search for books and compare prices
Tables of Contents for New Trends in Turbulence
Chapter/Section Title
Page #
Page Count
Lecturers
xi
Participants
xiii
Preface
xvii
Preface
xxiii
Contents
xxvii
The Century of Turbulence Theory: The Main Achievements and Unsolved Problems
A. Yaglom
1
52
Introduction
3
3
Flow instability and transition to turbulence
6
5
Development of the theory of turbulence in the 20th century: Exemplary achievements
11
28
Similarity laws of near-wall turbulent flows
11
19
Kolmogorov's theory of locally isotropic turbulence
30
9
Concluding remarks; possible role of Navier-Stokes equations
39
14
Measures of Anisotropy and the Universal Properties of Turbulence
S. Kurien and K.R. Sreenivasan
53
60
Introduction
56
2
Theoretical tools
58
11
The method of SO(3) decomposition
58
4
Foliation of the structure function into j-sectors
62
1
The velocity structure functions
63
1
The second-order structure function
64
2
Dimensional estimates for the lowest-order anisotropic scaling exponents
66
2
Summary
68
1
Some experimental considerations
69
5
Background
69
1
Relevance of the anisotropic contributions
69
1
The measurements
70
4
Anisotropic contribution in the case of homogeneity
74
11
General remarks on the data
74
2
The tensor form for the second-order structure function
76
1
The anisotropic tensor component derived under the assumption of axisymmetry
76
5
The complete j = 2 anisotropic contribution
81
4
Summary
85
1
Anisotropic contribution in the case of inhomogeneity
85
3
Extracting the j = 1 component
85
3
The higher-order structure functions
88
10
Introduction
88
1
Method and results
89
1
The second-order structure function
89
3
Higher-order structure functions
92
1
Summary
93
5
Conclusions
98
15
Appendix
99
1
Full form for the j = 2 contribution for the homogeneous case
99
6
The j = 1 component in the inhomogeneous case
105
1
Antisymmetric contribution
105
2
Symmetric contribution
107
2
Tests of the robustness of the interpolation formula
109
4
Large-Eddy Simulations of Turbulence
O. Metais
113
74
Introduction
117
2
LES and determinism: Unpredictability growth
118
1
Vortex dynamics
119
6
Coherent vortices
120
1
Definition
120
1
Pressure
120
1
The Q-criterion
120
1
Vortex identification
121
1
Isotropic turbulence
122
1
Backward-facing step
123
2
LES formalism in physical space
125
6
LES equations for a flow of constant density
125
3
LES Boussinesq equations in a rotating frame
128
1
Eddy-viscosity and diffusivity assumption
128
2
Smagorinsky's model
130
1
LES in Fourier space
131
12
Spectral eddy viscosity and diffusivity
131
1
EDQNM plateau-peak model
132
2
The spectral-dynamic model
134
1
Existence of the plateau-peak
135
2
Incompressible plane channel
137
1
Wall units
138
1
Streaks and hairpins
138
1
Spectral DNS and LES
139
4
Improved models for LES
143
15
Structure-function model
143
1
Formalism
143
2
Non-uniform grids
145
1
Structure-function versus Smagorinsky models
145
1
Isotropic turbulence
146
1
SF model, transition and wall flows
146
1
Selective structure-function model
146
1
Filtered structure-function model
147
1
Formalism
147
1
A test case for the models: The temporal mixing layer
147
2
Spatially growing mixing layer
149
2
Vortex control in a round jet
151
2
LES of spatially developing boundary layers
153
5
Dynamic approach in physical space
158
3
Dynamic models
158
3
Alternative models
161
2
Generalized hyperviscosities
161
1
Hyperviscosity
162
1
Scale-similarity and mixed models
162
1
Anisotropic subgrid-scale models
163
1
LES of rotating flows
163
6
Rotating shear flows
164
1
Free-shear flows
164
1
Wall flows
165
4
Homogeneous turbulence
169
1
LES of flows of geophysical interest
169
4
Baroclinic eddies
169
2
Synoptic-scale instability
171
1
Secondary cyclogenesis
172
1
LES of compressible turbulence
173
8
Compressible LES equations
174
1
Heated flows
175
1
The heated duct
176
1
Towards complex flow geometries
177
4
Conclusion
181
6
Statistical Turbulence Modelling for the Computation of Physically Complex Flows
M.A. Leschziner
187
72
Approaches to characterising turbulence
189
7
Some basic statistical properties of turbulence and associated implications
