUCTURES AND THE FRACTIONAL FICK LAW 194
11.7 DIFFUSIVE APPROXIMATION AND RANDOM SHEAR FLOWS 199 FURTHER READING
201
IMAGE 4
XII CONTENTS
PART VI ISOTROPIE TURBULENCE AND SCALING
12 ISOTROPIE TURBULENCE AND SPECTRA 205
12.1 THE REYNOLDS SIMILARITY LAW 205
12.2 CASCADE PHENOMENOLOGY 207
12.3 THE TAYLOR MICROSCALE 211
12.4 DISSIPATION AND KOLMOGOROV'S SCALING 213
12.5 ACCELERATION AND SIMILARITY APPROACH 215
FURTHER READING 216
13 TURBULENCE AND SCALAR 219
13.1 SCALAR IN INERTIAL SUBRANGE 219
13.2 THE BATCHELOR SCALAR SPECTRUM 222
13.3 THE SMALL PRANDTL NUMBER AND SCALAR SPECTRUM 225
13.4 SEED DIFFUSIVITY AND TURBULENT TRANSPORT 227
13.5 FLUCTUATION-DISSIPATIVE RELATION AND CASCADE ARGUMENTS 228 FURTHER
READING 229
14 RELATIVE DIFFUSION AND SCALING 231
14. 1 THE RICHARDSON LAW AND ANOMALOUS TRANSPORT 231
14.2 THE BATCHELOR INTERMEDIATE REGIME 234
14.3 DISSIPATION SUBRANGE AND EXPONENTIAL REGIME 237
14.4 GAUSSIAN APPROXIMATIONS AND RELATIVE DISPERSION 239 14.5 FRACTIONAL
EQUATION APPROACH 242
14.6 TURBULENCE SCALING AND FRACTALITY 244
FURTHER READING 246
15 TWO-DIMENSIONAL TURBULENCE AND TRANSPORT 249
15.1 TWO-DIMENSIONAL NAVIER-STOKES EQUATION 249
15.2 INVERSE CASCADE 252
15.3 FREELY EVOLVING TWO-DIMENSIONAL TURBULENCE 255
15.4 SCALAR SPECTRA IN TWO-DIMENSIONAL TURBULENCE 256
15.5 ATMOSPHERIC TURBULENCE AND RELATIVE DISPERSION 258 15.6 ROUGH OCEAN
AND RICHARDSON'S SCALING 260
FURTHER READING 263
PART VII CONVECTION AND SCALING
16 CONVECTION AND RAYLEIGH NUMBER 267
16.1 BUOYANCY FORCES 267
16.2 THE OBERBECK-BOUSSINESQ EQUATIONS 269
16.3 THE RAYLEIGH-BENARD INSTABILITY 270
16.4 THE LORENZ MODEL AND STRANGE ATTRACTOR 274
FURTHER READING 278
IMAGE 5
CONTENTS XIII
17 CONVECTION AND TURBULENCE 279
17.1 THE OBUKHOV-GOLITSYN SCALING FOR TURBULENT CONVECTION 279 17.2
QUASILINEAR REGIMES OF TURBULENT CONVECTION 281
17.3 STRONG CONVECTIVE TURBULENCE 283
17.4 DIFFUSIVE GROWTH OF BOUNDARY LAYER 285
17.5 CHICAGO SCALING 287
17.6 TURBULENT THERMAL CONVECTION AND SPECTRA 291
FURTHER READING 293
PART VIII STRUCTURES AND COMPLEX FLOW TOPOLOGY
18 COHERENT STRUCTURES AND TRANSPORT 297
18.1 REGULAR STRUCTURES 297
18.2 SCALING FOR DIFFUSIVE BOUNDARY LAYER 300
18.3 ANOMALOUS TRANSPORT IN A ROLL SYSTEM 303
18.4 CONVECTION TOWERS AND THERMAL FLUX 306
18.5 RANDOM FLOW LANDSCAPE AND TRANSPORT 308
18.6 TRANSIENT PERCOLATION REGIME 314
FURTHER READING 316
19 FLOW TOPOLOGY RECONSTRUCTION AND TRANSPORT 319
19.1 HIGH-FREQUENCY REGIMES 319
19.2 TIME DEPENDENCE AND THE TAYLOR SHEAR FLOW 321
19.3 OSCILLATORY ROLLS AND LOBE TRANSPORT 324
19.4 FLOW TOPOLOGY RECONSTRUCTION AND SCALING 329
FURTHER READING 333
REFERENCES 335
INDEX 345 |
| any_adam_object | 1 |
| author | Bakunin, Oleg G. |
| author_facet | Bakunin, Oleg G. |
| author_role | aut |
| author_sort | Bakunin, Oleg G. |
| author_variant | o g b og ogb |
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| dewey-full | 532.0527 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532.0527 |
| dewey-search | 532.0527 |
| dewey-sort | 3532.0527 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| series2 | Springer series in synergetics Springer complexity |
| spelling | Bakunin, Oleg G. Verfasser aut Chaotic flows correlation effects, transport, and structures Oleg G. Bakunin Berlin [u.a.] Springer 2011 XIII, 351 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in synergetics Springer complexity Anomale Diffusion (DE-588)4532384-7 gnd rswk-swf Turbulente Strömung (DE-588)4117265-6 gnd rswk-swf Turbulente Strömung (DE-588)4117265-6 s Anomale Diffusion (DE-588)4532384-7 s DE-604 Erscheint auch als Online-Ausgabe Chaotic Flows X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3683380&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=024721782&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bakunin, Oleg G. Chaotic flows correlation effects, transport, and structures Anomale Diffusion (DE-588)4532384-7 gnd Turbulente Strömung (DE-588)4117265-6 gnd |
| subject_GND | (DE-588)4532384-7 (DE-588)4117265-6 |
| title | Chaotic flows correlation effects, transport, and structures |
| title_auth | Chaotic flows correlation effects, transport, and structures |
| title_exact_search | Chaotic flows correlation effects, transport, and structures |
| title_full | Chaotic flows correlation effects, transport, and structures Oleg G. Bakunin |
| title_fullStr | Chaotic flows correlation effects, transport, and structures Oleg G. Bakunin |
| title_full_unstemmed | Chaotic flows correlation effects, transport, and structures Oleg G. Bakunin |
| title_short | Chaotic flows |
| title_sort | chaotic flows correlation effects transport and structures |
| title_sub | correlation effects, transport, and structures |
| topic | Anomale Diffusion (DE-588)4532384-7 gnd Turbulente Strömung (DE-588)4117265-6 gnd |
| topic_facet | Anomale Diffusion Turbulente Strömung |
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