Dynamics of spatio-temporal cellular structures

Cover......Page 1
Tracts in Modern Physics, 207......Page 2
Dynamics of Spatio-Temporal Cellular Structures......Page 4
ISBN-13: 9780387400983......Page 5
Preface......Page 6
Table Contents \r......Page 7
Contributors\r......Page 9
Part I Introduction......Page 12
1 The Context of Bénard Scientific Work and Nonlinear Science......Page 14
References......Page 18
2.1 Biographical Notes......Page 20
2.2 Convection Cells......Page 28
2.3 Vortex Shedding in Bluff Bodies......Page 34
2.4 Benard and Cinematography......Page 39
2.5 Physics and Dynamical Systems......Page 41
2.6 Conclusion......Page 42
A. General References......Page 43
B. Benard Papers......Page 45
Part II Bénard Cellular Structures......Page 50
3.1 Introduction......Page 52
3.2 RB Convection at Threshold......Page 54
3.3 RB Convection Beyond Threshold......Page 55
3.4 Weak Turbulence in Confined Systems and Chaos......Page 59
3.5 Patterns in Extended Systems at Large P......Page 62
3.6 Weak Turbulence in Extended Systems at Small P......Page 65
3.7 Space–Time Intermittency and Statistical Physics......Page 68
3.8 Convection at Large Rayleigh Numbers......Page 70
3.9 Conclusion......Page 72
References......Page 73
4.1 Introduction......Page 78
4.2 Fluctuations near the Onset of Convection......Page 82
4.3 Deterministic Patterns......Page 90
4.4.1 Early Measurements......Page 91
4.4.2 Spiral-Defect Chaos......Page 93
4.5.1 Domain Chaos......Page 94
4.5.2 Square Patterns at Modest σ......Page 96
4.5.3 The Range 0.16 < σ < 0.7......Page 97
4.6 Conclusion......Page 99
References......Page 100
Summary......Page 106
References......Page 112
6.1 Introduction......Page 114
6.2.1 Thermal Convection in the Atmosphere......Page 116
6.2.2 Some Remarks on Mantle Convection......Page 119
6.2.3 Solar Convection......Page 121
6.3 Convection in Rapidly Rotating Fluid Spheres......Page 123
6.4 Convection-Driven Dynamos in Spherical Fluid Shells......Page 129
References......Page 134
Part III Bénard–Marangoni Cellular Structures......Page 138
7.1 Introduction......Page 140
7.2 Heat Transfer and Capillary–Gravity Waves (Laplace–Kelvin Waves)......Page 142
7.3.1 Disturbance Equations......Page 146
7.3.2 Transverse Capillary-Gravity Waves (Laplace–Kelvin Waves)......Page 148
7.3.3 Transverse Waves Not Obeying the Laplace Law......Page 150
7.3.4 Longitudinal Waves (Lucassen Waves)......Page 152
7.4 Concluding Remarks......Page 154
References......Page 155
8.1.1 Nondimensional Numbers......Page 158
Horizontal Temperature Gradient......Page 160
8.2 Experiments......Page 161
Small Bond Number (Small Fluid Depth)......Page 163
Large Bond Number (Large Fluid Depth)......Page 165
Small Bond Number (Small Fluid Depth)......Page 168
8.2.3 Curvature and Localization......Page 169
8.3 Applications......Page 170
References......Page 171
9.1 Introduction......Page 174
9.2 Moderate Supercriticality......Page 175
9.2.1 The Hexagon–Square–Transition......Page 176
9.2.2 The Defect-Mediated Nature of the Transition......Page 181
9.3 High Supercriticality and Outlook......Page 183
References......Page 186
Part IV Bénard and Wakes......Page 189
10.1 Introduction and Historical Aspects......Page 190
10.2 The Instability Threshold and the Landau Model......Page 193
10.3 Three-Dimensional Patterns and the Ginzburg–Landau Model......Page 196
10.4 The Transition to Turbulence: The Modes A and B......Page 199
10.5 Diversity of Applications......Page 203
10.6 Conclusion......Page 206
References......Page 209
11.1 Envelope of Rayleigh–Benard Convection......Page 214
11.2 Downstream Evolution of the Benard–von Karman Street......Page 216
11.3 Current Developments......Page 218
References......Page 220
Part V Extension of Bénard\'s Work......Page 223
12.1 Introduction......Page 224
12.2 Primary Patterns......Page 225
12.3 Two-Frequency Forcing......Page 229
12.4 Spatio–Temporal Chaos and Other Complex Phenomena......Page 231
References......Page 234
13.1 Introduction......Page 236
13.2 Basic Flows and Instability Mechanisms......Page 237
13.3 Weakly Nonlinear Analysis and Secondary Modes......Page 242
13.4 Turbulent Regime......Page 243
13.4.1 Turbulent Transport......Page 244
13.4.2 Velocity Profile......Page 247
13.4.3 Fluctuations......Page 248
13.5 Conclusion......Page 249
References......Page 250
Index......Page 254