Frontiers in Turbulence and Coherent Structures: Proceedings of the COSNet/CSIRO Workshop on Turbulence and Coherent Structures in Fluids, Plasmas and ... Scientific Lecture Notes in Complex Systems)

CONTENTS......Page 9
Preface......Page 6
1. Introduction......Page 12
2. To understand stability is to understand dynamics......Page 18
3. Governor equations of motion: a simple case study......Page 21
4. The restricted three body problem, homoclinic chaos, and structural stability......Page 24
5. Discrete dynamics, blowflies, feedback, and stability......Page 29
5.1. Blowfly dynamics as a feedback system......Page 31
6. Stability of complex networks......Page 32
References......Page 35
1. Introduction......Page 40
2.1. Theoretical approach......Page 43
2.1.1. Separable Example......Page 44
2.2.1. Northern Hemisphere......Page 45
2.2.2. Southern Hemisphere......Page 47
2.3. Blocking......Page 49
3. Climate Regime Transitions......Page 51
4. Ensemble Weather Prediction during Regime Transitions......Page 53
4.1. Methodology......Page 54
4.3. Error growth and predictability......Page 55
4.4. Discussion......Page 57
5.1. Theory......Page 59
5.2. FTPOPs and FTNMs......Page 61
5.3. Discussion......Page 63
Acknowledgements......Page 64
References......Page 65
1. Introduction......Page 70
2. Governing Equations......Page 73
3. Three-Component System......Page 75
4. Direct Numerical Simulation......Page 78
5. Multi-mode Topographies......Page 84
6. Global Models......Page 85
7. Zonal Jets and Confinement of Rossby Waves......Page 88
8. Summary and Conclusion......Page 95
References......Page 96
1. Introduction......Page 98
2. Methodology......Page 101
2.1. Estimates using daily data......Page 102
2.2. Estimates using monthly data......Page 105
2.3. Coupled patterns of variability......Page 108
3. Monte Carlo Simulation — Synthetic Data......Page 111
4. Coherent Patterns of the Atmospheric Circulation......Page 115
4.1. Southern Hemisphere winter circulation......Page 116
4.2. Northern Hemisphere winter circulation......Page 122
4.3. Coherent atmospheric patterns and Australian surface temperature......Page 123
5. Conclusions......Page 127
Appendix A. Principal Component Analysis......Page 129
Appendix B. Singular Value Decomposition......Page 130
References......Page 131
1. Introduction......Page 132
2. Single-layer flows......Page 134
3.2. Double-gyre flows......Page 137
3.3. Connection between single-gyre and double-gyre flows......Page 140
4. Secondary bifurcations: double-gyre case......Page 141
4.1. Hopf bifurcations......Page 142
4.2. Homoclinic bifurcations......Page 144
5. Low-frequency variability......Page 147
6. Multi-layer flows......Page 149
7. Summary and outlook......Page 155
References......Page 156
1. Introduction......Page 160
2.1. Model geometry......Page 162
2.2. Governing equations......Page 163
2.3. Numerical scheme......Page 164
3.1. The basic state under steady forcing (A = 0)......Page 165
3.2. Response to variable forcing......Page 168
4. Conclusions......Page 177
References......Page 178
1. Introduction......Page 182
2. The quasi-geostrophic coupled model (Q-GCM)......Page 183
3.1. Mean circulation......Page 184
3.2. Variability......Page 185
3.3. Mechanisms of variability......Page 187
4.1. Mean flow......Page 189
4.2. Variability......Page 190
4.3. Mechanism of variability......Page 193
5. Conclusions......Page 194
References......Page 195
Periodic motion versus turbulent motion: scaling laws, bursting and Lyapunov spectra L. van Veen, S. Kida and G. Kawahara......Page 198
1. Introduction......Page 199
2. Turbulence, chaos and the cycle expansion......Page 201
3.1. The number of degrees of freedom......Page 204
3.2. Reduction by symmetry......Page 205
3.3. How to find unstable solutions?......Page 206
3.4. Continuation in the Reynolds number......Page 207
3.5. Analysis of embedded periodic motion......Page 208
4. Conclusions and outlook......Page 210
References......Page 212
1. Introduction......Page 214
2. The Lagrangian Representation......Page 215
3. Maximum Entropy Methods......Page 218
4. Conditioned Ensembles: Cluster Separation Conditioning......Page 219
5. Conditioned Ensembles: Joint Centre-of-Mass/Separation PDF......Page 222
6. Scaled Separations......Page 224
8. Applications to Scalar Statistics......Page 225
9. Conclusions......Page 232
Appendix A. The ortho-normal transformation......Page 233
Appendix C. Scale PDF......Page 234
References......Page 235
1. Introduction......Page 238
2.1. A Brief History of Mean Flow Scaling......Page 241
2.2. The Renaissance of the Power Law......Page 242
2.3. Curve-fitting the mean velocity profile......Page 244
3. Attached eddy model......Page 246
4. A very large boundary layer......Page 250
5. Conclusions and outlook......Page 254
References......Page 255
1. Introduction......Page 258
2. The structure of near-wall turbulence......Page 259
3. Exact solutions for the sublayer......Page 262
4. The logarithmic layer......Page 267
5. Conclusions......Page 268
References......Page 269
1. Introduction......Page 272
2. Apparatus and techniques......Page 273
3. Three-dimensional Tollmien–Schlichting waves......Page 276
4. Asymmetry and linearity with actuator amplitude......Page 278
5. Formation of instabilities and breakdown of disturbance......Page 280
6. Characteristics of the turbulent wedge......Page 287
References......Page 290
1.1. Renormalized perturbation theories and two-point turbulence closures......Page 292
1.2. A brief history of closures......Page 293
2. Basic equations in K-space......Page 294