196
7
Review of ``simple'' modelling approaches
203
9
The eddy-viscosity concept
203
1
Model categories
204
3
Model applicability
207
5
Second-moment equations and implied stress-strain interactions
212
10
Near-wall shear
215
2
Streamline curvature
217
1
Separation and recirculating flow
218
1
Rotation
219
1
Irrotational strain
220
1
Heat transfer and stratification
221
1
Second moment closure
222
6
Non-linear eddy-viscosity models
228
5
Application examples
233
18
Overview
233
2
Asymmetric diffuser
235
1
Aerospatiale aerofoil
235
3
Cascade blade
238
1
Axisymmetric impinging jet
239
1
Prolate spheroid
240
2
Round-to-rectangular transition duct
242
3
Wing/flat-plate junction
245
1
Fin-plate junction
246
5
Jet-afterbody combination
251
1
Concluding remarks
251
8
Computational Aeroacoustics
R. Mankbadi
259
60
Fundamentals of sound transmission
261
10
One-dimensional wave analysis
262
1
General solution of the wave equation
263
1
The particle velocity
263
1
Three-dimensional sound waves
264
1
Sound spectra
265
1
Spectral composition of a square pulse
266
1
Spectral composition of a harmonic signal
266
1
Logarithmic scales for rating noise
266
1
The Sound Power Level (PWL)
266
1
Sound Pressure Levels (SPL)
267
1
Pressure Band Level (PBL)
267
1
Pressure Spectral Level (PSL) per unit frequency
267
2
Acoustic intensity
269
1
Overall pressure levels
269
1
Subjective noise measures
269
1
Perceived Noise Level (PNL)
270
1
Tone Corrected Perceived Noise Level (PNLT)
270
1
Effective Perceived Noise Level (EPNL)
270
1
Aircraft noise sources
271
7
Noise regulations
271
1
Contribution from various components
271
1
Engine noise
271
1
Elements of the generation process
272
1
Noise measurements
272
6
Methodology for jet noise
278
12
Jet noise physics
278
1
CAA for jet noise
279
2
Wave-like sound source
281
4
Lighthill's theory
285
2
Application of Lighthill's theory
287
1
Kirckhoff's solution
288
2
Algorithms and boundary treatment
290
8
Algorithms for CAA
290
2
The 2-4 scheme
292
1
The compact scheme
292
1
The Dispersion-Relation-Preserving scheme
293
1
Boundary treatment for CAA
293
2
Wall boundary conditions
295
1
Outflow boundary treatment
295
1
Radiation boundary condition
295
1
Inflow treatments
296
2
Large-eddy simulations and linearized Euler
298
21
Large-eddy simulation
298
2
Filtering
300
1
Filtered equations
301
3
Modelling subgrid-scale turbulence
304
4
Linearized Euler equations
308
11
The Topology of Turbulence
H.K. Moffatt
319
22
Introduction
321
1
The family of helicity invariants
322
3
Chaotic fields
323
1
Simply degenerate fields
324
1
Doubly degenerate fields
324
1
The special case of Euler dynamics
325
1
Scalar field structure in 2D flows
326
1
Scalar field structure in 3D flows
327
1
Vector field structure in 3D flows
328
1
Helicity and the turbulent dynamo
329
5
The kinematic phase
330
3
The dynamic phase
333
1
Magnetic relaxation
334
2
The analogy with Euler flows
335
1
The blow-up problem
336
5
Interaction of skewed vortices
337
4
``Burgulence''
U. Frisch and J. Bec
341
44
Introduction
343
5
The Burgers equation in cosmology
344
3
The Burgers equation in condensed matter and statistical physics
347
1
The Burgers equation as testing ground for Navier-Stokes
347
1
Basic tools
348
8
The Hopf-Cole transformation and the maximum representation
348
2
Shocks in one dimension
350
4
Convex hull construction in more than one dimension
354
1
Remarks on numerical methods
355
1
The Fourier-Lagrange representation and artefacts
356
2
The law of energy decay
358
5
One-dimensional case with Brownian initial velocity
363
4
Preshocks and the pdf of velocity gradients in one dimension
367
3
The pdf of density
370
3
Kicked burgulence
373
12
Forced Burgers equation and variational formulation
373
3
Periodic kicks
376
4
Connections with Aubry-Mather theory
380
5
Two-Dimensional Turbulence
J. Sommeria
385
64
Introduction
387
4
Equations and conservation laws
391
6
Euler vs. Navier-Stokes equations
391
1
Vorticity representation
392
1
Conservation laws
393
3
Steady solutions of the Euler equations
396
1
Vortex dynamics
397
14
Systems of discrete vortices
398
1
Vortex pairs
399
4
Instability of shear flows and vortex lattices
