Joel C.A. Vorticity and Turbulence

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Springer-Verlag New York, Inc. , 1994. 173 р.
Introduction
1 The Equations of Motion
The Euler and Navier-Stokes Equations
Vorticity Form of the Equations
Discrete Vortex Representations
Magnetization Variables
Fourier Representation for Periodic Flow
2 Random Flow and Its Spectra
Introduction to Probability Theory
Random Fields
Random Solutions of the Navier-Stokes Equations
Random Fourier Transform of a Homogeneous Flow Field
Brownian Motion and Brownian Walks
3 The Kolmogorov Theory
The Goals of Turbulence Theory: Universal Equilibrium
Kolmogorov Theory: Dimensional Considerations
The Kolmogorov Spectrum and an Energy Cascade
Fractal Dimension
A First Discussion of Intermittency
4 Equilibrium Flow in Spectral Variables and in Two Space Dimensions
Statistical Equilibrium
The "Absolute" Statistical Equilibrium in Wave Number Space
The Combinatorial Method: The Approach to Equilibrium and Negative Temperatures
The Onsager Theory and the Joyce-Montgomery Equation
The Continuum Limit and the Role of Invariants
The Approach to Equilibrium, Viscosity, and Inertial Power Laws
5 Vortex Stretching
Vortex Lines Stretch
Vortex Filaments
Self-Energy and the Folding of Vortex Filaments
Fractalization and Capacity
Intermittency
Vortex Cross-Sections
Enstrophy and Equilibrium
6 Polymers, Percolation, Renormalization
Spins, Critical Points and Metropolis Flow
Polymers and the Flory Exponent
The Vector-Vector Correlation Exponent for Polymers
Percolation
Polymers and Percolation
Renormalization
The Kosterlitz-Thouless Transition
Vortex Percolation/Л Transition in Three Space Dimensions
7 Vortex Equilibria in Three-Dimensional Space
A Vortex Filament Model
Self-Avoiding Filaments of Finite Length
The Limit N — ? and the Kolmogorov Exponent
Dynamics of a Vortex Filament: Viscosity and Reconnection
Relation to the A Transition in Superfluids: Denser Suspen- Suspensions of Vortices
Renormalization of Vortex Dynamics in a Turbulent Regime
Bibliography
Index

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