Homogeneous turbulence dynamics:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
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| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | 463 S. |
| ISBN: | 9780521855488 |
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MARC
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| 100 | 1 | |a Sagaut, Pierre |d 1967- |e Verfasser |0 (DE-588)1049515781 |4 aut | |
| 245 | 1 | 0 | |a Homogeneous turbulence dynamics |c Pierre Sagaut ; Claude Cambon |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a 463 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Anisotropie | |
| 650 | 4 | |a Isotropie | |
| 650 | 4 | |a Turbulence - Modèles mathématiques | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Turbulence |x Mathematical models | |
| 650 | 4 | |a Anisotropy |x Mathematical models | |
| 650 | 4 | |a Shear waves |x Mathematical models | |
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| 650 | 0 | 7 | |a Scherwelle |0 (DE-588)4179501-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Turbulente Strömung |0 (DE-588)4117265-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Turbulente Strömung |0 (DE-588)4117265-6 |D s |
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| adam_text | Titel: Homogeneous turbulence dynamics
Autor: Sagaut, Pierre
Jahr: 2008
Contents
Abbreviations Used in This Book page xvi
1 Introduction.................................... 1
1.1 Scope of the Book 1
1.2 Structure and Contents of the Book 3
Bibliography.................................. 9
2 Statistical Analysis of Homogeneous Turbulent Flows: Reminders ... 10
2.1 Background Deterministic Equations 10
2.1.1 Mass Conservation 10
2.1.2 The Navier-Stokes Momentum Equations 12
2.1.3 Incompressible Turbulence 13
2.1.4 First Insight into Compressibility Effects 14
2.1.5 Reminder About Circulation and Vorticity 15
2.1.6 Adding Body Forces or Mean Gradients 16
2.2 Briefs About Statistical and Probabilistic Approaches 19
2.2.1 Ensemble Averaging, Statistical Homogeneity 19
2.2.2 Single-Point and Multipoint Moments 19
2.2.3 Statistics for Velocity Increments 20
2.2.4 Application of Reynolds Decomposition to Dynamical
Equations 20
2.3 Reynolds Stress Tensor and Related Equations 22
2.3.1 RST Equations 22
2.3.2 The Mean Flow Consistent With Homogeneity 24
2.3.3 Homogeneous RST Equations. Briefs About Closure Methods 26
2.4 Anisotropy in Physical Space. Single-Point and Two-Point
Correlations 27
2.5 Spectral Analysis, From Random Fields to Two-Point
Correlations. Local Frame, Helical Modes 28
2.5.1 Second-Order Statistics 28
2.5.2 Poloidal-Toroidal Decomposition and Craya-Herring
Frame of Reference 31
2.5.3 Helical-Mode Decomposition 32
2.5.4 Use of Projection Operators 33
2.5.5 Nonlinear Dynamics 35
2.5.6 Background Nonlinearity in Different Reference
Frames 36
VII
viii Contents
2.6 Anisotropy in Fourier Space 38
2.6.1 Second-Order Velocity Statistics 38
2.6.2 Some Comments About Higher-Order Statistics 43
2.7 A Synthetic Scheme of the Closure Problem: Nonlinearity and
Nonlocality 43
Bibliography..................................47
3 Incompressible Homogeneous Isotropie Turbulence........... 49
3.1 Observations and Measures in Forced and Freely Decaying
Turbulence 49
3.1.1 How to Generate Isotropie Turbulence? 49
3.1.2 Main Observed Statistical Features of Developed
Isotropie Turbulence 51
3.1.3 Energy Decay Regimes 57
3.1.4 Coherent Structures in Isotropie Turbulence 58
3.2 Self-Similar Decay Regimes, Symmetries, and Invariants 59
3.2.1 Symmetries of Navier-Stokes Equations and Existence
of Self-Similar Solutions 59
3.2.2 Algebraic Decay Exponents Deduced From Symmetry
Analysis 62
3.2.3 Time-Variation Exponent and Inviscid Global
Invariants 64
3.2.4 Refined Analysis Without PLE Hypothesis 65
3.2.5 Self-Similarity Breakdown 66
3.2.6 Self-Similar Decay in the Final Region 67
3.3 Reynolds Stress Tensor and Analysis of Related Equations 68
3.4 Classical Statistical Analysis: Energy Cascade, Local Isotropy,
Usual Characteristic Scales 70
3.4.1 Double Correlations and Typical Scales 70
3.4.2 (Very Brief) Reminder About Kolmogorov Legacy,
Structure Functions, Modern Scaling Approach 71
3.4.3 Turbulent Kinetic-Energy Cascade in Fourier Space 73
3.5 Advanced Analysis of Energy Transfers in Fourier Space 76
3.5.1 The Background Triadic Interaction 76
3.5.2 Nonlinear Energy Transfers and Triple Correlations 79
3.5.3 Global and Detailed Conservation Properties 80
3.5.4 Advanced Analysis of Triadic Transfers and Waleffe s
Instability Assumption 81
3.5.5 Further Discussions About the Instability Assumption 85
