ISBN: 3540429786
TITLE: New trends in turbulence
AUTHOR: Lesieur, Yaglom, David (Hrsg.)
TOC:

Lecturers xi
Participants xiii
Prface xvii
Preface xviii
Contents xxvii
Course 1. The Century of Turbulence Theory: The Main Achievements and Unsolved Problems
by A. Yaglom 1
1 Introduction 3
2 Flow instability and transition to turbulence 6
3 Development of the theory of turbulence in the 20th century: Exemplary achievements 11
3.1 Similarity laws of near-wall turbulent flows 11
3.2 Kolmogorov's theory of locally isotropic turbulence 30
4 Concluding remarks; possible role of Navier-Stokes equations 39
Course 2. Measures of Anisotropy and the Universal Properties of Turbulence
by S. Kurien and K.R. Sreenivasan 53
1 Introduction 56
2 Theoretical tools 58
2.1 The method of SO(3) decomposition 58
2.2 Foliation of the structure function into j-sectors 62
2.3 The velocity structure functions 63
2.3.1 The second-order structure function 64
2.4 Dimensional estimates for the lowest-order anisotropic scaling exponents 66
2.5 Summary 68
3 Some experimental considerations 69
3.1 Background 69
3.2 Relevance of the anisotropic contributions 69
3.3 The measurements 70
4 Anisotropic contribution in the case of homogeneity 74
4.1 General remarks on the data 74
4.2 The tensor form for the second-order structure function 76
4.2.1 The anisotropic tensor component derived under the assumption of axisymmetry 76
4.2.2 The complete j = 2 anisotropic contribution 81
4.3 Summary 85
5 Anisotropic contribution in the case of inhomogeneity 85
5.1 Extracting the j = 1 component 85
6 The higher-order structure functions 88
6.1 Introduction 88
6.2 Method and results 89
6.2.1 The second-order structure function 89
6.2.2 Higher-order structure functions 92
6.3 Summary 93
7 Conclusions 98
Appendix 99
A Full form for the j = 2 contribution for the homogeneous case 99
B The j = 1 component in the inhomogeneous case 105
B.1 Antisymmetric contribution 105
B.2 Symmetric contribution 107
C Tests of the robustness of the interpolation formula 109
Course 3. Large-Eddy Simulations of Turbulence
by O. Mtais 113
1 Introduction 117
1.1 LES and determinism: Unpredictability growth 118
2 Vortex dynamics 119
2.1 Coherent vortices 120
2.1.1 Definition 120
2.1.2 Pressure 120
2.1.3 The Q-criterion 120
2.2 Vortex identification 121
2.2.1 Isotropic turbulence 122
2.2.2 Backward-facing step 123
3 LES formalism in physical space 125
3.1 LES equations for a flow of constant density 125
3.2 LES Boussinesq equations in a rotating frame 128
3.3 Eddy-viscosity and diffusivity assumption 128
3.4 Smagorinsky's model 130
4 LES in Fourier space 131
4 1 Spectral eddy viscosity and diffusivity 131
4.2 EDQNM Plateau-peak model 132
4.2.1 The spectral-dynamic model 134
4.2.2 Existence of the Plateau-peak 135
4.3 Incompressible plane channel 137
4.3.1 Wall units 138
4.3.2 Streaks and hairpins 138
4.3.3 Spectral DNS and LES 139
5 Improved models for LES 143
5.1 Structure-function model 143
5.1.1 Formalism 143
5.1.2 Non-uniform grids 145
5.1.3 Structure-function versus Smagorinsky models 145
5.1.4 Isotropic turbulence 146
5.1.5 SF model, transition and wall flows 146
5.2 Selective structure-function model 146
5.3 Filtered structure-function model 147
5.3.1 Formalism 147
5 4 A test case for the models: The temporal mixing layer 147