403
1
Statistical mechanics of point vortices
404
7
Spectral properties, energy and enstrophy cascade
411
14
Spectrally truncated equilibrium states
412
3
The enstrophy and inverse energy cascades of forced turbulence
415
7
The enstrophy cascade of freely evolving turbulence
422
1
The emergence and evolution of isolated vortices
423
2
Equilibrium statistical mechanics and self-organization
425
10
Statistical mechanics of non-singular vorticity fields
425
3
The Gibbs states
428
4
Tests and discussion
432
3
Eddy diffusivity and sub-grid scale modeling
435
7
Thermodynamic approach
435
4
Kinetic models
439
3
Conclusions
442
7
Analysing and Computing Turbulent Flows Using Wavelets
M. Farge and K. Schneider
449
7
Introduction
453
3
I Wavelet Transforms
456
12
History
456
1
The continuous wavelet transform
457
4
One dimension
457
1
Analyzing wavelet
457
1
Wavelet analysis
458
1
Wavelet synthesis
459
1
Energy conservation
459
1
Higher dimensions
459
1
Algorithm
460
1
The orthogonal wavelet transform
461
7
One dimension
461
1
1D Multi-Resolution Analysis
461
2
Regularity and local decay of wavelet coefficients
463
1
Higher dimensions
463
1
Tensor product construction
463
1
2D Multi-Resolution Analysis
464
1
Periodic 2D Multi-Resolution Analysis
465
1
Algorithm
466
2
II Statistical Analysis
468
10
Classical tools
468
5
Methodology
468
1
Laboratory experiments
468
1
Numerical experiments
468
1
Averaging procedure
469
1
Statistical diagnostics
470
1
Probability Distribution Function (PDF)
470
1
Radon-Nikodyn's theorem
471
1
Definition of the joint probability
471
1
Statistical moments
471
1
Structure functions
472
1
Autocorrelation function
472
1
Fourier spectrum
472
1
Wiener-Khinchin's theorem
473
1
Statistical tools based on the continuous wavelet transform
473
3
Local and global wavelet spectra
473
1
Relation with Fourier spectrum
474
1
Application to turbulence
475
1
Statistical tools based on the orthogonal wavelet transform
476
2
Local and global wavelet spectra
476
1
Relation with Fourier spectrum
477
1
Intermittency measures
478
1
III Computation
478
22
Coherent vortex extraction
478
6
CVS filtering
478
1
Vorticity decomposition
479
1
Nonlinear thresholding
479
1
Vorticity and velocity reconstruction
480
1
Application to a 3D turbulent mixing layer
480
1
Comparison between CVS and LES filtering
481
3
Computation of turbulent flows
484
5
Navier-Stokes equations
484
1
Velocity-pressure formulation
484
1
Vorticity-velocity formulation
484
1
Classical numerical methods
485
1
Direct Numerical Simulation (DNS)
485
1
Modelled Numerical Simulation (MNS)
486
1
Coherent Vortex Simulation (CVS)
487
1
Principle of CVS
487
1
CVS without turbulence model
488
1
CVS with turbulence model
488
1
Adaptive wavelet computation
489
11
Adaptive wavelet scheme for nonlinear PDE's
489
1
Time discretization
490
1
Wavelet decomposition
490
2
Evaluation of the nonlinear term
492
1
Substraction strategy
493
1
Summary of the algorithm
494
1
Adaptive wavelet scheme for the 2D Navier-Stokes equations
494
3
Application to a 2D turbulent mixing layer
497
1
Adaptive wavelet computation
497
1
Comparison between CVS and Fourier pseudo-spectral DNS
497
3
IV Conclusion
500
5
Lagrangian Description of Turbulence
G. Falkovich K. Gawedzki and M. Vergassola
505
2
Particles in fluid turbulence
507
1
Single-particle diffusion
508
2
Two-particle dispersion in a spatially smooth velocity
510
1
General consideration
510
5
Solvable cases
515
3
Two-particle dispersion in a nonsmooth incompressible flow
518
7
Multiparticle configurations and breakdown of scale-invariance
525
1
Absolute and relative evolution of particles
526
1
Multiparticle motion in Kraichnan velocities
527
2
Zero modes and slow modes
529
3
Perturbative schemes
532
4
Passive fields in fluid turbulence
536
1
Unforced evolution of passive fields
536
2
Cascades of a passive scalar
538
1
Passive scalar in a spatially smooth velocity
539
4
Passive scalar in a spatially nonsmooth velocity
543
1
Navier-Stokes equation from a Lagrangian viewpoint
546
1
Enstrophy cascade in two dimensions
546
3
On the energy cascades in incompressible turbulence
549
2
Conclusion
551
<