Ten chapters in turbulence

Ten Chapters in Turbulence......Page 1
Contents......Page 5
Preface page......Page 9
Contributors......Page 11
1.1 Introduction......Page 13
1.2 Background supporting the idea of universality......Page 14
1.3 Examination of the ideas underlying the 4/5 law......Page 19
1.4 Intermittency of dissipation rate and velocity gradients......Page 26
1.5 Local structure......Page 33
1.6 Inertial subrange......Page 40
1.7 Concluding remarks......Page 46
References......Page 47
2.1 Introduction......Page 55
2.2 Basic relations......Page 56
2.3 Temporal growth of vorticity......Page 64
2.4 Spatial structure of the turbulent vorticity field......Page 72
2.5 Vorticity statistics in turbulence......Page 85
References......Page 92
3.1 Introduction......Page 99
3.2 Computational perspective......Page 101
3.3 Background theory......Page 105
3.4 Approach to low-order asymptotic state......Page 107
3.5 High-order statistics: fine-scale structure and intermittency......Page 120
3.6 Concluding remarks......Page 133
References......Page 136
4.1 Introduction......Page 144
4.2 Single particle motion and absolute dispersion......Page 147
4.3 Two particle motion and relative dispersion......Page 165
4.4 n-particle statistics......Page 174
4.5 Conclusions......Page 177
References......Page 179
5.1 Introduction......Page 188
5.2 Background......Page 191
5.3 Scales of coherent structures in wall turbulence......Page 202
5.4 Relationship between statistical fine-scales and eddy scales......Page 218
5.5 Summary and conclusions......Page 221
References......Page 226
6.1 Introduction......Page 233
6.2 The classical theory of wall-bounded turbulence......Page 239
6.3 The dynamics of the near-wall region......Page 243
6.4 The logarithmic and outer layers......Page 253
6.5 Coherent structures and dynamical systems......Page 261
6.6 Conclusions......Page 272
References......Page 273
7.1 Introduction......Page 281
7.2 Scaling, cascade and spectra......Page 283
7.3 Numerical simulations......Page 294
7.4 Laboratory experiments......Page 304
7.5 Field data......Page 309
7.6 Conclusions......Page 321
Appendix......Page 323
References......Page 324
8.1 The evidence of the early experiments......Page 330
8.2 Background: inertial waves and the formation of Taylor columns......Page 333
8.3 The spontaneous growth of Taylor columns from compact eddies at low Ro......Page 337
8.4 Anisotropic structuring via nonlinear wave interactions: resonant triads......Page 344
8.5 Recent experimental evidence on inertial waves and columnar vortex formation......Page 349
8.6 The cyclone–anticyclone asymmetry: speculative cartoons......Page 355
8.7 The rate of energy decay......Page 357
8.8 Concluding remarks......Page 359
References......Page 360
9.1 Introduction......Page 363
9.2 Dynamo......Page 368
9.3 Mean field......Page 386
9.4 Conclusions......Page 406
References......Page 409
10.1 Introduction......Page 417
10.2 Preliminary remarks on decaying QT......Page 422
10.3 Comparisons between QT and HIT: energy spectrum......Page 429
10.4 Decaying vorticity......Page 434
10.5 Decay of HIT when the shape of the energy spectra matters......Page 436
10.6 Effective viscosity......Page 440
10.7 Conclusions......Page 443
References......Page 444