3.5.6 Principle of Quasi-Normal Closures 86
3.5.7 EDQNM for Isotropie Turbulence. Final Equations
and Results 89
3.6 Topological Analysis, Coherent Events, and Related
Dynamics 97
Contents ¡x
3.6.1 Topological Analysis of Isotropie Turbulence 98
3.6.2 Vortex Tube: Statistical Properties and Dynamics 102
3.6.3 Bridging with Turbulence Dynamics and Intermittency 107
3.7 Nonlinear Dynamics in the Physical Space 109
3.7.1 On Vortices, Scales, Wavenumbers, and Wave
Vectors - What are the Small Scales? 109
3.7.2 Is There an Energy Cascade in the Physical Space? Ill
3.7.3 Self-Amplification of Velocity Gradients 112
3.7.4 Non-Gaussianity and Depletion of Nonlinearity 116
3.8 What are the Proper Features of Three-Dimensional
Navier-Stokes Turbulence? 117
3.8.1 Influence of the Space Dimension: Introduction to
¿/-Dimensional Turbulence 117
3.8.2 Pure 2D Turbulence and Dual Cascade 118
3.8.3 Role of Pressure: A View of Burgers Turbulence 120
3.8.4 Sensitivity with Respect to Energy-Pumping Process:
Turbulence with Hyperviscosity 122
Bibliography.................................123
4 Incompressible Homogeneous Anisotropie Turbulence:
Pure Rotation.................................127
4.1 Physical and Numerical Experiments 127
4.1.1 Brief Review of Experiments, More or Less in the
Configuration of Homogeneous Turbulence 129
4.2 Governing Equations 131
4.2.1 Generals 131
4.2.2 Important Nondimensional Numbers. Particular Regimes 131
4.3 Advanced Analysis of Energy Transfer by DNS 133
4.4 Balance of RST Equations. A Case Without Production.
New Tensorial Modeling 135
4.5 Inertial Waves. Linear Regime 139
4.5.1 Analysis of Deterministic Solutions 139
4.5.2 Analysis of Statistical Moments. Phase Mixing and
Low-Dimensional Manifolds 143
4.6 Nonlinear Theory and Modeling: Wave Turbulence and
EDQNM 145
4.6.1 Full Exact Nonlinear Equations. Wave Turbulence 145
4.6.2 Second-Order Statistics: Identification of Relevant
Spectral-Transfer Terms 148
4.6.3 Toward a Rational Closure with an EDQNM Model 149
4.6.4 Recovering the Asymptotic Theory of Inertial Wave
Turbulence 150
4.7 Fundamental Issues: Solved and Open Questions 153
4.7.1 Eventual Two-Dimensionalization or Not 153
Contents
4.7.2 Meaning of the Slow Manifold 155
4.7.3 Are Present DNS and LES Useful for Theoretical
Prediction? 156
4.7.4 Is the Pure Linear Theory Relevant? 157
4.7.5 Provisional Conclusions About Scaling Laws and
Quantified Values of Key Descriptors 158
4.8 Coherent Structures, Description, and Dynamics 159
Bibliography.................................164
5 Incompressible Homogeneous Anisotropie Turbulence: Strain .... 167
5.1 Main Observations 167
5.2 Experiments for Turbulence in the Presence of Mean Strain.
Kinematics of the Mean Flow 169
5.2.1 Pure Irrotational Strain, Planar Distortion 170
5.2.2 Axisymmetric (Irrotational) Strain 172
5.2.3 The Most General Case for 3D Irrotational Case 173
5.2.4 More General Distortions. Kinematics of Rotational
Mean Flows 173
5.3 First Approach in Physical Space to Irrotational Mean Flows 174
5.3.1 Governing Equations, RST Balance, and Single-Point
Modeling 174
5.3.2 General Assessment of RST Single-Point Closures 177
5.3.3 Linear Response of Turbulence to Irrotational Mean
Strain 178
5.4 The Fundamentals of Homogeneous RDT 180
5.4.1 Qualitative Trends Induced by the Green s Function 183
5.4.2 Results at Very Short Times. Relevance at Large
Elapsed Times 183
5.5 Final RDT Results for Mean Irrotational Strain 184
5.5.1 General RDT Solution 184
5.5.2 Linear Response of Turbulence to Axisymmetric
Strain 185
5.6 First Step Toward a Nonlinear Approach 186
5.7 Nonhomogeneous Flow Cases. Coherent Structures in
Strained Homogeneous Turbulence 187
Bibliography.................................189
6 Incompressible Homogeneous Anisotropie Turbulence:
Pure Shear...................................192
6.1 Physical and Numerical Experiments: Kinetic Energy, RST,
Length Scales, Anisotropy 192
6.1.1 Experimental and Numerical Realizations 193
6.1.2 Main Observations 193
Contents xi
6.2 Reynolds Stress Tensor and Analysis of Related Equations 197
6.3 Rapid Distortion Theory: Equations, Solutions, Algebraic
Growth 199
6.3.1 Some Properties of RDT Solutions 201
6.3.2 Relevance of Homogeneous RDT 204
6.4 Evidence and Uncertainties for Nonlinear Evolution:
Kinetic-Energy Exponential Growth Using Spectral Theory 206
6.5 Vortical-Structure Dynamics in Homogeneous Shear Turbulence 207
6.6 Self-Sustaining Turbulent Cycle in Homogeneous Sheared
Turbulence 209
6.7 Self-Sustaining Processes in Nonhomogeneous Sheared
Turbulence: Exact Coherent States and Traveling-Wave
Solutions 210
6.8 Local Isotropy in Homogeneous Shear Flows 214
