Call number:
MOP 47507 / Mitte
Type of Medium:
Monograph available for loan
Pages:
XVIII, 501 Seiten
,
Illustrationen
Edition:
Second edition
ISBN:
3540966854
,
0387966854
Series Statement:
Universitext
Language:
English
Note:
CONTENTS
Preface
Preface to the Second Edition
Introduction
1 Onset of Turbulence
Part One - Classical Concepts in Turbulence Modeling
Chapter I. Turbulent Flow
1. Equations of Fluid Dynamics and Their Consequences
1.1 Reynolds' Averaging Technique
1.2 Equations of Fluid Dynamics
1.3 Equation of Kinetic Energy
1.4 Equation of Heat Conduction
2. Reynolds' Stresses
2.1 Physical and Geometrical Interpretation of Reynolds' Stresses
2.2 Eddies and Eddy Viscosity
2.3 Poiseuille and Couette Flow
3. Length Theory
3.1 Prandtl's Mixing Length Theory
3.2 Mixing Length in Taylor's Sense
3.3 Betz's Interpretation of von Karman's Similarity Hypothesis
4. Universal Velocity Distribution Law
4.1 Prandtl's Approach
4.2 von Karman's Approach
4.3 Turbulent Pipe Flow with Porous Wall
5. The Turbulent Boundary Layer
5.1 Turbulent Flow Over a Solid Surface
5.2 Law of the Wall in Turbulent Channel Flow
5.3 Velocity Distribution in Transient Region of a Moving Viscous Turbulent Flow
5.4 A New Approach to the Turbulent Boundary Layer Theory Using Lumley's Extremum Principle
Part Two - Statistical Theories in Turbulence
Chapter II. Fundamental Concepts
6. Stochastic Processes
6.1 General Remarks
6.2 Fundamental Concepts in Probability
6.3 Random Variables and Stochastic Processes
6.4 Weakly Stationary Processes
6.5 A Simple Formulation of the Covariance and Variance for Incompressible Flow
6.6 The Correlation and Spectral Tensors in Turbulence
6.7 Theory of Invariants
6.8 The Correlation of Derivatives of the Velocity Components
7. Propagation of Correlations in Isotropic Incompressible Turbulent Flow
7.1 Equations of Motion
7.2 Vorticity Correlation and Vorticity Spectrum
7.3 Energy Spectrum Function
7.4 Three-Dimensional Spectrum Function
Chapter III. Basic Theories
8. Kolmogoroff's Theories of Locally Isotropic Turbulence
8.1 Local Homogeneity and Local Isotropy
8.2 The First and the Second Moments of Quantities w-j(x-j)
8.3 Hypotheses of Similarity
8.4 Propagation of Correlations in Locally Isotropic Flow
8.5 Remarks Concerning Kolmogoroff1s Theory
9. Heisenberg's Theory of Turbulence
9.1 The Dynamical Equation for the Energy Spectrum
9.2 Heisenberg's Mechanism of Energy Transfer
9.3 von Weiszacker's Form of the Spectrum
9.4 Objections to Heisenberg's Theory
10. Kraichnan's Theory of Turbulence
10.1 Burgers' Equation in Frequency Space
10.2 The Impulse Response Function
10.3 The Direct Interaction Approximation
10.4 Third Order Moments
10.5 Determination of Green's Function
10.6 Summary of Results of Burgers' Equation in Kraichnan's Sense
11. Application of Kraichnan's Method to Turbulent Flow
11.1 Derivation of Navier-Stokes Equation in Fourier Space
11.2 Impulse Response, Function for Full Turbulent Representation
11.3 Formal Statement by Direct-Interaction Procedure
11.4 Application of the Direct-Interaction Approximation
11.5 Averaged Green's Function for the Navier-Stokes Equations
12. Hopf's Theory of Turbulence
12.1 Formulation of the Problem in Phase Space and the Characteristic Functional
12.2 The Functional Differential Equation for Phase Motion
12.3 Derivation of the ϕ-Equation
12.4 Elimination of Pressure Functional π from the ϕ-Equation
12.5 Forms of the Correlation for n=l and n=2
Chapter IV. Magnetohydrodynamic Turbulence
13. Magnetohydrodynamic Turbulence by Means of a Characteristic Functional
13.1 Formulation of the Problem in Phase Space
13.2 ϕ-Equations in Magnetohydrodynamic Turbulence
13.3 Correlation Equations
14. Wave-Number Space
14.1 Transformation to Wave-Number Space
14.2 The Spectrum Equations and Additional Conservation Laws
14.3 Special Case of Isotropic Magnetohydrodynamic Turbulence
15. Stationary Solution for ϕ-Equations
15.1 Stationary Solution for the Case λ=ν=0
15.2 Solution to the ϕ-Equations for Final Stages of Decay
16. Energy Spectrin
16.1 Energy Spectrum in the Equilibrium Range
16.2 Extension of Heisenberg's Theory in Magnetohydrodynamic Turbulence
17. Temperature Dispersion in Magnetohydrodynamic Turbulence
17.1 Turbulent Dispersion
17.2 Formulation of the Problem
17.3 Universal Equilibrium
18. Temperature Spectrum for Small and Large Joule Heat Eddies
18.1 Small Joule Heat Eddies
18.2 Large Joule Heat Eddies
19. The Temperature Spectrum for the Joule Heat Eddies of Various Sizes
19.1 The Viscous Dissipation Process
19.2 The Joule Heat Model
19.3 The Calculation of the Temperature Spectrum
19.4 Effect of Viscous Dissipation on the Temperature Distribution
20. Thomas' Numerical Experiments
20.1 Turbulent Dynamo Competing Processes
20.2 Nondissipative Model System λ=ν=0
20.3 Numerical Experiments
21. Some Further Improvements of Dispersion Theory in Magnetohydrodynamic Turbulence
21.1 Remarks on the Turbulent Dispersion of Temperature for Rm〉〉R〉〉l
21.2 Heat Equation for Conductive Cut-Off Wave Number for H(k)
21.3 Solution of the Heat Equation
22. A Solution for the Joule-Heat Source Term
22.1 Physical Introduciton
22.2 Form of the Source Function and Particular Solution
22.3 The Joule Heating Spectrum
22.4 The Range of Values α1, α2, α3, σ and Asymptotic Solution of τ-integral
22.5 Evolution of τ-Integral Eq. (22.29)
23. Results for the θ2 Spectrum with Joule Heating
23.1 The Asymptotic Behavior of the Solutions
23.2 The Most Probable Form of the θ2-Spectrum
Chapter V. Contemporary Turbulence
24. Recent Developments in Turbulence Through Use of Experimental Mathematics - Attractor Theory
24.1 Things That Change Suddenly
24.2 Order in the Chaos
24.3 Attractor Theory in Turbulent Channel Flows
25. Recent Developments in Experimental Turbulence
25.1 Coherent Structure of Turbulent Shear Flows
Appendices
Appendix A -- Derivation of Correlation Equations (13.51-13.62)
Appendix B -- Derivation of Spectrum Equations (14.45-14.46)
Appendix C -- Fourier Transforms (18.10)
Appendix D -- The Time Variation of Eq. (18.3)
Appendix E -- The Time Variation of Eq. (18.19)
Bibliography
Author Index
Subject Index
Location:
MOP - must be ordered
Branch Library:
GFZ Library