2.2. Equation for the energy spectrum......Page 295
2.4. Inertial transfer in k-space......Page 296
3.1. Covariance equation from the quasi-normality (QN) hypothesis......Page 297
3.3. Second-order covariance equations......Page 298
3.5. Application of renormalization methods to turbulence......Page 299
4. Renormalised perturbation theory (RPT): the general idea......Page 300
4.1. Pioneering RPTs......Page 301
4.2. Kraichnan-Wyld perturbation theory......Page 302
4.3. The L coefficients in turbulence theory......Page 303
4.5. Renormalised response functions and RPTs......Page 304
4.6. Derivation of DIA......Page 305
4.7. The DIA and LET response equations......Page 306
5.1. The local energy transfer (LET) theory......Page 307
5.2. Numerical computation of RPTs......Page 308
6.1. What are the issues?......Page 310
6.2. Wider issues......Page 311
6.3. Incompatibility with K41: ‘Convective invariance’ versus ‘scale invariance’......Page 312
6.3.1. Random Galilean Invariance......Page 313
6.4. Wyld’s formalism versus MSR......Page 315
6.5. Lagrangian versus Eulerian formulations......Page 316
6.8. The wider issue of the K41 ‘-5/3’ power law......Page 317
7. New developments in LET......Page 318
7.2. Derivation of the mean propagator equation......Page 319
7.3. The fluctuation-dissipation relationship......Page 320
7.5. Group-closure properties of the LET......Page 321
9. Conclusion......Page 322
References......Page 323
1. Introduction......Page 326
2. Barotropic flow on a -plane......Page 330
3. The QDIA closure equations......Page 332
4. Diagnostics......Page 336
5. Topographic Rossby waves in a turbulent environment......Page 338
5.1. Case 1......Page 339
6. Homogeneous and isotropic closure theories......Page 341
7. Performance of DIA, SCFT and LET closures for moderate Reynolds number turbulence......Page 343
8. Inhomogeneous turbulence on an f-plane......Page 346
9. Vorticity equation and DIA closure on the sphere......Page 349
10. EDQNM closure on the sphere......Page 351
11.1. The EDQNM Closure......Page 353
11.2. The DIA closure......Page 354
12. Comparisons of DNS and LES with subgrid-scale parameterizations......Page 355
13. Discussion and conclusions......Page 358
References......Page 361
Statistical dynamical methods of ensemble prediction and data assimilation during blocking T. J. O’Kane and J. S. Frederiksen......Page 366
1. Introduction......Page 367
2. Ensemble prediction......Page 369
3. Barotropic flow on a -plane......Page 371
4. The QDIA closure equations with memory effects......Page 373
5. Diagnostics......Page 374
6. Error growth during blocking using initial bred perturbations......Page 375
7. Bred initial forecast errors......Page 377
8. Ensemble prediction results......Page 378
9. Discussion......Page 385
10. Data assimilation......Page 387
11. Statistical dynamical filters......Page 390
12. Quasi-diagonal statistical dynamical Kalman filter......Page 391
13. Ensemble Kalman filter......Page 392
14. Quasi-diagonal ensemble square root filter......Page 393
15.1. A comparison of quasi-diagonal ensemble Kalman and statistical dynamical filters......Page 394
15.2. The performance of the ensemble square root filter......Page 397
16. Discussion......Page 399
References......Page 402
1. Introduction......Page 406
2. Two-dimensional turbulence in plasmas......Page 407
3. Recipe for the reduced model......Page 409
4. Analysis of and modifications to the distilled model......Page 411
4.1. The case of the trapped singularity......Page 413
4.2. Energy must flow in both directions......Page 416
4.3. Thermal diffusivity is not negligible......Page 417
4.4. Strands (1) and (2) are unified......Page 419
5. Discussion......Page 420
Appendix A. Singularity theory......Page 421
References......Page 424
1. Introduction......Page 426
2. The CHM and MHM equations......Page 429
3. Waves and mean flow......Page 432
4. Nonlinear Schrodinger equation and modulational instability......Page 434
5. Nonlinear frequency shift......Page 435
5.1. Modulational instability for MHM equation......Page 436
5.2. Modulational instability for CHM equation......Page 438
References......Page 439
1. Introduction......Page 442
2. Modified Hasegawa-Wakatani Model......Page 443
2.1. Linear Stability Analysis......Page 446
3. Simulation Results......Page 447
4. Conclusion......Page 451
Acknowledgements......Page 452
References......Page 453
1.1. Drift waves and ion-temperature-gradient-driven modes......Page 454
1.3. Zonal flows......Page 456
2. Model building......Page 457
3. Bifurcation theory......Page 462
4. Discussion......Page 464
References......Page 465
1. Introduction......Page 468
1.2. Fluctuation measurement in H-1......Page 469
1.3. Justification of the single field model......Page 472
2. Experimental results of plasma turbulence studies in the H-1 heliac......Page 475
References......Page 479
1. Introduction......Page 482
2. Experimental Setup and Some Major Results......Page 484
2.3. Toroidal Diocotron Oscillations With Eext = 0......Page 485
3. Numerical Model......Page 488
3.1. Model and Assumptions:......Page 490
3.2. Equilibrium or Steady State......Page 492
3.3. Experimentally Relevant Initial Conditions and Their Evolution......Page 493
3.3.1. Numerical Evolution of Strip-1......Page 494
3.3.2. First Diocotron Period: Turbulence and Coherent Structure......Page 497
3.3.3. Nonlinearity and Matched Injection : Strip-1 and Strip-3......Page 498
4. Conclusion and Future work......Page 499
Acknowledgements......Page 500
References......Page 501