Bibliography.................................217
7 Incompressible Homogeneous Anisotropie Turbulence:
Buoyancy and Stable Stratification.....................219
7.1 Observations, Propagating and Nonpropagating Motion.
Collapse of Vertical Motion and Layering 219
7.2 Simplified Equations, Using Navier-Stokes and Boussinesq
Approximations, With Uniform Density Gradient 223
7.2.1 Reynolds Stress Equations With Additional Scalar
Variance and Flux 224
7.2.2 First Look at Gravity Waves 225
7.3 Eigenmode Decomposition. Physical Interpretation 226
7.4 The Toroidal Cascade as a Strong Nonlinear Mechanism
Explaining the Layering 229
7.5 The Viewpoint of Modeling and Theory: RDT, Wave
Turbulence, EDQNM 231
7.6 Coherent Structures: Dynamics and Scaling of the Layered
Flow, Pancake Dynamics, Instabilities 235
7.6.1 Simplified Scaling Laws 235
7.6.2 Pancake Structures, Zig-Zag, and Kelvin-Helmholtz
Instabilities 237
Bibliography.................................241
8 Coupled Effects: Rotation, Stratification, Strain, and Shear.......243
8.1 Rotating Stratified Turbulence 243
8.1.1 Basic Triadic Interaction for Quasi-Geostrophic
Cascade 246
8.1.2 About the Case With Small but Nonnegligible f/N
Ratio 247
xii Contents
8.1.3 The QG Model Revisited. Discussion 248
8.2 Rotation or Stratification With Mean Shear 250
8.2.1 The Rotating-Shear-Flow Case 253
8.2.2 The Stratified-Shear-Flow Case 255
8.2.3 Analogies and Differences Between the Two
Cases 255
8.3 Shear, Rotation, and Stratification. RDT Approach to
Baroclinic Instability 256
8.3.1 Physical Context, the Mean Flow 256
8.3.2 RDT Equations 258
8.4 Elliptical Flow Instability From Homogeneous RDT 259
8.5 Axisymmetric Strain With Rotation 265
8.6 Relevance of RDT and WKB RDT Variants for Analysis of
Classical Instabilities 266
Bibliography.................................270
9 Compressible Homogeneous Isotropie Turbulence............273
9.1 Introduction to Modal Decomposition of Turbulent
Fluctuations 273
9.1.1 Statement of the Problem 273
9.1.2 Kovasznay s Linear Decomposition 274
9.1.3 Weakly Nonlinear Corrected Kovasznay
Decomposition 278
9.1.4 Helmholtz Decomposition and Its Extension 279
9.1.5 Bridging Between Kovasznay and Helmholtz
Decomposition 281
9.1.6 On the Feasibility of a Fully General Modal
Decomposition 281
9.2 Mean-Flow Equations, Reynolds Stress Tensor, and Energy
Balance in Compressible Flows 281
9.2.1 Arbitrary Flows 281
9.2.2 Simplifications in the Isotropie Case 285
9.2.3 Quasi-Isentropic Isotropie Turbulence: Physical and
Spectral Descriptions 288
9.3 Different Regimes in Compressible Turbulence 291
9.3.1 Quasi-Isentropic Turbulent Regime 292
9.3.2 Weakly Compressible Thermal Regime 309
9.3.3 Nonlinear Subsonic Regime 315
9.3.4 Supersonic Regime 318
9.4 Structures in the Physical Space 319
9.4.1 Turbulent Structures in Compressible Turbulence 320
9.4.2 A Probabilistic Model for Shocklets 321
Bibliography.................................324
Contents xiii
10 Compressible Homogeneous Anisotropie Turbulence..........327
10.1 Effects of Compressibility in Free-Shear Flows. Observations 327
10.1.1 RST Equations and Single-Point Modeling 328
10.1.2 Preliminary Linear Approach: Pressure-Released
Limit and Irrotational Strain 330
10.2 A General Quasi-Isentropic Approach to Homogeneous
Compressible Shear Flows 332
10.2.1 Governing Equations and Admissible Mean Flows 333
10.2.2 Properties of Admissible Mean Flows 335
10.2.3 Linear Response in Fourier Space. Governing
Equations 336
10.3 Incompressible Turbulence With Compressible Mean-Flow
Effects: Compressed Turbulence 342
10.4 Compressible Turbulence in the Presence of Pure Plane Shear 344
10.4.1 Qualitative Results 344
10.4.2 Discussion of Results 345
10.4.3 Toward a Complete Linear Solution 348
10.5 Perspectives and Open Issues 349
10.5.1 Homogeneous Shear Flows 350
10.5.2 Perspectives Toward Inhomogeneous Shear Flows 350
10.6 Topological Analysis, Coherent Events and Related Dynamics 351
10.6.1 Nonlinear Dynamics in the Subsonic Regime 352
10.6.2 Topological Analysis of the Rate-of-Strain Tensor 354
10.6.3 Vortices, Shocklets, and Dynamics 355
Bibliography.................................356
11 Isotropie Turbulence-Shock Interaction..................358
11.1 Brief Survey of Existing Interaction Regimes 358
11.1.1 Destructive Interactions 358
11.1.2 Nondestructive Interactions 359
11.2 Linear Nondestructive Interaction 360
11.2.1 Shock Modeling and Jump Relations 360
11.2.2 Introduction to the Linear Interaction Approximation
Theory 361
11.2.3 Vortical Turbulence-Shock Interaction 363
11.2.4 Acoustic Turbulence-Shock Interaction 370
