Vorticity and Turbulence

Cover
Title page
Preface
Introduction
1. The Equations of Motion
1.1. The Euler and Navier-Stokes Equations
1.2. Vorticity Form of the Equations
1.3. Discrete Vortex Representations
1.4. Magnetization Variables
1.5. Fourier Representation for Periodic Flow
2. Random Flow and Its Spectra
2.1. Introduction to Probability Theory
2.2. Random Fields
2.3. Random Solutions of the Navier-Stokes Equations
2.4. Random Fourier Transform of a Homogeneous Flow Field
2.5. Brownian Motion and Brownian Walks
3. The Kolmogorov Theory
3.1. The Goals of Turbulence Theory: Universal Equilibrium
3.2. Kolmogorov Theory: Dimensional Considerations
3.3. The Kolmogorov Spectrum and an Energy Cascade
3.4. Fractal Dimension
3.5. A First Discussion of Intermittency
4. Equilibrium Flow in Spectral Variables and in Two Space Dimensions
4.1. Statistical Equilibrium
4.2. The "Absolute" Statistical Equilibrium in Wave Number Space
4.3. The Combinatorial Method: The Approach to Equilibrium and Negative Temperatures
4.4. The Onsager Theory and the Joyce-Montgomery Equation
4.5. The Continuum Limit and the Role of Invariants
4.6. The Approach to Equilibrium, Viscosity, and Inertial Power Laws
5. Vortex Stretching
5.1. Vortex Lines Stretch
5.2. Vortex Filaments
5.3. Self-Energy and the Folding of Vortex Filaments
5.4. Fractalization and Capacity
5.5. Intermittency
5.6. Vortex Cross-Sections
5.7. Enstrophy and Equilibrium
6. Polymers, Percolation, Renormalization
6.1. Spins, Critical Points and Metropolis Flow
6.2. Polymers and the Flory Exponent
6.3. The Vector-Vector Correlation Exponent for Polymers
6.4. Percolation
6.5. Polymers and Percolation
6.6. Renormalization
6.7. The Kosterlitz-Thouless Transition
6.8. Vortex Percolation/λ Transition in Three Space Dimensions
7. Vortex Equilibria in Three-Dimensional Space
7.1. A Vortex Filament Model
7.2. Self-Avoiding Filaments of Finite Length
7.3. The Limit N->∞ and the Kolmogorov Exponent
7.4. Dynamics of a Vortex Filament: Viscosity and Reconnection
7.5. Relation to the λ Transition in Superfluids: Denser Suspensions of Vortices
7.6. Renormalization of Vortex Dynamics in a Turbulent Regime
Bibliography
Index