5.5 Spatially growing mixing layer 149
5.6 Vortex control in a round jet 151
5.7 LES of spatially developing boundary layers 153
6 Dynamic approach in physical space 158
6.1 Dynamic models 158
7 Alternative models 161
7.1 Generalized hyperviscosities 161
7.2 Hyperviscosity 162
7.3 Scale-similarity and mixed models 162
7.4 Anisotropic subgrid-scale models 163
8 LES of rotating flows 163
8.1 Rotating shear flows 164
8.1.1 Free-shear flows 164
8.1.2 Wall flows 165
8.1.3 Homogeneous turbulence 169
9 LES of flows of geophysical interest 169
9.1 Baroclinic eddies 169
9.1.1 Synoptic-scale instability 171
9.1.2 Secondary cyclogenesis 172
10 LES of compressible turbulence 173
10.1 Compressible LES equations 174
10.2 Heated flows 175
10.2.1 The heated duct 176
10.2.2 Towards complex flow geometries 177
11 Conclusion 181
Course 4. Statistical Turbulence Modelling for the Computation of Physically Complex Flows
by M.A. Leschziner 187
1 Approaches to characterising turbulence 189
2 Some basic statistical properties of turbulence and associated implications 196
3 Review of "simple" modelling approaches 203
3.1 The eddy-viscosity concept 203
3.2 Model categories 204
3.3 Model applicability 207
4 Second-moment equations and implied stress-strain interactions 212
4.1 Near-wall shear 215
4.2 Streamline curvature 217
4.3 Separation and recirculating flow 218
4.4 Rotation 219
4.5 Irrotational strain 220
4.6 Heat transfer and stratification 221
5 Second moment closure 222
6 Non-linear eddy-viscosity models 228
7 Application examples 233
7.1 Overview 233
7.2 Asymmetric diffuser 235
7.3 Aerospatiale aerofoil 235
7.4 Cascade blade 238
7.5 Axisymmetric impinging jet 239
7.6 Prolate spheroid 240
7.7 Round-torectangular transition duct 242
7.8 Wing/flat-plate junction 245
7.9 Fin-plate junction 246
7.10 Jet-afterbody combination 251
8 Concluding remarks 251
Course 5. Computational Aeroacoustics
by R. Mankbadi 259
1 Fundamentals of sound transmission 261
1.1 One-dimensional wave analysis 262
1.1.1 General solution of the wave equation 263
1.1.2 The particle velocity 263
1.2 Three-dimensional sound waves 264
1.3 Sound spectra 265
1.3.1 Spectral composition of a square pulse 266
1.3.2 Spectral composition of a harmonic signal 266
1.4 Logarithmic scales for rating noise 266
1.4.1 The Sound Power Level (PWL) 266
1.4.2 Sound Pressure Levels (SPL) 267
1.4.3 Pressure Band Level (PBL) 267
1.4.4 Pressure Spectral Level (PSL) per unit frequency 267
1.4.5 Acoustic intensity 269
1.4.6 Overall pressure levels 269
1.4.7 Subjective noise measures 269
1.4.8 Perceived Noise Level (PNL) 270
1.4.9 Tone Corrected Perceived Noise Level (PNLT) 270
1.4.10 Effective Perceived Noise Level (EPNL) 270
2 Aircraft noise sources 271
2.1 Noise regulations 271
2.2 Contribution from various components 271
2.3 Engine noise 271
2.3.1 Elements of the generation process 272
2.3.2 Noise measurements 272
3 Methodology for jet noise 278
3.1 Jet noise physics 278
3.2 CAA for jet noise 279
3.3 Wave-like sound source 281
3.4 Lighthill's theory 285
3.4.1 Application of Lighthill's theory 287
3.5 Kirckhoff's solution 288
4 Algorithms and boundary treatment 290
4.1 Algorithms for CAA 290
4.1.1 The 224 scheme 292
4.1.2 The compact scheme 292
4.1.3 The Dispersion-Relation-Preserving scheme 293
4.2 Boundary treatment for CAA 293