11.2.5 Mixed Turbulence-Shock Interaction 373
11.2.6 On the Use of RDT for Linear Nondestructive
Interaction Modeling 378
11.3 Nonlinear Nondestructive Interactions 379
11.3.1 Turbulent Jump Conditions for the Mean Field 379
11.3.2 Jump Conditions for an Incident Isotropie Turbulence 381
Bibliography.................................382
xiv Contents
12 Linear Interaction Approximation for Shock-Perturbation
Interaction...................................384
12.1 Shock Description and Emitted Fluctuating Field 384
12.2 Calculation of Wave Vectors of Emitted Waves 386
12.2.1 General 386
12.2.2 Incident Entropy and Vorticity Waves 386
12.2.3 Incident Acoustic Waves 389
12.3 Calculation of Amplitude of Emitted Waves 391
12.3.1 General Decompositions of the Perturbation Field 391
12.3.2 Calculation of Amplitudes of Emitted Waves 393
12.4 Reconstruction of the Second-Order Moments 395
12.4.1 Case of a Single Incident Wave 395
12.4.2 Case of an Incident Turbulent Isotropie Field 399
12.5 A posteriori Assessment of LIA 403
Bibliography.................................405
13 Linear Theories. From Rapid Distortion Theory to WKB
Variants.....................................406
13.1 Rapid Distortion Theory for Homogeneous Turbulence 406
13.1.1 Solutions for ODEs in Orthonormal Fixed Frames of
Reference 406
13.1.2 Using Solenoidal Modes for a Green s Function with a
Minimal Number of Components 408
13.1.3 Prediction of Statistical Quantities 409
13.1.4 RDT for Two-Time Correlations 412
13.2 Zonal RDT and Short-Wave Stability Analysis 412
13.2.1 Irrotational Mean Flows 413
13.2.2 Zonal Stability Analysis With Disturbances Localized
Around Base-Flow Trajectories 413
13.2.3 Using Characteristic Rays Related to Waves Instead of
Trajectories 415
13.3 Application to Statistical Modeling of Inhomogeneous
Turbulence 417
13.3.1 Transport Models Along Mean Trajectories 417
13.3.2 Semiempirical Transport Shell Models 418
13.4 Conclusions, Recent Perspectives Including Subgrid-Scale
Dynamics Modeling 419
Bibliography.................................421
14 Anisotropie Nonlinear Triadic Closures..................423
14.1 Canonical HIT, Dependence on the Eddy Damping for the
Scaling of the Energy Spectrum in the Inertial Range 423
Contents xv
14.2 Solving the Linear Operator to Account for Strong
Anisotropy 425
14.2.1 Random and Averaged Nonlinear Green s Functions 425
14.2.2 Homogeneous Anisotropie Turbulence with a Mean
Flow 426
14.3 A General EDQN Closure. Different Levels of
Markovianization 428
14.3.1 EDQNM2 Version 429
14.3.2 A Simplified Version: EDQNM1 430
14.3.3 The Most Sophisticated Version: EDQNM3 431
14.4 Application of Three Versions to the Rotating Turbulence 433
14.5 Other Cases of Flows With and Without Production 437
14.5.1 Effects of the Distorting Mean Flow 437
14.5.2 Flows Without Production Combining Strong and
Weak Turbulence 438
14.5.3 Role of the Nonlinear Decorrelation Time Scale 440
14.6 Connection with Self-Consistent Theories: Single Time or
Two Time? 441
14.7 Applications to Weak Anisotropy 443
14.7.1 A Self-Consistent Representation of the Spectral
Tensor for Weak Anisotropy 443
14.7.2 Brief Discussion of Concepts, Results, and Open Issues 445
14.8 Open Numerical Problems 446
Bibliography.................................447
15 Conclusions and Perspectives........................449
15.1 Homogenization of Turbulence. Local or Global
Homogeneity? Physical Space or Fourier Space? 449
15.2 Linear Theory, Homogeneous RDT, WKB Variants, and
LIA 451
15.3 Multipoint Closures for Weak and Strong Turbulence 453
15.3.1 The Wave-Turbulence Limit 454
15.3.2 Coexistence of Weak and Strong Turbulence, With
Interactions 455
15.3.3 Revisiting Basic Assumptions in MPC 455
15.4 Structure Formation, Structuring Effects, and Individual
Coherent Structures 456
15.5 Anisotropy Including Dimensionality, a Main Theme 457
15.6 Deriving Practical Models 459
Bibliography.................................460
Index 461
|
| adam_txt |
Titel: Homogeneous turbulence dynamics
Autor: Sagaut, Pierre
Jahr: 2008
Contents
Abbreviations Used in This Book page xvi
1 Introduction. 1
1.1 Scope of the Book 1
1.2 Structure and Contents of the Book 3
Bibliography. 9
2 Statistical Analysis of Homogeneous Turbulent Flows: Reminders . 10
2.1 Background Deterministic Equations 10
2.1.1 Mass Conservation 10
2.1.2 The Navier-Stokes Momentum Equations 12
2.1.3 Incompressible Turbulence 13
2.1.4 First Insight into Compressibility Effects 14
2.1.5 Reminder About Circulation and Vorticity 15
2.1.6 Adding Body Forces or Mean Gradients 16
2.2 Briefs About Statistical and Probabilistic Approaches 19
2.2.1 Ensemble Averaging, Statistical Homogeneity 19
