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Table of Contents
Intro; Foreword to Second Edition; Preface to Second Edition; Contents; Abstract; 1 Introduction; 1.1 Scope of the Book; 1.2 Structure and Contents of the Second Edition of the Book; References; 2 Governing Equations, from Dynamics to Statistics; 2.1 Background Deterministic Equations; 2.1.1 Mass Conservation; 2.1.2 The Momentum, Navier
Stokes, Equations; 2.1.3 Incompressible Turbulence; 2.1.4 First Insight into Compressibility Effects; 2.1.5 Splitting the Velocity Field: Helmholtz Decomposition, Poloidal-Toroidal Decomposition and Clebsh Potentials
2.1.6 Reminder About Circulation and Vorticity2.1.7 Evolution Equation for Velocity Gradient and Vorticity; 2.1.8 Biot
Savart Relationship and Non-local Closure of Vorticity Equation; 2.1.9 Adding Body Forces or Mean Gradients; 2.2 Briefs About Statistical and Probabilistic Approaches; 2.2.1 Ensemble Averaging; 2.2.2 Single-Point and Multi-point Moments; 2.2.3 Statistics for Velocity Increments; 2.2.4 Application of the Reynolds Decomposition to Dynamical Equations; 2.3 Reynolds Stress Tensor and Related Equations; 2.3.1 RST Equations
2.3.2 The Mean Flow Consistent with Homogeneity Restricted to Fluctuations2.3.3 Homogeneous RST Equations. Briefs About Closure Methods; 2.4 Anisotropy in Physical Space. Single-Point Correlations; 2.5 Spectral Analysis, from Random Fields to Two-Point …; 2.5.1 Second Order Statistics; 2.5.2 Poloidal-Toroidal Decomposition, and Craya
Herring Frame of Reference; 2.5.3 The Helical Mode Decomposition; 2.5.4 On the Use of Projection Operators; 2.5.5 Nonlinear Dynamics; 2.5.6 Background Nonlinearity in the Different Reference Frames
2.5.7 Inverting Linear Operators: Introduction to Green Functions2.6 Anisotropy for Multipoint Correlations; 2.6.1 Second Order Velocity Statistics; 2.6.2 Induced Anisotropic Structure of Arbitrary Second-Order Statistical Quantities; 2.6.3 Some Comments About Higher Order Statistics; 2.7 A Synthetic Scheme of the Closure Problem: Non-linearity
2.8 On the Use of Lagrangian Formalism; 2.8.1 From RDT to Visco-Elastic Mechanisms; 2.8.2 Lagrangian Stochastic Models; References; 3 Additional Reminders: Compressible Turbulence Description
3.1 Navier
Stokes Equations for Compressible Flows and Shock Jump Conditions3.1.1 Governing Conservation Equations; 3.1.2 Rankine
Hugoniot Jump Relations; 3.1.3 Linearization of Rankine-Hugoniot Jump Relations; 3.2 Introduction to Modal Decomposition of Turbulent Fluctuations; 3.2.1 Statement of the Problem; 3.2.2 Kovasznay's Linear Decomposition; 3.2.3 Weakly Nonlinear Corrected Kovasznay Decomposition; 3.2.4 Bridging Between Kovasznay and Helmholtz Decomposition; 3.2.5 Helmholtz-Decomposition-Based Kinematic Relations for Isotropic Turbulence
Stokes, Equations; 2.1.3 Incompressible Turbulence; 2.1.4 First Insight into Compressibility Effects; 2.1.5 Splitting the Velocity Field: Helmholtz Decomposition, Poloidal-Toroidal Decomposition and Clebsh Potentials
2.1.6 Reminder About Circulation and Vorticity2.1.7 Evolution Equation for Velocity Gradient and Vorticity; 2.1.8 Biot
Savart Relationship and Non-local Closure of Vorticity Equation; 2.1.9 Adding Body Forces or Mean Gradients; 2.2 Briefs About Statistical and Probabilistic Approaches; 2.2.1 Ensemble Averaging; 2.2.2 Single-Point and Multi-point Moments; 2.2.3 Statistics for Velocity Increments; 2.2.4 Application of the Reynolds Decomposition to Dynamical Equations; 2.3 Reynolds Stress Tensor and Related Equations; 2.3.1 RST Equations
2.3.2 The Mean Flow Consistent with Homogeneity Restricted to Fluctuations2.3.3 Homogeneous RST Equations. Briefs About Closure Methods; 2.4 Anisotropy in Physical Space. Single-Point Correlations; 2.5 Spectral Analysis, from Random Fields to Two-Point …; 2.5.1 Second Order Statistics; 2.5.2 Poloidal-Toroidal Decomposition, and Craya
Herring Frame of Reference; 2.5.3 The Helical Mode Decomposition; 2.5.4 On the Use of Projection Operators; 2.5.5 Nonlinear Dynamics; 2.5.6 Background Nonlinearity in the Different Reference Frames
2.5.7 Inverting Linear Operators: Introduction to Green Functions2.6 Anisotropy for Multipoint Correlations; 2.6.1 Second Order Velocity Statistics; 2.6.2 Induced Anisotropic Structure of Arbitrary Second-Order Statistical Quantities; 2.6.3 Some Comments About Higher Order Statistics; 2.7 A Synthetic Scheme of the Closure Problem: Non-linearity
2.8 On the Use of Lagrangian Formalism; 2.8.1 From RDT to Visco-Elastic Mechanisms; 2.8.2 Lagrangian Stochastic Models; References; 3 Additional Reminders: Compressible Turbulence Description
3.1 Navier
Stokes Equations for Compressible Flows and Shock Jump Conditions3.1.1 Governing Conservation Equations; 3.1.2 Rankine
Hugoniot Jump Relations; 3.1.3 Linearization of Rankine-Hugoniot Jump Relations; 3.2 Introduction to Modal Decomposition of Turbulent Fluctuations; 3.2.1 Statement of the Problem; 3.2.2 Kovasznay's Linear Decomposition; 3.2.3 Weakly Nonlinear Corrected Kovasznay Decomposition; 3.2.4 Bridging Between Kovasznay and Helmholtz Decomposition; 3.2.5 Helmholtz-Decomposition-Based Kinematic Relations for Isotropic Turbulence