4.2.1 Wall boundary conditions 295
4.2.2 Outflow boundary treatment 295
4.2.3 Radiation boundary condition 295
4.2.4 Inflow treatments 296
5 Large-eddy simulations and linearized Euler 298
5.1 Large-eddy simulation 298
5.1.1 Filtering 300
5.1.2 Filtered equations 301
5.1.3 Modelling subgrid-scale turbulence 304
5.2 Linearized Euler equations 308
Course 6. The Topology of Turbulence
by H.K. Moffatt 319
1 Introduction 321
2 The family of helicity invariants 322
2.1 Chaotic fields 323
2.2 Simply degenerate fields 324
2.3 Doubly degenerate fields 324
3 The special case of Euler dynamics 325
4 Scalar field structure in 2D flows 326
5 Scalar field structure in 3D flows 327
6 Vector field structure in 3D flows 328
7 Helicity and the turbulent dynamo 329
7.1 The kinematic phase 330
7.2 The dynamic phase 333
8 Magnetic relaxation 334
8.1 The analogy with Euler flows 335
9 The blow-up problem 336
9.1 Interaction of skewed vortices 337
Course 7. "Burgulence"
by U. Frisch and J. Bec 341
Introduction 343
1.1 The Burgers equation in cosmology 344
1 2 The Burgers equation in condensed matter and statistical physics 347
1.3 The Burgers equation as testing ground for Navier-Stokes 347
Basic tools 348
2.1 The Hopf-Cole transformation and the maximum representation 348
2.2 Shocks in one dimension 350
2.3 Convex hull construction in more than one dimension 354
2.4 Remarks on numerical methods 355
The Fourier-Lagrange representation and artefacts 356
The law of energy decay 358
One-dimensional case with Brownian initial velocity 363
Preshocks and the pdf of velocity gradients in one dimension 367
The pdf of density 370
Kicked burgulence 373
8.1 Forced Burgers equation and variational formulation 373
8 2 Periodic kicks 376
8.3 Connections with Aubry-Mather theory 380
Course 8. Two-Dimensional Turbulence
by J. Sommeria 385
1 Introduction 387
2 Equations and conservation laws 391
2.1 Euler vs. Navier-Stokes equations 391
2.2 Vorticity representation 392
2.3 Conservation laws 393
2.4 Steady solutions of the Euler equations 396
3 Vortex dynamics 397
3.1 Systems of discrete vortices 398
3.2 Vortex pairs 399
3.3 Instability of shear flows and vortex lattices 403
3.4 Statistical mechanics of point vortices 404
4 Spectral properties, energy and enstrophy cascade 411
4.1 Spectrally truncated equilibrium states 412
4.2 The enstrophy and inverse energy cascades of forced turbulence 415
4.3 The enstrophy csscade of freely evolving turbulence 422
4.4 The emergence and evolution of isolated vortices 423
5 Equilibrium statistical mechanics and self-organization 425
5.1 Statistical mechanics of non-singular vorticity fields 425
5.2 The Gibbs states 428
5.3 Tests and discussion 432
6 Eddy diffusivity and sub-grid scale modeling 435
6.1 Thermodynamic approach 435
6.2 Kinetic models 439
7 Conclusions 442
Course 9. Analysing and Computing Turbulent Flows Using Wavelets
by M. Farge and K. Schneider 449
1 Introduction 453
I Wavelet Transforms 456
2 History 456
3 The continuous wavelet transform 457
3.1 One dimension 457
3.1.1 Analyzing wavelet 457
3.1.2 Wavelet analysis 458
3.1.3 Wavelet Synthesis 459
3.1.4 Energy conservation 459
3.2 Higher dimensions 459
3.3 Algorithm 460
4 The orthogonal wavelet transform 461
4.1 One dimension 461
4.1.1 1D Multi-Resolution Analysis 461