2.2.2 Single-Point and Multipoint Moments 19
2.2.3 Statistics for Velocity Increments 20
2.2.4 Application of Reynolds Decomposition to Dynamical
Equations 20
2.3 Reynolds Stress Tensor and Related Equations 22
2.3.1 RST Equations 22
2.3.2 The Mean Flow Consistent With Homogeneity 24
2.3.3 Homogeneous RST Equations. Briefs About Closure Methods 26
2.4 Anisotropy in Physical Space. Single-Point and Two-Point
Correlations 27
2.5 Spectral Analysis, From Random Fields to Two-Point
Correlations. Local Frame, Helical Modes 28
2.5.1 Second-Order Statistics 28
2.5.2 Poloidal-Toroidal Decomposition and Craya-Herring
Frame of Reference 31
2.5.3 Helical-Mode Decomposition 32
2.5.4 Use of Projection Operators 33
2.5.5 Nonlinear Dynamics 35
2.5.6 Background Nonlinearity in Different Reference
Frames 36
VII
viii Contents
2.6 Anisotropy in Fourier Space 38
2.6.1 Second-Order Velocity Statistics 38
2.6.2 Some Comments About Higher-Order Statistics 43
2.7 A Synthetic Scheme of the Closure Problem: Nonlinearity and
Nonlocality 43
Bibliography.47
3 Incompressible Homogeneous Isotropie Turbulence. 49
3.1 Observations and Measures in Forced and Freely Decaying
Turbulence 49
3.1.1 How to Generate Isotropie Turbulence? 49
3.1.2 Main Observed Statistical Features of Developed
Isotropie Turbulence 51
3.1.3 Energy Decay Regimes 57
3.1.4 Coherent Structures in Isotropie Turbulence 58
3.2 Self-Similar Decay Regimes, Symmetries, and Invariants 59
3.2.1 Symmetries of Navier-Stokes Equations and Existence
of Self-Similar Solutions 59
3.2.2 Algebraic Decay Exponents Deduced From Symmetry
Analysis 62
3.2.3 Time-Variation Exponent and Inviscid Global
Invariants 64
3.2.4 Refined Analysis Without PLE Hypothesis 65
3.2.5 Self-Similarity Breakdown 66
3.2.6 Self-Similar Decay in the Final Region 67
3.3 Reynolds Stress Tensor and Analysis of Related Equations 68
3.4 Classical Statistical Analysis: Energy Cascade, Local Isotropy,
Usual Characteristic Scales 70
3.4.1 Double Correlations and Typical Scales 70
3.4.2 (Very Brief) Reminder About Kolmogorov Legacy,
Structure Functions, "Modern" Scaling Approach 71
3.4.3 Turbulent Kinetic-Energy Cascade in Fourier Space 73
3.5 Advanced Analysis of Energy Transfers in Fourier Space 76
3.5.1 The Background Triadic Interaction 76
3.5.2 Nonlinear Energy Transfers and Triple Correlations 79
3.5.3 Global and Detailed Conservation Properties 80
3.5.4 Advanced Analysis of Triadic Transfers and Waleffe's
Instability Assumption 81
3.5.5 Further Discussions About the Instability Assumption 85
3.5.6 Principle of Quasi-Normal Closures 86
3.5.7 EDQNM for Isotropie Turbulence. Final Equations
and Results 89
3.6 Topological Analysis, Coherent Events, and Related
Dynamics 97
Contents ¡x
3.6.1 Topological Analysis of Isotropie Turbulence 98
3.6.2 Vortex Tube: Statistical Properties and Dynamics 102
3.6.3 Bridging with Turbulence Dynamics and Intermittency 107
3.7 Nonlinear Dynamics in the Physical Space 109
3.7.1 On Vortices, Scales, Wavenumbers, and Wave
Vectors - What are the Small Scales? 109
3.7.2 Is There an Energy Cascade in the Physical Space? Ill
3.7.3 Self-Amplification of Velocity Gradients 112
3.7.4 Non-Gaussianity and Depletion of Nonlinearity 116
3.8 What are the Proper Features of Three-Dimensional
Navier-Stokes Turbulence? 117
3.8.1 Influence of the Space Dimension: Introduction to
¿/-Dimensional Turbulence 117
3.8.2 Pure 2D Turbulence and Dual Cascade 118
3.8.3 Role of Pressure: A View of Burgers' Turbulence 120
3.8.4 Sensitivity with Respect to Energy-Pumping Process:
Turbulence with Hyperviscosity 122
Bibliography.123
4 Incompressible Homogeneous Anisotropie Turbulence:
Pure Rotation.127
4.1 Physical and Numerical Experiments 127
4.1.1 Brief Review of Experiments, More or Less in the
Configuration of Homogeneous Turbulence 129
4.2 Governing Equations 131
4.2.1 Generals 131
4.2.2 Important Nondimensional Numbers. Particular Regimes 131
4.3 Advanced Analysis of Energy Transfer by DNS 133
4.4 Balance of RST Equations. A Case Without "Production."
New Tensorial Modeling 135
4.5 Inertial Waves. Linear Regime 139
4.5.1 Analysis of Deterministic Solutions 139
4.5.2 Analysis of Statistical Moments. Phase Mixing and
Low-Dimensional Manifolds 143
4.6 Nonlinear Theory and Modeling: Wave Turbulence and
EDQNM 145
4.6.1 Full Exact Nonlinear Equations. Wave Turbulence 145
4.6.2 Second-Order Statistics: Identification of Relevant
Spectral-Transfer Terms 148
4.6.3 Toward a Rational Closure with an EDQNM Model 149
4.6.4 Recovering the Asymptotic Theory of Inertial Wave
Turbulence 150
4.7 Fundamental Issues: Solved and Open Questions 153
