دانلود کتاب Nonlinear, nonlocal and fractional turbulence

فهرست مطالب :

Preface......Page 5
References......Page 15
Contents......Page 16
Roman Symbols......Page 20
Greek Symbols......Page 31
Special Symbols......Page 36
1.1 Aims and Scopes of This Book......Page 37
1.2 A Brief Tour d´Horizon Through Today´s Turbulence Field and Modeling......Page 39
References......Page 43
Chapter 2: Reynold´s Averaging of the Navier-Stokes Equations (RANS)......Page 49
References......Page 54
Chapter 3: The Closure Problem......Page 55
References......Page 58
Chapter 4: Boussinesq´s ``Constitutive Law´´......Page 60
References......Page 62
5.1 Shear Flows and the Works of Prandtl, Taylor, and Contemporaries......Page 63
5.2.1 Prandtl´s Mixing Length Model......Page 65
5.2.2 von Krmn´s Local Model......Page 68
5.2.3 Reichardt´s Inductive Model......Page 69
5.2.4 Prandtl´s Mean Gradient Model......Page 71
5.2.5 Prandtl´s Shear Layer Model......Page 72
5.2.6 Taylor´s Vorticity Transfer Model......Page 73
5.3 Overview of Deficiencies of Local Models......Page 76
5.4 More General Deficiencies and Fallacies......Page 78
5.5 Questioning the Logarithmic Law......Page 93
5.6 Logarithmic Versus (Deficit) Power Law......Page 98
References......Page 104
6.1 Nonlocality in Phase Space......Page 109
6.2 Atomic and Continuum Theories......Page 112
6.3 Stress as an Objective Polynomial Function of the Mean Rate of Strain Tensor......Page 114
6.4 Modified Diffusivity Models......Page 116
6.5 Truly History Dependent and Nonlocal Models......Page 122
References......Page 136
7.1 The Discovery and Prandtl´s Models......Page 140
7.2.1 Molecular Transport......Page 144
7.2.2 Transport by Eddies......Page 150
7.2.4.1 Introduction......Page 157
7.2.4.2 Lévy Walks on a One-Dimensional Lattice......Page 159
7.2.4.3 Lévy Walks, Lévy Flights, Lévy Pairs, and Eddies in Turbulence......Page 162
7.2.4.4 Eddy Class Statistics......Page 165
7.2.4.5 The Lifetime of Eddies......Page 167
7.2.4.6 The Eddy Diameters......Page 168
7.2.4.7 A Fractal Eddy Cascade Model......Page 170
7.2.4.8 The Occupation Number......Page 173
7.2.4.9 The Occupation Probability......Page 175
7.2.4.10 The Momenta of Eddies......Page 177
7.2.4.11 The Number of Eddy Classes......Page 178
7.2.4.12 Lévy Flight Statistics, β-Fractal Model, and the DQTM......Page 181
7.3.1 Introduction......Page 190
7.3.2 Liouville Fractional Derivative......Page 193
7.3.3 Overview of the Derivation of Important Nonlocal Turbulence Models......Page 194
7.3.4 Liouville-Prandtl Mixing Length Model......Page 195
7.3.6 The Liouville-Heaviside Turbulence Model......Page 197
7.3.7 The Difference-Quotient Turbulence Model......Page 198
7.3.8 Summary......Page 201
References......Page 203
Chapter 8: Self-Similar RANS......Page 206
Reference......Page 211
9.1 Plane Wake Flows......Page 212
9.2.1 Jet in a Quiescent Surrounding......Page 221
9.2.2 Jet in a Parallel Co-flow......Page 253
9.3 Plane Couette Flows......Page 258
9.4 Plane Poiseuille Flows......Page 280
9.5 ``Wall Turbulent´´ Flows......Page 304
References......Page 326
10.1.1 Microscopic and Macroscopic Theories......Page 330
10.1.3 Reduction of the Degrees of Freedom by Scaling......Page 331
10.1.4 Different Thermodynamic Concepts......Page 332
10.2 A Brief Review of Some Essentials of Boltzmann-Gibbs Thermodynamics......Page 334
10.3 Kraichnan´s BG Equilibrium Thermodynamics of 2-d and 3-d Turbulent Fields......Page 336
10.4 An Introduction to the Nonextensive Thermodynamics of Tsallis......Page 347
10.5 Relation Between Lévy Statistics and Tsallis Nonextensive Thermodynamics......Page 353
10.6 Escort Probability Distribution and Expectation Values......Page 357
10.7 Generalized Thermodynamic Potentials......Page 359
10.8 Fractional Calculus: A Promising Future-Oriented Method to Describe Turbulence......Page 360
10.9 Jackson´s Fractional Derivative and the DQTM......Page 362
10.10 Beck-Tsallis Thermodynamics of Turbulence......Page 364
10.11 Fractional Generalization of Kraichnan´s Energy-Enstrophy Spectrum and Its Validation by Numerical Experiments......Page 365
10.12 Velocity Structure Functions......Page 369
10.13 Justification of the Quadratic Form of the Energy as a Function of the Space Coordinates......Page 371
10.14 A Generalized Temperature of Turbulence......Page 375
10.15 Final Discussion on Nonextensive Thermodynamics of Turbulence......Page 380
References......Page 382
11.1 Introduction......Page 387
11.2.1 What Is a Critical or a Cooperative Phenomenon?......Page 390
11.2.2 Stress and Order Parameter......Page 392
11.2.3 Symmetry Breaking......Page 394
11.2.4 Response Functions and Critical Exponents......Page 396
11.2.5 Pair Correlation Function and Correlation Length......Page 400
11.2.6 Universality: Yes or No ?......Page 402
11.2.7 Turbulent Phase Transition with Its Two Phases......Page 404
11.3 Mean Field Theory of a Paramagnetic to Ferromagnetic Phase Transition......Page 406
11.4 Mean Field Theory of Turbulence......Page 411
11.5 First Experiments for a Qualitative Comparison......Page 418
11.6 Discussion of Results......Page 421
References......Page 423
Chapter 12: Conclusions and Outlook......Page 426
References......Page 431
Appendix A: Normalization of Probability Distribution......Page 433
Appendix B: The Variance of Lévy Flight Processes......Page 434
Appendix C: The Structure Function......Page 435
Appendix D: Circular Mean Velocity Profile of Plane Turbulent Poiseuille Flows......Page 436
Appendix E: Fourier Transformation for q-Generalized Energy Spectrum of Turbulent Flows......Page 443
References......Page 449
Author Index......Page 450
Subject Index......Page 456