4.1.2 Regularity and local decay of wavelet coefficients 463
4.2 Higher dimensions 463
4.2.1 Tensor product construction 463
4.2.2 2D Multi-Resolution Analysis 464
4.2.3 Periodic 2D Multi-Resolution Analysis 465
4.3 Algorithm 466
11 Statistical Analysis 468
5 Classical tools 468
5.1 Met hodology 468
5.1.1 Laboratory experiments 468
5.1.2 Numerical experiments 468
5.2 Averaging procedure 469
5.3 Statistical diagnostics 470
5.3.1 Probability Distribution Function (PDF) 470
5.3.2 Radon-Nikodyn's theorem 471
5.3.3 Definition of the joint probability 471
5.3.4 Statistical moments 471
5.3.5 Structure functions 472
5.3.6 Autotorrelation function 472
5.3.7 Fourier spectrum 472
5.3.8 Wiener-Khinchin's theorem 473
6 Statistical tools based on the continuous wavelet transform 473
6.1 Local and global wavelet spectra 473
6.2 Relation with Fourier spectrum 474
6.3 Application to turbulence 475
7 Statistical tools based on the orthogonal wavelet transform 476
7.1 Local and global wavelet spectra 476
7.2 Relation with Fourier spectrum 477
7.3 Intermittency messures 478
III Computation 478
8 Coherent vortex extraction 478
8.1 CVS filtering 478
8.1.1 Vorticity decomposition 479
8.1.2 Nonlinear thresholding 479
8.1.3 Vorticity and velocity reconstruction 480
8.2 Application to a 3D turbulent mixing layer 480
8.3 Comparison between CVS and LES filtering 481
9 Computation of turbulent flows 484
9.1 Navier-Stokes equations 484
9.1.1 Velocity-pressure formulation 484
9.1.2 Vorticity-velocity formulation 484
9.2 Classical numerical methods 485
9.2.1 Direct Numerical Simulation (DNS) 485
9.2.2 Modelled Numerical Simulation (MNS) 486
9.3 Coherent Vortex Simulation (CVS) 487
9.3.1 Principle of CVS 487
9.3.2 CVS without turbulence model 488
9.3.3 CVS with turbulence model 488
10 Adaptive wavelet computation 489
10.1 Adaptive wavelet scheme for nonlinear PDE's 489
10.1.1 Time discretization 490
10.1.2 Wavelet decomposition 490
10.1.3 Evaluation of the nonlinear term 492
10.1.4 Substraction strategy 493
10.1.5 Summary of the algorithm 494
10.2 Adaptive wavelet scheme for the 2D Navier-Stokes equations 494
10.3 Application to a 2D turbulent mixing layer 497
10.3.1 Adaptive wavelet computation 497
10.3.2 Comparison between CVS and Fourier pseudo-spectral DNS 497
IV Conclusion 500
Course 10. Lagrangian Description of Turbulence
by G. Falkovich, K. Gawedzki and M. Vergassoja 505
1 Particles in fluid turbulence 507
1.1 Single-particle diffusion 508
1.2 Two-particle dispersion in a spatially smooth velocity 510
1.2.1 General consideration 510
1.2.2 Solvable cases 515
1.3 Two-particle dispersion in a nonsmooth incompressible flow 518
1.4 Multiparticle configurations and breakdown of scale-invariance 525
1.4.1 Absolute and relative evolution of particles 526
1.4.2 Multiparticle motion in Kraichnan velocities 527
1.4.3 Zero modes and slow modes 529
1.4.4 Perturbative schemes 532
2 Passive fields in fluid turbulence 536
2.1 Unforced evolution of passive fields 536
2.2 Cascades of a passive scalar 538
2.2.1 Passive scalar in a spatially smooth velocity 539
2.3 Passive scalar in a spatially nonsmooth velocity 543
3 Navier-Stokes equation from a Lagrangian viewpoint 546
3.1 Enstrophy cascade in two dimensions 546
3.2 On the energy cascades in incompressible turbulence 549
4 Conclusion 551
END