4.7.1 Eventual Two-Dimensionalization or Not 153
Contents
4.7.2 Meaning of the Slow Manifold 155
4.7.3 Are Present DNS and LES Useful for Theoretical
Prediction? 156
4.7.4 Is the Pure Linear Theory Relevant? 157
4.7.5 Provisional Conclusions About Scaling Laws and
Quantified Values of Key Descriptors 158
4.8 Coherent Structures, Description, and Dynamics 159
Bibliography.164
5 Incompressible Homogeneous Anisotropie Turbulence: Strain . 167
5.1 Main Observations 167
5.2 Experiments for Turbulence in the Presence of Mean Strain.
Kinematics of the Mean Flow 169
5.2.1 Pure Irrotational Strain, Planar Distortion 170
5.2.2 Axisymmetric (Irrotational) Strain 172
5.2.3 The Most General Case for 3D Irrotational Case 173
5.2.4 More General Distortions. Kinematics of Rotational
Mean Flows 173
5.3 First Approach in Physical Space to Irrotational Mean Flows 174
5.3.1 Governing Equations, RST Balance, and Single-Point
Modeling 174
5.3.2 General Assessment of RST Single-Point Closures 177
5.3.3 Linear Response of Turbulence to Irrotational Mean
Strain 178
5.4 The Fundamentals of Homogeneous RDT 180
5.4.1 Qualitative Trends Induced by the Green's Function 183
5.4.2 Results at Very Short Times. Relevance at Large
Elapsed Times 183
5.5 Final RDT Results for Mean Irrotational Strain 184
5.5.1 General RDT Solution 184
5.5.2 Linear Response of Turbulence to Axisymmetric
Strain 185
5.6 First Step Toward a Nonlinear Approach 186
5.7 Nonhomogeneous Flow Cases. Coherent Structures in
Strained Homogeneous Turbulence 187
Bibliography.189
6 Incompressible Homogeneous Anisotropie Turbulence:
Pure Shear.192
6.1 Physical and Numerical Experiments: Kinetic Energy, RST,
Length Scales, Anisotropy 192
6.1.1 Experimental and Numerical Realizations 193
6.1.2 Main Observations 193
Contents xi
6.2 Reynolds Stress Tensor and Analysis of Related Equations 197
6.3 Rapid Distortion Theory: Equations, Solutions, Algebraic
Growth 199
6.3.1 Some Properties of RDT Solutions 201
6.3.2 Relevance of Homogeneous RDT 204
6.4 Evidence and Uncertainties for Nonlinear Evolution:
Kinetic-Energy Exponential Growth Using Spectral Theory 206
6.5 Vortical-Structure Dynamics in Homogeneous Shear Turbulence 207
6.6 Self-Sustaining Turbulent Cycle in Homogeneous Sheared
Turbulence 209
6.7 Self-Sustaining Processes in Nonhomogeneous Sheared
Turbulence: Exact Coherent States and Traveling-Wave
Solutions 210
6.8 Local Isotropy in Homogeneous Shear Flows 214
Bibliography.217
7 Incompressible Homogeneous Anisotropie Turbulence:
Buoyancy and Stable Stratification.219
7.1 Observations, Propagating and Nonpropagating Motion.
Collapse of Vertical Motion and Layering 219
7.2 Simplified Equations, Using Navier-Stokes and Boussinesq
Approximations, With Uniform Density Gradient 223
7.2.1 Reynolds Stress Equations With Additional Scalar
Variance and Flux 224
7.2.2 First Look at Gravity Waves 225
7.3 Eigenmode Decomposition. Physical Interpretation 226
7.4 The Toroidal Cascade as a Strong Nonlinear Mechanism
Explaining the Layering 229
7.5 The Viewpoint of Modeling and Theory: RDT, Wave
Turbulence, EDQNM 231
7.6 Coherent Structures: Dynamics and Scaling of the Layered
Flow, "Pancake" Dynamics, Instabilities 235
7.6.1 Simplified Scaling Laws 235
7.6.2 Pancake Structures, Zig-Zag, and Kelvin-Helmholtz
Instabilities 237
Bibliography.241
8 Coupled Effects: Rotation, Stratification, Strain, and Shear.243
8.1 Rotating Stratified Turbulence 243
8.1.1 Basic Triadic Interaction for Quasi-Geostrophic
Cascade 246
8.1.2 About the Case With Small but Nonnegligible f/N
Ratio 247
xii Contents
8.1.3 The QG Model Revisited. Discussion 248
8.2 Rotation or Stratification With Mean Shear 250
8.2.1 The Rotating-Shear-Flow Case 253
8.2.2 The Stratified-Shear-Flow Case 255
8.2.3 Analogies and Differences Between the Two
Cases 255
8.3 Shear, Rotation, and Stratification. RDT Approach to
Baroclinic Instability 256
8.3.1 Physical Context, the Mean Flow 256
8.3.2 RDT Equations 258
8.4 Elliptical Flow Instability From "Homogeneous" RDT 259
8.5 Axisymmetric Strain With Rotation 265
8.6 Relevance of RDT and WKB RDT Variants for Analysis of
Classical Instabilities 266
Bibliography.270
9 Compressible Homogeneous Isotropie Turbulence.273
9.1 Introduction to Modal Decomposition of Turbulent
Fluctuations 273
9.1.1 Statement of the Problem 273
9.1.2 Kovasznay's Linear Decomposition 274
9.1.3 Weakly Nonlinear Corrected Kovasznay
Decomposition 278
9.1.4 Helmholtz Decomposition and Its Extension 279
9.1.5 Bridging Between Kovasznay and Helmholtz
Decomposition 281
9.1.6 On the Feasibility of a Fully General Modal
Decomposition 281
9.2 Mean-Flow Equations, Reynolds Stress Tensor, and Energy
Balance in Compressible Flows 281
9.2.1 Arbitrary Flows 281
9.2.2 Simplifications in the Isotropie Case 285
9.2.3 Quasi-Isentropic Isotropie Turbulence: Physical and
Spectral Descriptions 288
9.3 Different Regimes in Compressible Turbulence 291
9.3.1 Quasi-Isentropic Turbulent Regime 292
9.3.2 Weakly Compressible Thermal Regime 309
9.3.3 Nonlinear Subsonic Regime 315
9.3.4 Supersonic Regime 318
9.4 Structures in the Physical Space 319
9.4.1 Turbulent Structures in Compressible Turbulence 320
9.4.2 A Probabilistic Model for Shocklets 321
Bibliography.324
Contents xiii
10 Compressible Homogeneous Anisotropie Turbulence.327
10.1 Effects of Compressibility in Free-Shear Flows. Observations 327
10.1.1 RST Equations and Single-Point Modeling 328
10.1.2 Preliminary Linear Approach: Pressure-Released
Limit and Irrotational Strain 330
10.2 A General Quasi-Isentropic Approach to Homogeneous
Compressible Shear Flows 332
10.2.1 Governing Equations and Admissible Mean Flows 333
10.2.2 Properties of Admissible Mean Flows 335
10.2.3 Linear Response in Fourier Space. Governing
Equations 336
10.3 Incompressible Turbulence With Compressible Mean-Flow
Effects: Compressed Turbulence 342
10.4 Compressible Turbulence in the Presence of Pure Plane Shear 344
10.4.1 Qualitative Results 344
10.4.2 Discussion of Results 345
10.4.3 Toward a Complete Linear Solution 348
10.5 Perspectives and Open Issues 349
10.5.1 Homogeneous Shear Flows 350
10.5.2 Perspectives Toward Inhomogeneous Shear Flows 350
10.6 Topological Analysis, Coherent Events and Related Dynamics 351
10.6.1 Nonlinear Dynamics in the Subsonic Regime 352
10.6.2 Topological Analysis of the Rate-of-Strain Tensor 354
10.6.3 Vortices, Shocklets, and Dynamics 355
Bibliography.356
11 Isotropie Turbulence-Shock Interaction.358
11.1 Brief Survey of Existing Interaction Regimes 358
11.1.1 Destructive Interactions 358
11.1.2 Nondestructive Interactions 359
11.2 Linear Nondestructive Interaction 360
11.2.1 Shock Modeling and Jump Relations 360
11.2.2 Introduction to the Linear Interaction Approximation
Theory 361
11.2.3 Vortical Turbulence-Shock Interaction 363
11.2.4 Acoustic Turbulence-Shock Interaction 370
11.2.5 Mixed Turbulence-Shock Interaction 373
11.2.6 On the Use of RDT for Linear Nondestructive
Interaction Modeling 378
11.3 Nonlinear Nondestructive Interactions 379
11.3.1 Turbulent Jump Conditions for the Mean Field 379
11.3.2 Jump Conditions for an Incident Isotropie Turbulence 381
Bibliography.382
xiv Contents
12 Linear Interaction Approximation for Shock-Perturbation
Interaction.384
12.1 Shock Description and Emitted Fluctuating Field 384
12.2 Calculation of Wave Vectors of Emitted Waves 386
12.2.1 General 386
12.2.2 Incident Entropy and Vorticity Waves 386
12.2.3 Incident Acoustic Waves 389
12.3 Calculation of Amplitude of Emitted Waves 391
12.3.1 General Decompositions of the Perturbation Field 391
12.3.2 Calculation of Amplitudes of Emitted Waves 393
12.4 Reconstruction of the Second-Order Moments 395
12.4.1 Case of a Single Incident Wave 395
12.4.2 Case of an Incident Turbulent Isotropie Field 399
12.5 A posteriori Assessment of LIA 403
Bibliography.405
13 Linear Theories. From Rapid Distortion Theory to WKB
Variants.406
13.1 Rapid Distortion Theory for Homogeneous Turbulence 406
13.1.1 Solutions for ODEs in Orthonormal Fixed Frames of
Reference 406
13.1.2 Using Solenoidal Modes for a Green's Function with a
Minimal Number of Components 408
13.1.3 Prediction of Statistical Quantities 409
13.1.4 RDT for Two-Time Correlations 412
13.2 Zonal RDT and Short-Wave Stability Analysis 412
13.2.1 Irrotational Mean Flows 413
13.2.2 Zonal Stability Analysis With Disturbances Localized
Around Base-Flow Trajectories 413
13.2.3 Using Characteristic Rays Related to Waves Instead of
Trajectories 415
13.3 Application to Statistical Modeling of Inhomogeneous
Turbulence 417
13.3.1 Transport Models Along Mean Trajectories 417
13.3.2 Semiempirical Transport "Shell" Models 418
13.4 Conclusions, Recent Perspectives Including Subgrid-Scale
Dynamics Modeling 419
Bibliography.421
14 Anisotropie Nonlinear Triadic Closures.423
14.1 Canonical HIT, Dependence on the Eddy Damping for the
Scaling of the Energy Spectrum in the Inertial Range 423
Contents xv
14.2 Solving the Linear Operator to Account for Strong
Anisotropy 425
14.2.1 Random and Averaged Nonlinear Green's Functions 425
14.2.2 Homogeneous Anisotropie Turbulence with a Mean
Flow 426
14.3 A General EDQN Closure. Different Levels of
Markovianization 428
14.3.1 EDQNM2 Version 429
14.3.2 A Simplified Version: EDQNM1 430
14.3.3 The Most Sophisticated Version: EDQNM3 431
14.4 Application of Three Versions to the Rotating Turbulence 433
14.5 Other Cases of Flows With and Without Production 437
14.5.1 Effects of the Distorting Mean Flow 437
14.5.2 Flows Without Production Combining Strong and
Weak Turbulence 438
14.5.3 Role of the Nonlinear Decorrelation Time Scale 440
14.6 Connection with Self-Consistent Theories: Single Time or
Two Time? 441
14.7 Applications to Weak Anisotropy 443
14.7.1 A Self-Consistent Representation of the Spectral
Tensor for Weak Anisotropy 443
14.7.2 Brief Discussion of Concepts, Results, and Open Issues 445
14.8 Open Numerical Problems 446
Bibliography.447
15 Conclusions and Perspectives.449
15.1 Homogenization of Turbulence. Local or Global
Homogeneity? Physical Space or Fourier Space? 449
15.2 Linear Theory, "Homogeneous" RDT, WKB Variants, and
LIA 451
15.3 Multipoint Closures for Weak and Strong Turbulence 453
15.3.1 The Wave-Turbulence Limit 454
15.3.2 Coexistence of Weak and Strong Turbulence, With
Interactions 455
15.3.3 Revisiting Basic Assumptions in MPC 455
15.4 Structure Formation, Structuring Effects, and Individual
Coherent Structures 456
15.5 Anisotropy Including Dimensionality, a Main Theme 457
15.6 Deriving Practical Models 459
Bibliography.460
Index 461 |
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| any_adam_object_boolean | 1 |
| author | Sagaut, Pierre 1967- Cambon, Claude |
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| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.1/064 |
| dewey-search | 620.1/064 |
| dewey-sort | 3620.1 264 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | 1. publ. |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:29:47Z |
| indexdate | 2024-07-09T21:18:11Z |
| institution | BVB |
| isbn | 9780521855488 |
| language | English |
| lccn | 2008008774 |
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| spelling | Sagaut, Pierre 1967- Verfasser (DE-588)1049515781 aut Homogeneous turbulence dynamics Pierre Sagaut ; Claude Cambon 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2008 463 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Anisotropie Isotropie Turbulence - Modèles mathématiques Mathematisches Modell Turbulence Mathematical models Anisotropy Mathematical models Shear waves Mathematical models Anisotropie (DE-588)4002073-3 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Scherwelle (DE-588)4179501-5 gnd rswk-swf Turbulente Strömung (DE-588)4117265-6 gnd rswk-swf Turbulente Strömung (DE-588)4117265-6 s Anisotropie (DE-588)4002073-3 s Scherwelle (DE-588)4179501-5 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Cambon, Claude Verfasser (DE-588)1156278538 aut http://www.loc.gov/catdir/enhancements/fy0810/2008008774-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0810/2008008774-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0810/2008008774-t.html Table of contents only HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016599826&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sagaut, Pierre 1967- Cambon, Claude Homogeneous turbulence dynamics Anisotropie Isotropie Turbulence - Modèles mathématiques Mathematisches Modell Turbulence Mathematical models Anisotropy Mathematical models Shear waves Mathematical models Anisotropie (DE-588)4002073-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd Scherwelle (DE-588)4179501-5 gnd Turbulente Strömung (DE-588)4117265-6 gnd |
| subject_GND | (DE-588)4002073-3 (DE-588)4114528-8 (DE-588)4179501-5 (DE-588)4117265-6 |
| title | Homogeneous turbulence dynamics |
| title_auth | Homogeneous turbulence dynamics |
| title_exact_search | Homogeneous turbulence dynamics |
| title_exact_search_txtP | Homogeneous turbulence dynamics |
| title_full | Homogeneous turbulence dynamics Pierre Sagaut ; Claude Cambon |
| title_fullStr | Homogeneous turbulence dynamics Pierre Sagaut ; Claude Cambon |
| title_full_unstemmed | Homogeneous turbulence dynamics Pierre Sagaut ; Claude Cambon |
| title_short | Homogeneous turbulence dynamics |
| title_sort | homogeneous turbulence dynamics |
| topic | Anisotropie Isotropie Turbulence - Modèles mathématiques Mathematisches Modell Turbulence Mathematical models Anisotropy Mathematical models Shear waves Mathematical models Anisotropie (DE-588)4002073-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd Scherwelle (DE-588)4179501-5 gnd Turbulente Strömung (DE-588)4117265-6 gnd |
| topic_facet | Anisotropie Isotropie Turbulence - Modèles mathématiques Mathematisches Modell Turbulence Mathematical models Anisotropy Mathematical models Shear waves Mathematical models Scherwelle Turbulente Strömung |
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